CN111914463B - Subgroup optimization method and system for reactor assembly resonance simulation - Google Patents
Subgroup optimization method and system for reactor assembly resonance simulation Download PDFInfo
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Abstract
The invention discloses a subgroup optimization method for resonance simulation of a reactor assembly, which comprises the following steps: establishing resonance energy groups, and unifying the resonance energy groups into combined energy groups; obtaining equivalent macroscopic cross section and source item information of the combined energy group; constructing a neutron transport equation; the subgroup absorbing section corresponds to the subgroup flux; acquiring a subgroup escape section of the combined energy group; acquiring a subgroup escape section corresponding to each resonance energy group, and acquiring an equivalent microscopic background section corresponding to each resonance energy group; obtaining an equivalent absorption section and an equivalent generation section; a reactor assembly resonance simulation was performed. The invention also discloses a subgroup optimization system for the resonance simulation of the reactor assembly. According to the subgroup optimization method and system for the resonance simulation of the reactor assembly, the concept of the equivalent escape cross section is introduced, the subgroup flux is uniformly solved for the whole resonance energy region on the premise of not influencing the precision, the characteristic line method calculation time is reduced, and therefore the calculation efficiency is improved.
Description
Technical Field
The invention relates to the technical field of nuclear reactor core design, in particular to a subgroup optimization method and a subgroup optimization system for reactor assembly resonance simulation.
Background
When a multi-population cross-section library is created, since the absorption cross section of a resonance nuclear species changes drastically in the resonance energy region, the flux distribution (i.e., the energy spectrum) in the energy population region cannot be known in advance, and therefore, information such as the multi-population microscopic absorption cross section of the resonance nuclear species in the resonance energy region cannot be directly given in the database. The subgroup method converts information contained in the effective resonance integral table into related subgroup information (namely subgroup parameters including subgroup cross section and subgroup probability), solves a subgroup equation by using the related theories of the subgroup parameters and the subgroup method, and calculates equivalent cross section information according to calculated subgroup flux information and the like.
The conventional calculation process of the subgroup method is shown in fig. 1, and the basic process is as follows: 1) calculating the number of virtual energy groups, wherein the value of the number of the virtual energy groups is the number of resonance energy groups multiplied by the number of subgroups; 2) calculating the macroscopic cross section information and the source information of each virtual energy group and each grid; 3) solving the fixed source problem by using a characteristic line method, and calculating to obtain the flux of each virtual energy group and each grid subgroup; 4) and calculating an equivalent absorption cross section and an equivalent generation cross section according to the subgroup flux and the subgroup parameters.
For the problems of large number of grids and large number of resonance energy groups, the time for solving the flux of the subgroups in the characteristic line method is long in the traditional method, so that the calculation time cannot meet the engineering requirements.
Disclosure of Invention
The technical problem to be solved by the invention is that the calculation time cannot meet the engineering requirement due to long time for solving the subgroup flux caused by the problems of large grid number and large number of resonance energy groups in the prior art, and the invention aims to provide the subgroup optimization method and the subgroup optimization system for the resonance simulation of the reactor assembly to solve the problems.
The invention is realized by the following technical scheme:
a subgroup optimization method for resonance simulation of a reactor assembly, comprising the steps of:
s1: establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide, and unifying all the resonance energy groups into a combined energy group;
s2: constructing a neutron transport equation according to a subgroup flux calculation formula;
s3: obtaining equivalent macroscopic cross section and source item information of a combined energy group in a neutron transport equation;
s4: acquiring subgroup flux corresponding to the subgroup absorption cross section of the combined energy group according to the neutron transport equation;
s5: acquiring a subgroup escape cross section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption cross section of the combined energy group;
s6: acquiring a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquiring an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group;
s7: obtaining an equivalent absorption section and an equivalent generation section of each resonance energy group according to a background section corresponding to each resonance energy group;
s8: and carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
When the present invention is applied, all the resonance energy clusters are unified into one combined energy cluster when the number of virtual energy clusters is calculated in the prior art, so that the calculation amount can be reduced in the subsequent solution, and the operation processing is performed based on the combined energy clusters in steps S2 and S3. Meanwhile, an escape section is introduced in the step S5, in a classical equivalence theory, the non-uniform problem is equivalent to a uniform problem, the background section of the equivalent uniform problem is increased, the increased terms represent non-uniform influence factors, and the escape section does not change violently along with the energy group, so that the method is beneficial to integrally solving the resonance energy region and adopting the whole energy region to solve can reduce the calculation time on the premise of ensuring the calculation accuracy.
After the operation process of combining the energy groups is completed, the subgroup escape cross section corresponding to each resonance energy group can be obtained through an interpolation method, so that the subsequent operation is completed, the process of solving through a neutron transport equation only needs to be performed once, and the operation law is greatly reduced. By introducing the concept of equivalent escape cross section, the invention uniformly solves the subgroup flux of the whole resonance energy region on the premise of not influencing the precision, reduces the calculation time of the characteristic line method and improves the calculation efficiency.
Further, the neutron transport equation uses the following equation:
Q＝λΣp
Σa＝Nσn
Σself-s＝Σp-λΣp
Σt＝Σa+Σp
in the formula, sigmapIs a potential scattering macroscopic cross section, lambda is an intermediate approximation factor, N is the nuclear density of the resonant nuclide, sigmaself-sFor self-scattering macroscopic cross-sections, sigmatTo total macroscopic cross section, ΣaTo absorb the macroscopic cross-section, σnAbsorbing the cross-section for the subgroup.
Further, step S4 includes the following sub-steps:
merging the subgroup absorption cross sections of the merged energy group, and integrally solving the cross sections after merging through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgScattering cross section or potential scattering cross section of energy group g, IxgIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy-drop width of the energy group g, R∞gIs the infinite resonance integral of the energy group g.
Further, step S6 includes the following sub-steps:
using ln (σ)n) LinearityFor the subgroup of the combined energy group escape cross section sigmae(σm) Interpolating to obtain the section sigma of each resonance energy group subgroupnCorresponding subgroup escape cross section ∑e(σn)。
Further, obtaining the equivalent microscopic background section corresponding to each resonance energy group according to the following formula:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
Further, the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group are obtained according to the following formula:
in the formula, ωnProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
A subgroup optimization system for resonance simulation of a reactor assembly, comprising:
a merging unit: the nuclear power generation device is used for establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide and unifying all the resonance energy groups into a combined energy group;
an acquisition unit: the source item information and the equivalent macroscopic section of the combined energy group are obtained;
a construction unit: the neutron transport equation is constructed according to a subgroup flux calculation formula;
a processing unit: the neutron transport system is used for acquiring subgroup flux corresponding to a subgroup absorption cross section of the combined energy group according to the neutron transport equation; the processing unit acquires a subgroup escape section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption section of the combined energy group; the processing unit acquires a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquires an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group; the processing unit acquires an equivalent absorption section and an equivalent generation section of each resonance energy group according to the corresponding background section of each resonance energy group;
an analog unit: the method is used for carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
Further, the processing unit performs grouping on the subgroup absorption cross sections of the combined energy group, and integrally solves the grouped cross sections through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgScattering cross section or potential scattering cross section of energy group g, IxgIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy-drop width of the energy group g, R∞gIs the infinite resonance integral of the energy group g.
Further, the processing unit obtains the equivalent microscopic background section corresponding to each resonance energy group according to the following formula:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
Further, the processing unit obtains an equivalent absorption cross section and an equivalent generation cross section of each resonance energy group according to the following formula:
in the formula, ωnProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
Compared with the prior art, the invention has the following advantages and beneficial effects:
according to the subgroup optimization method and system for the resonance simulation of the reactor assembly, the concept of the equivalent escape cross section is introduced, the subgroup flux is uniformly solved for the whole resonance energy region on the premise of not influencing the precision, the characteristic line method calculation time is reduced, and therefore the calculation efficiency is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic diagram of the steps of a prior art process;
FIG. 2 is a schematic diagram of the process steps of the present invention;
FIG. 3 is a schematic diagram of the method steps according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Examples
As shown in fig. 2, a subgroup optimization method for resonance simulation of a reactor assembly according to the present invention includes the steps of:
s1: establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide, and unifying all the resonance energy groups into a combined energy group;
s2: constructing a neutron transport equation according to a subgroup flux calculation formula;
s3: obtaining equivalent macroscopic cross section and source item information of a combined energy group in a neutron transport equation;
s4: acquiring subgroup flux corresponding to the subgroup absorption cross section of the combined energy group according to the neutron transport equation;
s5: acquiring a subgroup escape cross section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption cross section of the combined energy group;
s6: acquiring a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquiring an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group;
s7: obtaining an equivalent absorption section and an equivalent generation section of each resonance energy group according to a background section corresponding to each resonance energy group;
s8: and carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
In the implementation of this embodiment, first, when the number of virtual energy clusters is calculated in the prior art, all the resonant energy clusters are unified into one combined energy cluster, so that the calculation amount can be reduced in the subsequent solution, and the operation processing is performed based on the combined energy clusters in steps S2, S3, and S4. Meanwhile, an escape section is introduced in the step S5, in a classical equivalence theory, the non-uniform problem is equivalent to a uniform problem, the background section of the equivalent uniform problem is increased, the increased terms represent non-uniform influence factors, and the escape section does not change violently along with the energy group, so that the method is beneficial to integrally solving the resonance energy region and adopting the whole energy region to solve can reduce the calculation time on the premise of ensuring the calculation accuracy.
After the operation process of combining the energy groups is completed, the subgroup escape cross section corresponding to each resonance energy group can be obtained through an interpolation method, so that the subsequent operation is completed, the number of the energy groups solved by a neutron transport equation is reduced, and the operation law is greatly reduced. By introducing the concept of equivalent escape cross section, the invention uniformly solves the subgroup flux of the whole resonance energy region on the premise of not influencing the precision, reduces the calculation time of the characteristic line method and improves the calculation efficiency.
To further illustrate the operation of this embodiment, the neutron transport equation uses the following equation:
Q＝λΣp
Σa＝Nσn
Σself-s＝Σp-λΣp
Σt＝Σa+Σp
in the formula, sigmapIs a potential scattering macroscopic cross section, lambda is an intermediate approximation factor, N is the nuclear density of the resonant nuclide, sigmaself-sFor self-scattering macroscopic cross-sections, sigmatTo total macroscopic cross section, ΣaTo absorb the macroscopic cross-section, σnAbsorbing the cross-section for the subgroup.
To further explain the operation of the present embodiment, step S4 includes the following sub-steps:
merging the subgroup absorption cross sections of the merged energy group, and integrally solving the cross sections after merging through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgScattering cross section or potential scattering cross section of energy group g, IxgIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy of the energy group gAnd reducing the width.
To further explain the operation of the present embodiment, step S6 includes the following sub-steps:
using ln (σ)n) Linear method for subgroup escape cross section sigma of combined energy groupe(σm) Interpolating to obtain the section sigma of each resonance energy group subgroupnCorresponding subgroup escape cross section ∑e(σn)。
To further illustrate the operation of this embodiment, the equivalent microscopic background cross-section corresponding to each resonance energy group is obtained according to the following formula:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
To further illustrate the operation of the present embodiment, the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group are obtained according to the following formula:
in the formula, ωnProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
A subgroup optimization system for resonance simulation of a reactor assembly, comprising:
a merging unit: the nuclear power generation device is used for establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide and unifying all the resonance energy groups into a combined energy group;
an acquisition unit: the source item information and the equivalent macroscopic section of the combined energy group are obtained;
a construction unit: the neutron transport equation is constructed according to a subgroup flux calculation formula;
a processing unit: the neutron transport system is used for acquiring subgroup flux corresponding to a subgroup absorption cross section of the combined energy group according to the neutron transport equation; the processing unit acquires a subgroup escape section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption section of the combined energy group; the processing unit acquires a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquires an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group; the processing unit acquires an equivalent absorption section and an equivalent generation section of each resonance energy group according to the corresponding background section of each resonance energy group;
an analog unit: the method is used for carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
For further explaining the working process of the embodiment, the processing unit performs grouping on the subgroup absorption cross sections of the combined energy group, and integrally solves the grouped cross sections through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgScattering cross section or potential scattering cross section of energy group g, IxgIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy drop width of the energy group g.
To further illustrate the operation of this embodiment, the processing unit obtains the equivalent microscopic background cross-section corresponding to each resonance energy group according to the following formula:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
To further illustrate the operation of the present embodiment, the processing unit obtains the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group according to the following formula:
in the formula, ωnProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
As shown in fig. 3, to further illustrate the working process of this embodiment, in this embodiment, the main steps of solving are as follows:
1) calculating the number of virtual energy groups, wherein the value of the number of the virtual energy groups is the number of subgroups;
2) calculating the macroscopic cross section information and the source information of each virtual energy group and each grid;
3) solving the fixed source problem by using a characteristic line method, and calculating to obtain the flux of each virtual energy group and each grid subgroup;
4) calculating an equivalent escape cross section according to the flux of the subgroup;
5) calculating an equivalent microscopic background section according to the equivalent escape section;
6) and calculating an equivalent absorption section and an equivalent generation section according to the equivalent microscopic background section and the subgroup parameters.
Compared with the conventional subgroup method, the subgroup method of combining resonance energy groups and solving subgroup fluxes is mainly distinguished as follows: 1) unifying the resonance energy groups into one energy group when the number of the virtual energy groups is calculated in the step 1; 2) the resonance energy groups are unified into one energy group to carry out section and subgroup flux solution during the calculation in the step 2 and the step 3; 3) calculating an equivalent escape section in the 4 th step; 4) micro background cross section calculations are performed at step 5.
To further illustrate the working process of this embodiment, in this embodiment, the solution concept of the subgroup method is to transform the integral of energy in the effective resonance section calculation formula into the integral of the absorption section, and then perform discrete numerical integration on the absorption section, so that the calculation formula is:
wherein (sigma)n,ωn) For a subgroup parameter of the absorption cross-sections, [ phi ]nThe neutron flux corresponding to the subgroup parameter. The calculation formula for the effective generated cross section can also be defined:
wherein (sigma)νn,ωνn) To generate cross-section subgroup parameters.
According to the flux calculation formula:
the calculation formula of the background section of the non-uniformity problem can be deduced:
from the significance of equation (3), the following neutron transport problem is constructed, assuming that the sources and cross sections within each grid are:
in the above problem, it is assumed that the absorption cross section of other non-resonant species than the resonant species is negligible, which is approximately true in the range of the resonant energy group. In formula (5), σnAre the subgroup absorption cross-sections used for flux calculations, the remaining cross-sections being smooth cross-sections. Solving the problem of non-uniform neutron transport in step (5) by using a characteristic line method to obtain sigmanNeutron flux phi at the correspondingn。
The conventional method relies on the neutron flux phi being solved fornThat is, the equation (1) can be applied to obtain an equivalent absorption cross section and an equivalent generation cross section. In order to reduce the number of transportation solution times and save the calculation time, the concept of equivalent escape cross section is introduced, in the classical equivalence theory, the non-uniform problem is equivalent to the uniform problem, the background cross section of the equivalent uniform problem is increased, and the added terms represent non-uniform influence factors:
Σb＝λΣp+Σe (6)
wherein: sigmaeThe cross section is constant for escape, and does not vary with energy, cross section, etc.
By solving equation (5), the subgroup absorption cross section σ can be determinedmCorresponding sub-group flux phimThus, the escape cross section corresponding to the absorption cross section of the subgroup is obtained. Because the escape cross section does not change violently along with the energy group, the resonance energy region is solved integrally, namely lambda sigmapAnd sigmapPerforming group combining, wherein the group combining formula is as follows:
the mode of integrally solving the resonance energy region only solves the neutron transport problem once to obtain the sigma-delta universal for the whole resonance energy regione(σm) And the calculation time can be reduced by adopting the whole energy region solving method on the premise of ensuring the calculation precision.Since the escape cross section and the subgroup cross section are in a logarithmic linear relationship, the number of subgroups for solving the subgroup flux can be less than the number of subgroups for calculating the effective cross section, and according to all M escape cross sections sigma of the subgroups obtained by solvinge(σm) Using ln (σ)n) Interpolating by a linear method to obtain the cross section (N in total and larger than M) sigma of each subgroupnCorresponding sigmae(σn). According to sigmae(σn) Value, the equivalent microscopic background section σ of the problem can be calculatedbn：
Thereby calculating the equivalent absorption cross section and the equivalent generation cross section of each energy group of the problem:
in this embodiment, the main process of calculating the equivalent absorption cross section and the equivalent generation cross section by the fast subgroup method is as follows:
1) calculating the number of virtual energy groups as the number (M) of subgroups;
2) calculating equivalent macroscopic cross section and source item information of the combined energy group, and obtaining a formula (5) and a formula (7);
3) solving the fixed source by applying a characteristic line method to obtain the absorption section sigma of the combined energy group subgroupmCorresponding sub-group flux phim；
4) Calculating equivalent escape cross section according to the flux phi of the subgroupmSolving to obtain escape cross sections sigma of all M sub-groups of the combined energy groupe(σm)；
5) Calculating equivalent microscopic background section sigmabnAccording to the section merging energy group M sub-groups escaping section sigmae(σm) All right (1)Using ln (sigma)n) The linear method interpolates to obtain the section (N in total, N) of each subgroup of each resonance energy group>M)σnCorresponding equivalent escape cross section ∑e(σn) Then, calculating a background section by using a formula (8);
6) the equivalent absorption cross section and the equivalent generation cross section are calculated, see equations (9) and (10).
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A subgroup optimization method for resonance simulation of a reactor assembly, comprising the steps of:
s1: establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide, and unifying all the resonance energy groups into a combined energy group;
s2: constructing a neutron transport equation according to a subgroup flux calculation formula;
s3: obtaining equivalent macroscopic cross section and source item information of a combined energy group in a neutron transport equation;
s4: acquiring subgroup flux corresponding to the subgroup absorption cross section of the combined energy group according to the neutron transport equation;
s5: acquiring a subgroup escape cross section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption cross section of the combined energy group;
s6: acquiring a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquiring an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group;
s7: obtaining an equivalent absorption section and an equivalent generation section of each resonance energy group according to a background section corresponding to each resonance energy group;
s8: and carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
2. The subgroup optimization method for reactor assembly resonance simulation of claim 1, wherein said neutron transport equation employs the following equation:
Q＝λΣp
Σa＝Nσn
Σself-s＝Σp-λΣp
Σt＝Σa+Σp
in the formula, sigmapIs a potential scattering macroscopic cross section, lambda is an intermediate approximation factor, N is the nuclear density of the resonant nuclide, sigmaself-sFor self-scattering macroscopic cross-sections, sigmatTo total macroscopic cross section, ΣaTo absorb the macroscopic cross-section, σnAbsorbing the cross-section for the subgroup.
3. The subgroup optimization method for reactor assembly resonance simulation of claim 2, wherein step S3 comprises the sub-steps of:
merging the scattering cross section and the potential scattering cross section of the merged energy group, and integrally solving the cross section after merging through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgScattering cross section or potential scattering cross section of energy group g, I∞gIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy-drop width of the energy group g, R∞gIs the infinite resonance integral of the energy group g.
4. A subgroup optimization method for resonance simulation of a reactor assembly according to claim 3, wherein step S6 comprises the sub-steps of:
using ln (σ)n) Linear method for subgroup escape cross section sigma of combined energy groupe(σm) Interpolating to obtain the section sigma of each resonance energy group subgroupnCorresponding subgroup escape cross section ∑e(σn)。
5. The subgroup optimization method for resonance simulation of a reactor assembly of claim 4, wherein the equivalent microscopic background section corresponding to each resonance energy group is obtained according to the following formula:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
6. The subgroup optimization method for reactor assembly resonance simulation of claim 5, wherein the equivalent absorption cross-section and the equivalent generation cross-section of each resonance energy group are obtained according to the following formula:
in the formula: omeganProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
7. A subgroup optimization system for resonance simulation of a reactor assembly, comprising:
a merging unit: the nuclear power generation device is used for establishing a resonance energy group according to the resonance characteristics of the reactor component resonance nuclide and unifying all the resonance energy groups into a combined energy group;
an acquisition unit: the source item information and the equivalent macroscopic section of the combined energy group are obtained;
a construction unit: the neutron transport equation is constructed according to a subgroup flux calculation formula;
a processing unit: the neutron transport system is used for acquiring subgroup flux corresponding to a subgroup absorption cross section of the combined energy group according to the neutron transport equation; the processing unit acquires a subgroup escape section of the combined energy group according to the subgroup flux corresponding to the subgroup absorption section of the combined energy group; the processing unit acquires a subgroup escape section corresponding to each resonance energy group according to the subgroup escape section of the combined energy group, and acquires an equivalent microscopic background section corresponding to each resonance energy group according to the subgroup escape section corresponding to each resonance energy group; the processing unit acquires an equivalent absorption section and an equivalent generation section of each resonance energy group according to the corresponding background section of each resonance energy group;
an analog unit: the method is used for carrying out the resonance simulation of the reactor assembly based on the equivalent absorption cross section and the equivalent generation cross section of each resonance energy group.
8. The subgroup optimization system for resonance simulation of a reactor assembly of claim 7, wherein said processing unit performs group combining on the subgroup absorption cross sections of the combined energy group and integrally solves the combined cross sections through a neutron transport equation;
and the population is performed by the following formula:
in the formula: sigmaxFor scattering cross-section or potential scattering macroscopic cross-section after merging of energy clustersxgIs group g of energyScattering cross section or potential scattering cross section of∞gIs the infinite dilution absorption cross-section of the energy group g, Δ ugIs the logarithmic energy-drop width of the energy group g, R∞gIs the infinite resonance integral of the energy group g.
9. The subgroup optimization system for resonance simulation of a reactor assembly of claim 8, wherein said processing unit obtains equivalent microscopic background sections for each resonance energy group according to the following equation:
in the formula: lambda sigmapFor scattering macroscopic cross-sections, ∑e(σn) Absorption cross section σ for the subgroupnCorresponding to the escape cross section, N is the nuclear density.
10. The subgroup optimization system for resonance simulation of a reactor assembly of claim 9, wherein said processing unit obtains an equivalent absorption cross-section and an equivalent generation cross-section for each resonance energy group according to the following equations:
in the formula, ωnProbability of subgroup, σ, for absorption cross sectionnAbsorption cross section, σ, for subgroupbnBackground section, ω, of subgroupvnTo generate the subgroup probability, σ, corresponding to the cross sectionvnA cross-section is generated for the subgroup.
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| CN107038294A (en) * | 2017-04-05 | 2017-08-11 | 西安交通大学 | For the Resonance self-shielding computational methods based on equivalent one-dimensional rod model of light water reactor |
| CN107092782A (en) * | 2017-04-05 | 2017-08-25 | 西安交通大学 | A kind of pseudo- nucleic method of the resonance for handling resonance interference method effect |
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| CN107038294A (en) * | 2017-04-05 | 2017-08-11 | 西安交通大学 | For the Resonance self-shielding computational methods based on equivalent one-dimensional rod model of light water reactor |
| CN107092782A (en) * | 2017-04-05 | 2017-08-25 | 西安交通大学 | A kind of pseudo- nucleic method of the resonance for handling resonance interference method effect |
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| 先进中子学栅格程序ＫＹＬＩＮ－Ⅱ输运模块并行优化开发;涂晓兰等;《原子能科学技术》;20200531;第54卷(第5期);930-936 * |
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