CN106503446A - A kind of computational methods of strong neutron field fission-product nucleus burnup - Google Patents
A kind of computational methods of strong neutron field fission-product nucleus burnup Download PDFInfo
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Abstract
The present invention relates to a kind of computational methods of strong neutron field fission-product nucleus burnup, 51 subnets of the nuclear reaction network split of the product core that fission is produced by the method for charge number Z=22 72, and set up the sub-network data file of fission-product nucleus, according to the sub-network data file of fission-product nucleus, the cuclear density of each fission-product nucleus function over time is solved by implicit expression Runge Kutta method.The present invention can significantly improve the computational efficiency of strong neutron field fission-product nucleus burnup.
Description
Technical field
The present invention relates to the burnup computational methods of fission-product nucleus, and in particular to a kind of strong neutron field fission-product nucleus burnup
Computational methods.
Background technology
In highdensity strong neutron field, fission-product nucleus may occur considerable secondary response so that the product of product core
Volume (or burden) changes, it is therefore desirable to calculated by burnup, determines the knots modification of yield.
At present except the brilliant thesis for the doctorate of domestic money has write FIRENEQ calculation procedures, discovery is there is no to have open source information to be situated between
The computational methods of the strong neutron field burnup that continues.Close with the present invention is the burn-up calculation code of reactor.Reactor burnup is calculated
Method mainly has two big class：Numerical computation method based on burn up equation group Matrix Solving and the parsing side based on single burnup chain
Method.Such as the Origen2 programs that Los Alamos laboratory was developed in the eighties in last century, it is the parsing side based on Taylor expansion
Method.Burnup computing module, the burnup of France's exploitation in the Serpent systems that Finland VTT centers based on numerical computations are developed
Nucleic storage calculation procedure FISPACT in program MENDEL, the activation computing system of Europe exploitation, with regard to Jie of this respect
Continue, may refer to the thesis for the doctorate of Wu Mingyu《Based on the exploitation that the transporting of STEP1.0 and MCMG-II-burnup couples computing system
With research》.Be described below is with the closest CINDER90 programs based on analytic method of the invention and based on numerical method
FIRENEQ calculation procedures.
CINDER90 programs obtain single nucleic chain by splitting to nuclear reaction network, then pass through analytic method
Obtain the change of the nucleic density in each step-length.One of its key issue is the fractionation of reaction network, when occur circulation and
During loop nesting, split relatively difficult；Key issue two is to ensure that the approximate constant of within step-length time neutron flux.By examination
Calculate, the step-length of CINDER90 can not be less than 0.1ns, and in this step-length, the neutron flux of strong neutron field changes very greatly, so
CINDER90 is not suitable for the burnup of strong neutron field and calculates, and result of calculation can malfunction.FIRENEQ programs are calculated using the GEAR of numerical value
Method, calculates to whole nuclear reaction network and localized network.The product core of fission yield life has more than 1300, the ginseng of product core
With reaction have (n, γ), (n, 2n), (n, 3n), (n, p), (n, d), (n, t), (n, 3He) and (n, α) etc., be one
The matrix numerical solution of 1300x1300, calculating once needs several hours, or even needs 1 day or several days.
Content of the invention
It is an object of the invention to provide a kind of computational methods of strong neutron field fission-product nucleus burnup, for solving strong neutron
The burnup correction of field fission-product nucleus, and effectively improve computational efficiency.
Technical scheme is as follows：A kind of computational methods of strong neutron field fission-product nucleus burnup, including following step
Suddenly：
(1) 51 subnets of the nuclear reaction network split of the product core that fission is produced for charge number Z=22-72；
(2) the sub-network data file of fission-product nucleus is set up；
(3) according to the sub-network data file of fission-product nucleus, the cuclear density of each fission-product nucleus is solved over time
Function, the fission-product nucleus i cuclear density change differential equation are as follows：
Wherein,
It is expressed as i-th product nucleic density to change over；
The right Section 1 be the unit time fission produce i cores number, f (t) be fission rate, yiFor fission yield；
The right Section 2 for i cores consumption item, n (t) be neutron fluence rate, σoutFor composing average disappearance section, including the core
(n, γ), (n, 2n), (n, 3n) reaction cross-section；
Generation item of the right Section 3 for i cores, is respectively other cores j and is produced by (n, γ), (n, 2n), (n, 3n) reaction
The contribution of i cores, corresponding NjFor other product core j cuclear density, σinFor corresponding averga cross section.
Further, the computational methods of strong neutron field fission-product nucleus burnup as above, the subnet described in step (2)
Data file includes the ID and Nuclear Data of the fission-product nucleus of identical charges, and wherein, for charge number Z, mass number A, same core are different
Energy state I, its ID=A × 1000+Z × 10+I；Nuclear Data includes (n, γ), (n, 2n), the reaction cross-section of (n, 3n), independent yield
Y.
Further, the computational methods of strong neutron field fission-product nucleus burnup as above, by implicit expression dragon in step (3)
Ge-Ku Ta methods solve the cuclear density of each fission-product nucleus function over time, and described implicit expression Runge-Kutta methods are adopted
With PERL code software bag MATH-ODE, the realization of CABOR programs is write with PERL language.
Beneficial effects of the present invention are as follows：Using the computational methods of the present invention, corresponding model is set up, rapidly can be entered
Row is calculated, and is calculated and is once only needed to a few minutes.The raising of speed, has benefited from the segmentation of whole network.Fission product probably has
More than 1300, whole network is solved, need to solve differential equation group of the moment coefficient matrix for 1300*1300；Into 51 after segmentation
After subnet, the product core of each subnet only has more than ten, and by taking the subnet of Z=58 as an example, its nucleic only has 11, and its matrix is
/ the 14000 of 11*11, about whole network.Circulate 1/the 280 of all 51 subnets about whole net.According to so
"ball-park" estimate, time can shorten to the 1/280 of whole network event.If solving whole network needs 24 hours, then
The about 6 seconds time of single subnet, the time of all 51 subnets are cumulative about 5 minutes.It can be seen that, the present invention significantly can be carried
The computational efficiency of high-strength neutron field fission-product nucleus burnup.
Description of the drawings
Fig. 1 is the possibility reaction path diagram that any fission-product nucleus are generated under strong neutron field and disappeared；
Fig. 2 is the nuclear reaction network diagram being made up of fission-product nucleus, nuclear reaction, nuclear decay, and node represents product core,
The nuclear reaction (referring to Fig. 1) that arrow expresses possibility, be given in figure are the networks of mass number scope A=118-162, and dotted line is with arrow
Head be Z=58 subnet split line；
Fig. 3 is that Ce (Z=58, A=142-153) isotope reacts sub-network schematic diagram, and middle expression (n, γ) to the right is anti-
Should, the subnet includes many circulations, it is adaptable to numerical solution；
Fig. 4 is the flow chart that method of the present invention PERL language writes the realization of CABOR programs；
Flow charts of the Fig. 5 for specific embodiments of the present invention.
Specific embodiment
With reference to the accompanying drawings and examples the present invention is described in detail.
In strong neutron field, the i products cuclear density change differential equation is：
Wherein,It is expressed as i-th product nucleic density [unit：/ b-cm] change over, the right Section 1 is single
Position the time fission produce i cores number, f (t) be fission rate [1/s], yiFor fission yield；Consumption of the right Section 2 for i cores
, n (t) is neutron fluence rate [1/cm2- s], σoutFor composing average disappearance section, mainly include the core (n, γ), (n, 2n),
(n, 3n) reaction cross-section；The right Section 3 for i cores generation item, be respectively other cores (j) by (n, γ), (n, 2n), (n,
3n) etc. reaction produces the contribution of i cores, corresponding NjFor other product core cuclear density, σinFor corresponding averga cross section.
Each product core can pass through the decay of other cores or neutron reaction is produced, it is also possible to by itself decay and core
Reaction disappears.These decays and nuclear reaction include β-Decay, (n, γ), (n, 2n), (n, 3n), (n, p), (n, d), (n, t),
(n,3He), (n, a) reaction etc., as shown in Figure 1.Fission produces more than 1300 product core, the nuclear reaction of its nucleic and reaction composition
Network as shown in Fig. 2 mass number scope be A=66-172, charge number Z=22-72.
The duration of strong neutron field is shorter, far smaller than decay process, and decay process can be ignored, the differential equation (1)
Formula eliminates decay process, other neutron reactions, such as (n, p), (n, d), (n, t), (n,3He), (n, a) etc. reaction cross-section is much
Less than (n, γ), (n, 2n), (n, 3n) reaction cross-section sum, therefore can also ignore.According to above-mentioned it is assumed that fission-product nucleus ginseng
Plus nuclear process, charge number is constant, and corresponding nuclear reaction network equation can split into the subnet of identical charges number, and whole net can be with
It is split as 51 subnets of Z=22-72.Network range before fractionation is A=72-172, and Z=22-72, Fig. 2 (schematic diagram) are given
The subnetwork of Z=54-62 (Xe-Sm).The method of fractionation is in Z=22.5, laterally cuts where 23.5 ..., 71.5
Open, (in Fig. 2, the dotted line with arrow splits line for the subnet of Z=58) obtains the subnet of Z=22,23 ..., 72, and Fig. 3 is fractionation
The subnet of Z=58 afterwards, and marked (n, γ), (n, 2n), the nuclear reaction of (n, 3n)；As Fig. 3 be split after Ce (Z=58) with
The subnet of position element composition., there is all multicycle complex networks in the isotopic reaction subnets of Ce, therefore it is difficult to the subnet is split
Into loop-free single line network, it is impossible to function N (t) over time for providing cuclear density with the method for parsing.But, due to
The subnet only has 11 product cores, it is possible to solved with numerical solution, nucleic is few, speed can be avoided slow and rigidity is asked
Topic.The Runge-Kutta methods of conventional implicit expression can meet requirement.Implicit expression Runge-Kutta methods have ready-made code, the present invention
Using disclosing free PERL code software bag MATH-ODE (http：//search.cpan.org/dist/MATH-ODE-
0.07/).
Nuclear reaction subnet is generated, including data file and code, technical scheme is following (as shown in Figure 4)：
1) ID and Nuclear Data of the fission-product nucleus of identical charges are read in from data file library (including section and product
Volume)；
A) for a certain electric charge Z, mass number A, isomeric state I, its identity code are ID=A*1000+Z*10+I；
B) Nuclear Data includes (n, g), (n, 2n) and (n, 3n) section, independent yield Y；
2) subnet embedded code Pu239_Z.code is generated according to product core ID, Z represents charge number, by taking Z=58 as an example,
As shown in 1 row B1-B27 of table, information includes ID, yield, differential code to the code of generation；
3) using require (" Pu239_ Z.code ") in main code, subnet embedded code is introduced, and is solved；
4) result of calculation is obtained.
Based on principles above, CABOR programs have been write with PERL language, flow chart is as shown in Figure 5.Key step is as follows：
A. the data form with reference to CINDER90 sets up input data table, the entitled library of file；
B. according to library files, the product core according to identical charges sets up subnet, generates sub-network data file OD-
Z.dat, Z=51-72. this document includes reaction cross-section and yield；
C. subnet embedded code Pu239_Z.code is generated, and Z=51-72, the code can be embedded in using PERL language
Main program；
D. main program Cabor.pl is executed, is calculated, code is shown in Table 1；
E. calculate and generate output file sum.out, be shown in Table 2；
F. terminate.
Key sentence is as shown in table 1.As a example by solving Z=58, Ce133-Ce162 nucleic density, table 1 lists core language
Sentence and module.Row A5 insertions subnet code (B1-B27).Row A7-A16 initializes differential equation group.Row A18-29 is to solve for differential
The circulation of equation group, each circulation complete a burnup step-length, and the burn up time arrival given time stops.Thus can be with
Cuclear density not in the same time is obtained, yield is then convert into, you can obtains the delta data of yield, example of the table 2 for output.
By above method, it is achieved that the numerical solution of network segmentation and subnet, the delta data of yield is finally obtained.
1 Cabor.pl main codes (A) of table and PU239_Z.code embedded codes (B)
The calculating knot destination file sum.out of 2 Ce of table
Obviously, those skilled in the art can carry out the essence of various changes and modification without deviating from the present invention to the present invention
God and scope.So, if these modifications of the invention and modification are belonged to the model of the claims in the present invention and its equivalent technology
Within enclosing, then the present invention is also intended to comprising these changes and modification.
Claims (3)
1. a kind of computational methods of strong neutron field fission-product nucleus burnup, comprise the steps：
(1) 51 subnets of the nuclear reaction network split of the product core that fission is produced for charge number Z=22-72；
(2) the sub-network data file of fission-product nucleus is set up；
(3) according to the sub-network data file of fission-product nucleus, the cuclear density of each fission-product nucleus function over time is solved,
The fission-product nucleus i cuclear density change differential equation is as follows：
Wherein,
It is expressed as i-th product nucleic density to change over；
The right Section 1 be the unit time fission produce i cores number, f (t) be fission rate, yiFor fission yield；
The right Section 2 for i cores consumption item, n (t) be neutron fluence rate, σoutFor composing average disappearance section, including the core
(n, γ), (n, 2n), (n, 3n) reaction cross-section；
Generation item of the right Section 3 for i cores, is respectively other cores j and produces i cores by (n, γ), (n, 2n), (n, 3n) reaction
Contribution, corresponding NjFor other product core j cuclear density, σinFor corresponding averga cross section.
2. computational methods of neutron field fission-product nucleus burnup as claimed in claim 1 strong, it is characterised in that：In step (2)
Described sub-network data file includes the ID and Nuclear Data of the fission-product nucleus of identical charges, wherein, for charge number Z, quality
Number A, isomeric state I, its ID=A × 1000+Z × 10+I；Nuclear Data includes that (n, γ), (n, 2n), the reaction of (n, 3n) cut
Face, independent yield Y.
3. computational methods of neutron field fission-product nucleus burnup as claimed in claim 1 or 2 strong, it is characterised in that：Step (3)
In solve the cuclear density of each fission-product nucleus function over time, described implicit expression dragon by implicit expression Runge-Kutta methods
Ge-Ku Ta methods adopt PERL code software bag MATH-ODE, write the realization of CABOR programs with PERL language.
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| CN113470766A (en) * | 2021-06-23 | 2021-10-01 | 中国原子能科学研究院 | Automatic fission product fuel consumption chain testing method and device |
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| CN107092732A (en) * | 2017-04-05 | 2017-08-25 | 西安交通大学 | A kind of weighting Monte Carlo calculations method of neutron dynamics |
| CN107092732B (en) * | 2017-04-05 | 2020-11-17 | 西安交通大学 | Weighted Monte Carlo calculation method for neutron dynamics |
| CN110991809A (en) * | 2019-11-06 | 2020-04-10 | 中国辐射防护研究院 | Reactor core inventory real-time estimation method based on Hualong I |
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| CN113591024A (en) * | 2021-06-22 | 2021-11-02 | 中国原子能科学研究院 | Fission product burnup chain compression method and device |
| CN113591024B (en) * | 2021-06-22 | 2023-10-27 | 中国原子能科学研究院 | Fission product burnup chain compression method and device |
| CN113470766A (en) * | 2021-06-23 | 2021-10-01 | 中国原子能科学研究院 | Automatic fission product fuel consumption chain testing method and device |
| CN113470766B (en) * | 2021-06-23 | 2023-11-10 | 中国原子能科学研究院 | Automatic fission product burnup chain testing method and device |
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