CN107145721B - A kind of mixing calculation method for obtaining fast neutron reactor and lacking group cross-section parameter - Google Patents
A kind of mixing calculation method for obtaining fast neutron reactor and lacking group cross-section parameter Download PDFInfo
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Abstract
A kind of mixing calculation method for obtaining fast neutron reactor and lacking group cross-section parameter, by the way that monte carlo method is combined with determining by method, the resonance effects of fast pile component is finely considered using monte carlo method, calculate the microcosmic total cross section of the accurate multigroup of each nucleic, fission cross section, elastic scattering cross-section, simultaneously using determine the method for discussing solve fast pile component each rank elastic scattering cross-section and each rank neutron flux square, and be few group cross-section by multigroup cross section merger with this；This mixing calculation method is versatile, applied widely, can produce high-precision fast pile component and lacks group cross-section, provides accurate reliable cross section parameter for the nuclear design task of reactor core.
Description
Technical field
The present invention relates to nuclear reactor design and nuclear reactor physical computing fields, are a kind of acquisition fast neutron reactions
Heap lacks the mixing calculation method of group cross-section parameter.
Background technique
In order to quickly and accurately solve reactor core neutronics parameter, the method based on " two-step method " becomes fast reactor engineering calculation
Main method.So-called " two-step method ", the first step are that heap in-core various assemblies material is modeled and calculated, and are obtained in component
Netron-flux density distribution to merger go out less group homogenize group cross-section；Second step is the homogenization being calculated by back
Parameter carries out the solution of few group's neutron-transport equation to reactor core, obtains the physics such as reactor core Effective multiplication factor, core power distribution
Amount.
Monte carlo method can be divided into and determine the method for discussing by calculating the method that few group cross-section uses.Monte carlo method is
One kind being based on statistical method, it carries out the simulation of neutronics characteristic by a large amount of particles of sampling, to obtain neutronics phase
The parameter of pass.It determines that the method for discussing is to describe the math equation group of neutronics characteristic by various theoretical or Numerical Methods Solves, leads to
It crosses acquisition solution of equations and obtains the relevant parameter of neutronics.
Since monte carlo method can be used the database of Continuous Energy, at the same to geometrical model can with Accurate Model,
Therefore its calculated result has high precision.In Monte Carlo calculations, the calculating of few group cross-section need to nuclear reaction rate, in
The information such as sub- flux density distribution are counted.But when these numerical value very littles, it can be difficult to obtain accurately as a result, such as high-order
Neutron flux square.Due to needing to use high-order neutron flux square in the calculating in high-order scattering section, and high-order neutron flux square
It is difficult to obtain again, therefore introduces approximation in monte carlo method, it is using zeroth order neutron flux square to high-order scattering section
It is calculated.And in determining the method for discussing, can use numerical calculations goes out accurate high-order neutron flux square, avoids number
The problem of calculated result inaccuracy when being worth very little.But in determining the method for discussing, the accuracy of few group cross-section calculated result is depended on
The calculated result of multigroup cross section, and the calculating of multigroup cross section to resonance calculation method it is related, therefore using determine discuss method when
It must be based on the higher resonance calculation method of precision.
Since monte carlo method is used alone or determines that the method for discussing is difficult to the shortcomings that overcoming, it is therefore necessary to by this
Two methods are combined, and invent the mixing calculation method that a kind of high-precision fast reactor lacks group cross-section.
Summary of the invention
The shortcomings that in order to overcome fast reactor to lack monte carlo method in the calculating of group cross-section and determine the method for discussing, the present invention is counting
It calculates fast reactor to lack in the process of group cross-section while discussing method using monte carlo method with determining, utilizes monte carlo method generation core
Microcosmic total cross section, the fission cross section, elastic scattering cross-section of element calculate other cross section informations by method using determination and neutron are logical
Metric density distribution, obtains high-precision fast pile component with this and lacks group cross-section.
It is practiced in order to achieve the goal above, the invention adopts the following technical scheme:
A kind of mixing calculation method for obtaining fast neutron reactor and lacking group cross-section parameter, includes the following steps:
Step 1: for any fast pile component of required calculating, reading the geological information and respective material component of the component
Nucleic information；
Step 2: the geological information and material component information read for step 1 reads each nucleic in all material
Microcosmic inelastic scattering cross section value, every time fission release neutron population, fission spectrum information；
Step 3: the information read according to step 1, by specifying the input information of Monte Carlo calculations to establish corresponding meter
It calculates model and is calculated；Multigroup overall reaction rate of each nucleic in each region, fission reaction are counted in calculating process
Rate, elastic scattering reactivity and netron-flux density distribution；
Step 4: the multigroup overall reaction rate of each nucleic that is obtained using step 3, fission reaction rate, elastic scattering reactivity with
And netron-flux density distribution, the microcosmic total cross section of multigroup of each nucleic, microscopic fission cross section and microcosmic are acquired using formula (1)
Elastic scattering cross-section；
In formula:
σx,g--- g groups of microscopic cross, subscript x refer to microcosmic total cross section, fission cross section or elastic scattering cross-section
Rx,g--- g groups of microreaction rates, it is anti-that subscript x refers to microcosmic overall reaction rate, fission reaction rate or elastic scattering
It should rate
φg--- g groups of netron-flux density distributions
Step 5:: each nucleic group is calculated to the probability of scattering of group using formula (2), is calculated further according to step 4
The microcosmic elastic scattering cross-section of the multigroup of each nucleic and the elastic scattering matrix that each nucleic is calculated using formula (3)；
In formula:
Fl(g → g') --- l rank scatters to the probability of scattering of g ' group by g groups
α——(A‐1)2/(A+1)2, A is the atomic mass of nucleic
μc--- the angle of scattering cosine value under geocentric coordinate system
f(E,μc) --- probability of scattering function
Pl(μs) --- about μsL rank Legnedre polynomial
μs--- the angle of scattering cosine value under laboratory coordinate
ΔEg--- g groups of energy group intervals
In formula:
--- l rank scatters to the elastic scattering cross-section of g ' group by g groups
σs,g--- g groups of elastic scattering cross-sections
Step 6: according to the multigroup microscopic cross information of each nucleic obtained by step 2 to step 5, being read in conjunction with step 1
The component geological information and material information taken obtained based on the solution for the neutron-transport equation for determining the method for discussing with this more
Each rank neutron flux square distribution of group；
Step 7: the multigroup microscopic cross information and step 6 obtained based on step 2 to step 5 solves obtained multigroup
Each rank neutron flux square distribution, and the merger using formula (4), (5) to multigroup microscopic cross progress energy group, space, thus
To few group cross-section of component；
In formula:
σx,G,I--- G groups, belong to the microscopic cross in I area, subscript x refers to microcosmic total cross section, microscopic fission cross section
σx,g,i--- g groups, belong to the microscopic cross in the i-thth area, subscript x refers to microcosmic total cross section, microscopic fission cross section
φg,i--- g groups, belong to the i-thth area netron-flux density distribution
Vi--- the volume of the i-th subregion
In formula:
--- l rank is by the G groups of microscopic scattering cross sections for scattering to G ' group, belonging to I area
--- l rank is by the g groups of microscopic scattering cross sections for scattering to g ' group, belonging to the i-thth area
--- g groups, belong to the i-thth area l rank netron-flux density distribution.
Compared with prior art, the present invention has following advantage outstanding:
1. the microcosmic total cross section of multigroup, fission cross section, elastic scattering cross-section information are by Monte Carlo in mixing calculation method
Method is calculated, and ensure that high-precision；
2. it is special to avoid illiteracy by determining that the method for discussing is calculated for the elastic scattering matrix of each rank in mixing calculation method
Approximation in the method for Carlow ensure that scattering section precision；
3. the neutron flux square of each rank avoids Meng Teka by determining that the method for discussing is calculated in mixing calculation method
Approximation in the method for Lip river；The merger for being carried out energy group and region to high-order scattering section using high-order neutron flux square simultaneously, is obtained
More accurately lack group cross-section.
Detailed description of the invention
Fig. 1 is the mixed method flow chart that fast reactor lacks group cross-section calculating.
Fig. 2 is the error of each 24 groups of microscopic cross of nucleic of uniformity problem.
Fig. 3 is the error of one-dimensional 24 groups of volumic total cross-sections of cylinder problem.
Specific embodiment
The present invention is described in further details with reference to the accompanying drawings and detailed description:
The present invention is finely considered fast by combining by method monte carlo method with determining using monte carlo method
The resonance effects of pile component calculates the microcosmic total cross section of the accurate multigroup of each nucleic, fission cross section, elastic scattering cross-section, simultaneously
Using determine the method for discussing solve fast pile component each rank elastic scattering cross-section and each rank neutron flux square, with this by multigroup cross section
Merger is few group cross-section, as shown in Figure 1, the invention includes the following steps:
Step 1: for any fast pile component of required calculating, reading the geological information and respective material component of the component
Nucleic information；
Step 2: the geological information and material component information read for step 1 reads each nucleic in all material
Microcosmic inelastic scattering cross section value, every time fission release neutron population, fission spectrum information；
Step 3: the information read according to step 1, by specifying the input information of Monte Carlo calculations to establish corresponding meter
It calculates model and is calculated；Multigroup overall reaction rate of each nucleic in each region, fission reaction are counted in calculating process
Rate, elastic scattering reactivity and netron-flux density distribution；
Step 4: the multigroup overall reaction rate of each nucleic that is obtained using step 3, fission reaction rate, elastic scattering reactivity with
And netron-flux density distribution, the microcosmic total cross section of multigroup of each nucleic, microscopic fission cross section and microcosmic are acquired using formula (1)
Elastic scattering cross-section；
In formula:
σx,g--- g groups of microscopic cross, subscript x refer to microcosmic total cross section, microscopic fission cross section or microcosmic elastic scattering
Section
Rx,g--- g groups of microreaction rates, subscript x refer to microcosmic overall reaction rate, microcosmic fission reaction rate or microcosmic bullet
Property scattering reaction rate
φg--- g groups of netron-flux density distributions
Step 5:: each nucleic group is calculated to the probability of scattering of group using formula (2), is calculated further according to step 4
The microcosmic elastic scattering cross-section of the multigroup of each nucleic and the elastic scattering matrix that each nucleic is calculated using formula (3)；
In formula:
Fl(g → g') --- l rank scatters to the probability of scattering of g ' group by g groups
α——(A‐1)2/(A+1)2, A is the atomic mass of nucleic
μc--- the angle of scattering cosine value under geocentric coordinate system
f(E,μc) --- probability of scattering function
Pl(μs) --- about μsL rank Legnedre polynomial
μs--- the angle of scattering cosine value under laboratory coordinate
ΔEg--- g groups of energy group intervals
In formula:
--- l rank scatters to the elastic scattering cross-section of g ' group by g groups
σs,g--- g groups of elastic scattering cross-sections
Step 6: according to the multigroup microscopic cross information of each nucleic obtained by step 2 to step 5, being read in conjunction with step 1
The component geological information and material information taken obtained based on the solution for the neutron-transport equation for determining the method for discussing with this more
Each rank neutron flux square distribution of group；
Step 7: the multigroup microscopic cross information and step 6 obtained based on step 2 to step 5 solves obtained multigroup
Each rank neutron flux square distribution, and the merger using formula (4), (5) to multigroup microscopic cross progress energy group, space, thus
To few group cross-section of component.
In formula:
σx,G,I--- G groups, belong to the microscopic cross in I area, subscript x refers to microcosmic total cross section, microscopic fission cross section
σx,g,i--- g groups, belong to the microscopic cross in the i-thth area, subscript x refers to microcosmic total cross section, microscopic fission cross section
φg,i--- g groups, belong to the i-thth area netron-flux density distribution
Vi--- the volume of the i-th subregion
In formula:
--- l rank is by the G groups of microscopic scattering cross sections for scattering to G ' group, belonging to I area
--- l rank is by the g groups of microscopic scattering cross sections for scattering to g ' group, belonging to the i-thth area
--- g groups, belong to the i-thth area l rank netron-flux density distribution
In the present invention, the geometry of any fast pile component and material information are read in by step 1, the letter read according to step 1
Breath must by step 2 be read in Multi-group data library each nucleic microcosmic inelastic scattering cross section value, every time fission release in
Subnumber, fission spectrum information.The Multi-group data library calculated suitable for reactor physics includes above- mentioned information, and the present invention is to multigroup number
According to library selection there is no limit.
In the Monte Carlo calculations of step 3, must statistical regions be made with definition, i.e. the space of setting statistical regions is included
Range, the name information of bound locating for energy section and specific statistics nucleic, when statistics can be used it is arbitrary cover it is special
Carlow statistical method, such as collision count method or track lenth counting method, the present invention does not count the statistics of reactivity and flux
The limitation of method.
The neutron-transport equation solution side of different spaces dimension can be used in the solution of each rank neutron flux square distribution in step 6
Method, such as collision probability method, Discrete-ordinates method, characteristic line method, Spatial Dimension includes uniformity problem, one-dimensional problem.This hair
The bright solution procedure for the distribution of each rank neutron flux square and few group cross-section merger is not by neutron-transport equation method for solving
Limitation.
To verify effectiveness of the invention, Fig. 2 illustrates the uniform fast reactor component problem being calculated using the present invention
The relative error of the microcosmic total cross section in the 24 of each nucleic and reference solution.Calculated result shows to lack using what the present invention was calculated
Compared with reference solution, few group cross-section has a high precision for group cross-section, each nucleic it is each can group cross-section error 1% with
It is interior.Monte Carlo side is respectively adopted for the fast pile component of one-dimensional cylindrical geometry in the ability for calculating authentic component for the verifying present invention
Method determines that the method for discussing and mixing calculation method are calculated, and is with reference to solution, more other two methods with monte carlo method
24 groups of few group's volumic total cross-sections errors.As shown in figure 3, being cut caused by mixing calculation method compared to the method for discussing is determined
Face has higher precision, and cross-section error is within 1%.
Utilize accurate group cross-section less, so that it may the various Neutronics calculations for carrying out fast reactor reactor core, as stable state calculates, burnup
Calculating, transient state calculating etc..The present invention can obtain the fast pile components of degree of precision to lack group cross-section, can be applied to actual engineering
In calculation.
Claims (1)
1. a kind of mixing calculation method for obtaining fast neutron reactor and lacking group cross-section parameter, characterized by the following steps:
Step 1: for any fast pile component of required calculating, reading the geological information of the component and the core of respective material component
Prime information；
Step 2: for the geological information and material component information of step 1 reading, each nucleic is microcosmic in reading all material
Inelastic scattering cross section value, every time fission release neutron population, fission spectrum information；
Step 3: the information read according to step 1, by specifying the input information of Monte Carlo calculations to establish corresponding calculating mould
Type is simultaneously calculated；Multigroup overall reaction rate of each nucleic in each region, fission reaction rate, bullet are counted in calculating process
Property scattering reaction rate and netron-flux density distribution；
Step 4: the multigroup overall reaction rate of each nucleic that is obtained using step 3, fission reaction rate, elastic scattering reactivity and in
Sub- flux density distribution, the microcosmic total cross section of multigroup, microscopic fission cross section and the microcosmic elasticity of each nucleic are acquired using formula (1)
Scattering section；
In formula:
σx,g--- g groups of microscopic cross, subscript x refer to microcosmic total cross section, microscopic fission cross section or microcosmic elastic scattering cross-section
Rx,g--- g groups of microreaction rates, subscript x refer to microcosmic overall reaction rate, microcosmic fission reaction rate or microcosmic elasticity and dissipate
Penetrate reactivity
φg--- g groups of netron-flux density distributions
Step 5: calculating probability of scattering of each nucleic group to group, each nucleic being calculated further according to step 4 using formula (2)
The microcosmic elastic scattering cross-section of multigroup and the elastic scattering matrix of each nucleic is calculated using formula (3)；
In formula:
Fl(g → g') --- l rank scatters to the probability of scattering of g ' group by g groups
α——(A-1)2/(A+1)2, A is the atomic mass of nucleic
μc--- the angle of scattering cosine value under geocentric coordinate system
f(E,μc) --- probability of scattering function
Pl(μs) --- about μsL rank Legnedre polynomial
μs--- the angle of scattering cosine value under laboratory coordinate
ΔEg--- g groups of energy group intervals
In formula:
--- l rank scatters to the microcosmic elastic scattering cross-section of g ' group by g groups
σs,g--- g groups of microcosmic elastic scattering cross-sections
Step 6: according to the multigroup microscopic cross information of each nucleic obtained by step 2 to step 5, being read in conjunction with step 1
Component geological information and material information carry out obtaining multigroup based on the solution for the neutron-transport equation for determining the method for discussing with this
Each rank neutron flux square distribution；
Step 7: the multigroup microscopic cross information and step 6 obtained based on step 2 to step 5 solves each rank of obtained multigroup
The distribution of neutron flux square, and the merger using formula (4), (5) to multigroup microscopic cross progress energy group, space, to obtain group
Few group cross-section of part；
In formula:
σx,G,I--- G groups, belong to the microscopic cross in I area, subscript x refers to microcosmic total cross section, microscopic fission cross section
σx,g,i--- g groups, belong to the microscopic cross in the i-thth area, subscript x refers to microcosmic total cross section, microscopic fission cross section
φg,i--- g groups, belong to the i-thth area netron-flux density distribution
Vi--- the volume of the i-th subregion
In formula:
--- the microcosmic elastic scattering cross-section that l rank scatters to G ' group by G groups, belongs to I area
--- the microcosmic elastic scattering cross-section that l rank scatters to g ' group by g groups, belongs to the i-thth area
--- g groups, belong to the i-thth area l rank netron-flux density distribution.
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| CN109493924A (en) * | 2018-11-13 | 2019-03-19 | 西安交通大学 | A method of obtaining the effective multigroup cross section of FCM fuel |
| CN110704806B (en) * | 2019-09-19 | 2021-03-02 | 西安交通大学 | Rapid online calculation method for one-dimensional cylindrical geometric collision probability |
| CN112966428B (en) * | 2021-03-31 | 2022-08-05 | 清华大学 | Cross-section treatment system for reactor core |
| CN113868591B (en) * | 2021-09-28 | 2022-12-09 | 西安交通大学 | Method for obtaining high-precision total reaction cross section of unresolved resonance region |
| CN117150829B (en) * | 2023-10-31 | 2024-01-23 | 西安交通大学 | Method for generating stack-used few-group cross-section energy group structure for neutron analysis of intermediate energy spectrum |
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