CN107038293A - For the Resonance self-shielding computational methods based on equivalent one-dimensional Slab of plate type fuel element - Google Patents
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Abstract
For the Resonance self-shielding computational methods based on equivalent one-dimensional Slab of plate type fuel element, 1, the Resonance self-shielding computational problem for plate type fuel element, the Dan Kefu modifying factors of each piece of each section of plate type fuel element are calculated using neutron current method；2nd, according to Dan Kefu modifying factors and the functional relation of one-dimensional plate moderator thickness, in the case of known Dan Kefu modifying factors, moderator thickness is obtained using binary chop method；3rd, equivalent one-dimensional fuel slab is calculated using subgroup method or ultra-fine group's method, obtain each layer of fuel slab effectively shields section certainly；Compared to traditional Resonance self-shielding computational methods, the present invention can calculate the plate type fuel element problem of complicated arrangement, with higher computational efficiency, and can obtain the effective from screen section of space correlation.
Description
Technical field
The present invention relates to nuclear reactor design and security technology area, and in particular to a kind of base for plate type fuel element
In the Resonance self-shielding computational methods of equivalent plate Slab.
Background technology
Plate type fuel element reactor core has the characteristics of arrangement is complicated, therefore the geometry of problem is non-construction geometry, it is desirable to which resonance is certainly
Screen computational methods can handle this complicated geometry.The calculating requirement of high-fidelity one-step method is not any equal to spatially doing simultaneously
Homogenize, the step calculating for only carrying out Whole core obtains effective multiplier factor and power distribution etc., therefore amount of calculation is very big, it is desirable to
Resonance self-shielding is calculated with very high computational efficiency.Traditional burnup calculates the average nucleon density of a computing board, for poison
The computational accuracy of thing is not high, can not also meet the requirement of fuel performance analysis.Therefore the burnup in future calculates meeting to plate type fuel element
Layered method is carried out, this requires that Resonance self-shielding calculates layering and provides the effective from screen section of space correlation.
Existing Resonance self-shielding computational methods are broadly divided into equivalent theoretical, subgroup method and the ultra-fine class of group's method three.It is of equal value
Theory is broadly divided into the calculating of lattice cell effective resonance integral and Dan Kefu corrects two steps.When calculating lattice cell effective resonance integral,
Scattering source item is simplified using narrow resonance approximation, rational approximation is used to the first collision probability of lattice cell, by the solution of lattice cell
Analysis power spectrum is write as the parsing power spectrum identical form with homogeneous system, and then the resonance integral of lattice cell is of equal value into one or more
The weight sum of homogeneous system resonance integral.The resonance integral of homogeneous system can make the form of form and be stored in multigroup number
According to only needing to enter row interpolation according to coefficient in storehouse, during calculating, therefore with very high efficiency.Dan Kefu modifying factors are typically adopted
Calculated with neutron current method, neutron current transports method for solving using multigroup and calculated, it is adaptable to the calculating of complicated geometry.It is all common
Energy group shake only using a Dan Kefu modifying factor, computational efficiency is higher, it is adaptable to the calculating of large scale problem.But reason of equal value
By the averga cross section using Dan Kefu modifying factor amendment plate type fuel elements, it is impossible to obtain the section of space correlation.Subgroup method pair
Cross-sectional sizes carry out the division of subgroup, by the integration to Continuous Energy transport equation on subgroup, obtain subgroup stationary source side
Journey.Because subgroup stationary source equation is similar to multigroup transport equation, method for solving can be transported using ripe multigroup and it is asked
Solution, therefore subgroup method can be used for the calculating of full heap in theory, the problem of can solve the problem that complex geometry and obtains space phase
What is closed effectively shields section certainly.But be due to full heap yardstick multigroup transport calculating very take, and subgroup method need solve it is many
Secondary multigroup transport equation, thus directly by subgroup method be applied to the full heap of plate type fuel element reactor core Resonance self-shielding computational efficiency compared with
It is low.Ultra-fine group's method carries out the division of ultra-fine group to energy variable, and moderation of neutrons equation is solved on the basis of ultra-fine group, is had
Very high precision.But the amount of calculation of ultra-fine group is very big, it is impossible to be directly used in the Resonance self-shielding of the full heap of plate type fuel element reactor core
Calculate.
Therefore existing three kinds of methods all cannot be directly used to the Resonance self-shielding calculating of the full heap of plate type fuel element reactor core, it is necessary to
Study a kind of new Resonance self-shielding computational methods and solve the challenge that plate type fuel element reactor core is brought.
The content of the invention
In order to overcome the problem of above-mentioned prior art is present, it is an object of the invention to provide a kind of for plate type fuel element
Resonance self-shielding computational methods based on equivalent one-dimensional Slab, this method transports solver using neutron current method meter using multigroup
Calculate the Dan Kefu modifying factors of plate type fuel element；The equivalence defined with collision probability is defined using the neutron current of Dan Kefu modifying factors
Property, in the case of known plate type fuel element Dan Kefu modifying factors, according to red in Dan Kefu modifying factor collision probability definitions
Can husband's factor and equivalent one-dimensional plate moderator thickness functional relation, equivalent one-dimensional plate moderator is obtained using binary chop method
Thickness；Equivalent one-dimensional plate problem is solved using subgroup method or ultra-fine group's method, effectively being cut from screen for each layer of one-dimensional plate is obtained
Face.
To achieve these goals, it is practiced this invention takes following technical scheme：
A kind of Resonance self-shielding computational methods based on equivalent one-dimensional Slab for plate type fuel element, this method includes following
Step：
Step 1：Resonance self-shielding computational problem is that known materials composition and geological information solve having for fuel region resonance nucleic
Effect for plate type fuel element problem, i.e., is segmented from screen section to each piece of plate type fuel element so that the grid that Resonance self-shielding is calculated
Border and multigroup, which are transported, to be calculated and burnup calculating is consistent；
Step 2：It is zero to make fuel region scattering section, and absorption cross-section is equal to 1, and source item is zero, makes on-fuel area scattering section
It is zero, the value of absorption cross-section and source item is equal to elastic potential scattering section, transporting solver solution below equation using multigroup obtains
Neutron angular flux：
Wherein Ω is angle,It is locus,It is angular flux,It is total cross section,It is elastic potential scattering
Section；The neutron scalar flux of each piece of each section of plate type fuel element is obtained using formula (2)：
Wherein i is the numbering of plate type fuel element segmentation, φiIt is i-th section of scalar flux；
Step 3：For each section of plate type fuel element, build the isolated Slab of correspondence and fuel slab is placed in spatially infinity
Moderator in, it is zero to make fuel region scattering section, absorption cross-section be equal to 1, source item is zero, and on-fuel area scattering section is zero,
The value of absorption cross-section and source item is equal to elastic potential scattering section, and solution formula (1) obtains neutron angular flux, is counted using formula (2)
Calculation obtains neutron scalar flux；
Step 4：The Dan Kefu modifying factors for obtaining each section of plate type fuel element are calculated using formula (3)：
Wherein CiIt is the Dan Kefu modifying factors of i-th section of plate type fuel element, φi,1And φi,2It is step one and step 2 respectively
The scalar flux of i-th section of obtained plate type fuel element；
Step 5：The resonance of the corresponding equivalent one-dimensional plate of each section of plate type fuel element is built according to Dan Kefu modifying factor conservations
From screen computational problem, equivalent one-dimensional plate material composition and fuel region thickness and fuel rod it is consistent, equivalent one is solved below
The moderator thickness of plate is tieed up, Dan Kefu modifying factors and the functional relation such as formula (4) of equivalent one-dimensional plate moderator thickness are shown：
Wherein CiIt is the Dan Kefu modifying factors for i-th section of plate type fuel element that step 3 is obtained, D is one-dimensional plate moderator thickness,
Pe,iIt is the neutron escape probability of i-th section of isolated plate of plate type fuel element correspondence, Pmf(D) it is that the neutron that fuel region is produced in one-dimensional plate exists
The probability of initial collision occurs in other regions；I-th section of plate type fuel element correspondence is obtained using binary chop method according to formula (4)
Equivalent one-dimensional plate moderator thickness；
Step 6：The Resonance self-shielding computational problem of equivalent one-dimensional plate is solved using subgroup method or ultra-fine group's method, institute is obtained
Have each layer of equivalent one-dimensional plate effectively from screen section, equivalent one-dimensional plate effectively from screen section be plate type fuel element effectively from
Shield section, the Resonance self-shielding for so far completing plate type fuel element is calculated.
Compared with prior art, the present invention has following outstanding advantages：
The present invention calculates the Dan Kefu modifying factors of plate type fuel element, all resonance energy groups using utilizing using neutron current method
Only need to using a Dan Kefu modifying factor, it is only necessary to which once the simple group of full heap transports calculating, and computational efficiency is higher；Using many
Group transports solver and calculates neutron current, and Dan Kefu modifying factors can be obtained in the case where there is complex geometry；Using subgroup
Method or ultra-fine group's method calculate equivalent one-dimensional plate, can obtain the effectively each from screen section, i.e. plate type fuel element of space correlation
Effective screen section certainly of layer.
Brief description of the drawings
Fig. 1 is the equivalent process schematic diagram of one-dimensional plate.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and detailed description：
The present invention solves Dan Kefu modifying factors using neutron current method, according to the definition of Dan Kefu modifying factors neutron current and
The equivalence that collision probability is defined, the moderator external diameter of equivalent one-dimensional plate is obtained by binary chop method, finally using subgroup
Method or ultra-fine group's method solve equivalent one-dimensional plate problem, and obtain space correlation effectively shields section certainly.This method is specifically calculated
Flow includes following aspect：
1) Resonance self-shielding computational problem be known materials composition and geological information solve fuel region resonance nucleic effectively from
Shield section, for plate type fuel element problem, each piece of plate type fuel element is segmented so that Resonance self-shielding calculate net boundary and
Multigroup, which is transported, to be calculated and being consistent that burnup is calculated；It is zero to make fuel region scattering section, and absorption cross-section is equal to 1, and source item is zero,
Other regions scatter sections are zero, and the value of absorption cross-section and source item is equal to elastic potential scattering section, and solver is transported using multigroup
Solution formula (1) obtains neutron angular flux；Obtain after neutron angular flux, angular flux is integrated using formula (2), obtained
The neutron scalar flux of each piece of each section of plate type fuel element；
2) for each section of plate type fuel element, the isolated Slab of correspondence is built, i.e., is placed in plate type fuel element spatially infinitely great
Moderator in, in numerical computations the thickness of general area moderator be 10cm, boundary condition is vacuum boundary；Fuel region is made to scatter
Section is zero, and absorption cross-section is equal to 1, and source item is zero, and other regions scatter sections are zero, and the value of absorption cross-section and source item is equal to gesture
Elastic scattering cross-section, solution formula (1) obtains neutron angular flux, is calculated using formula (2) and obtains neutron scalar flux；
3) the Dan Kefu modifying factors of each section of plate type fuel element are calculated using formula (3)；
4) because the neutron current of Dan Kefu modifying factors is defined, to define with collision probability be of equal value, therefore plate type fuel element
Dan Kefu factors flux can be represented with formula (4), and the thickness of equivalent one-dimensional plate moderator can be obtained by binary chop method
Degree；As shown in figure 1, the corresponding equivalent one-dimensional plate of one section of plate type fuel element in reactor core is obtained by above-mentioned steps, its material composition
Consistent with the fuel depth of plate type fuel element plate type fuel element corresponding with reactor core, the external diameter of moderator is obtained by above-mentioned calculating；
5) the Resonance self-shielding computational problem of equivalent one-dimensional plate is solved using subgroup method or ultra-fine group's method, equivalent one is obtained
Tie up effective screen section certainly of the space correlation of plate；Compared to equivalent theoretical method, this method can obtain the effective of space correlation
From screen section；Compared to subgroup method and ultra-fine group's method, this method has higher computational efficiency.
Claims (1)
1. a kind of Resonance self-shielding computational methods based on equivalent one-dimensional Slab for plate type fuel element, it is characterised in that：The party
Method comprises the following steps：
Step 1：Resonance self-shielding computational problem be known materials composition and geological information solve fuel region resonance nucleic effectively from
Shield section, for plate type fuel element problem, i.e., each piece of plate type fuel element is segmented so that the net boundary that Resonance self-shielding is calculated
With multigroup transport calculate and burnup calculating be consistent；
Step 2：It is zero to make fuel region scattering section, and absorption cross-section is equal to 1, and source item is zero, and it is zero to make on-fuel area scattering section,
The value of absorption cross-section and source item is equal to elastic potential scattering section, and transporting solver solution below equation using multigroup obtains Neutron Angular
Flux：
Wherein Ω is angle,It is locus,It is angular flux,It is total cross section,It is elastic potential scattering section；
The neutron scalar flux of each piece of each section of plate type fuel element is obtained using formula (2)：
Wherein i is the numbering of plate type fuel element segmentation, φiIt is i-th section of scalar flux；
Step 3：For each section of plate type fuel element, it is that fuel slab is placed in into the slow of spatially infinity to build the isolated Slab of correspondence
In agent, it is zero to make fuel region scattering section, and absorption cross-section is equal to 1, and source item is zero, and on-fuel area scattering section is zero, is absorbed
The value of section and source item is equal to elastic potential scattering section, and solution formula (1) is obtained neutron angular flux, calculated using formula (2)
To neutron scalar flux；
Step 4：The Dan Kefu modifying factors for obtaining each section of plate type fuel element are calculated using formula (3)：
Wherein CiIt is the Dan Kefu modifying factors of i-th section of plate type fuel element, φi,1And φi,2It is that step one and step 2 are obtained respectively
The scalar flux of i-th section of plate type fuel element；
Step 5：The Resonance self-shielding of the corresponding equivalent one-dimensional plate of each section of plate type fuel element is built according to Dan Kefu modifying factor conservations
Computational problem, equivalent one-dimensional plate material composition and fuel region thickness and fuel rod it is consistent, below solution equivalent one-dimensional plate
Moderator thickness, functional relation such as the formula (4) of Dan Kefu modifying factors and equivalent one-dimensional plate moderator thickness is shown：
Wherein CiIt is the Dan Kefu modifying factors for i-th section of plate type fuel element that step 3 is obtained, D is one-dimensional plate moderator thickness, Pe,iIt is
The neutron escape probability of i-th section of isolated plate of plate type fuel element correspondence, Pmf(D) it is fuel region is produced in one-dimensional plate neutron in other areas
The probability of initial collision occurs in domain；Binary chop method is used to obtain i-th section of plate type fuel element according to formula (4) corresponding equivalent
One-dimensional plate moderator thickness；
Step 6：The Resonance self-shielding computational problem of equivalent one-dimensional plate is solved using subgroup method or ultra-fine group's method, obtains all etc.
The effective from screen section of each layer of one-dimensional plate is imitated, equivalent one-dimensional plate is effectively being cut from screen for plate type fuel element effectively from section is shielded
Face, the Resonance self-shielding for so far completing plate type fuel element is calculated.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107929958A (en) * | 2018-01-04 | 2018-04-20 | 北京新核医疗科技有限公司 | A kind of MNSR Reactor neutron therapy device |
| CN110704806A (en) * | 2019-09-19 | 2020-01-17 | 西安交通大学 | Rapid online calculation method for one-dimensional cylindrical geometric collision probability |
| CN114491902A (en) * | 2020-10-27 | 2022-05-13 | 中国核动力研究设计院 | Tone's method based on vacuum boundary and resonance algorithm combining superfine group |
| CN114491901A (en) * | 2020-10-27 | 2022-05-13 | 中国核动力研究设计院 | Equivalent homogenization dual-heterogeneity calculation method based on cubic stochastic model |
| CN114510861A (en) * | 2022-04-19 | 2022-05-17 | 西安交通大学 | Resonance calculation method for studying reactor based on equivalent geometric theory |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107929958A (en) * | 2018-01-04 | 2018-04-20 | 北京新核医疗科技有限公司 | A kind of MNSR Reactor neutron therapy device |
| CN110704806A (en) * | 2019-09-19 | 2020-01-17 | 西安交通大学 | Rapid online calculation method for one-dimensional cylindrical geometric collision probability |
| CN114491902A (en) * | 2020-10-27 | 2022-05-13 | 中国核动力研究设计院 | Tone's method based on vacuum boundary and resonance algorithm combining superfine group |
| CN114491901A (en) * | 2020-10-27 | 2022-05-13 | 中国核动力研究设计院 | Equivalent homogenization dual-heterogeneity calculation method based on cubic stochastic model |
| CN114491902B (en) * | 2020-10-27 | 2023-10-20 | 中国核动力研究设计院 | Tone's method based on vacuum boundary and ultra-fine group combined resonance algorithm |
| CN114491901B (en) * | 2020-10-27 | 2023-10-31 | 中国核动力研究设计院 | Equivalent homogenization double non-uniformity calculation method based on cube random model |
| CN114510861A (en) * | 2022-04-19 | 2022-05-17 | 西安交通大学 | Resonance calculation method for studying reactor based on equivalent geometric theory |
| CN114510861B (en) * | 2022-04-19 | 2022-07-15 | 西安交通大学 | Resonance calculation method for studying reactor based on equivalent geometric theory |
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