CN106503446B - A kind of calculation method of strong neutron field fission-product nucleus burnup - Google Patents
A kind of calculation method of strong neutron field fission-product nucleus burnup Download PDFInfo
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Abstract
The present invention relates to a kind of calculation methods of strong neutron field fission-product nucleus burnup, the nuclear reaction network split for the product core that this method generates fission is 51 subnets of charge number Z=22-72, and establish the sub-network data file of fission-product nucleus, according to the sub-network data file of fission-product nucleus, changed with time function by the cuclear density that implicit Runge-Kutta methods solve each fission-product nucleus.The present invention can significantly improve the computational efficiency of strong neutron field fission-product nucleus burnup.
Description
Technical Field
The invention relates to a method for calculating the nuclear burnup of fission products, in particular to a method for calculating the nuclear burnup of fission products in a strong neutron field.
Background
In a high-density strong neutron field, considerable secondary reactions may occur in fission product nuclei, causing a change in the yield (or inventory) of the product nuclei, and thus the amount of yield change needs to be determined through a fuel-up calculation.
At present, except for writing a FIRENEQ calculation program in domestic Ph paper of Qiangjing, no open data is found to introduce a strong neutron field fuel consumption calculation method. Close to the present invention is a burnup calculation program for a reactor. The method for calculating the fuel consumption of the reactor mainly comprises two main types: a numerical calculation method based on the fuel consumption equation set matrix solution and an analytic method based on a single fuel consumption chain. Such as origin 2 program developed by los alamos laboratories in the last 80 th century, is an analytical method based on taylor's expansion. For the introduction of the fuel consumption calculation module in the Serpent system developed by VTT center in finland, the fuel consumption program MENDEL in france, and the nuclide stock calculation program FISPACT in the activation calculation system developed in europe, see "development and research of transport-fuel consumption coupled calculation system based on STEP1.0 and MCMG-II" by the doctrine of wumingyu. Described below are the analytical method-based CINDER90 program and the numerical method-based fienenq calculation program that are closest to the present invention.
The CINDER90 program splits the nuclear reaction network to obtain a single nuclide chain, and then obtains the nuclide density change in each step by an analytical method, wherein one of the key problems is the splitting of the reaction network, and the splitting is difficult when circulation and circulation nesting occur, and the other key problem is to ensure that the neutron flux is approximately unchanged in the step time.
Disclosure of Invention
The invention aims to provide a method for calculating the nuclear burnup of fission products of a strong neutron field, which is used for solving the problem of the nuclear burnup correction of the fission products of the strong neutron field and effectively improving the calculation efficiency.
The technical scheme of the invention is as follows: a method for calculating nuclear burnup of fission products of a strong neutron field comprises the following steps:
(1) splitting a nuclear reaction network of a fission-generated product nucleus into 51 subnets with charge numbers Z being 22-72;
(2) establishing a subnet data file of the fission product nucleus;
(3) according to the subnet data file of the fission product nucleus, solving the variation function of the nuclear density of each fission product nucleus along with time, wherein the fission product nucleus i nuclear density variation differential equation is as follows:
wherein,
expressed as the ith product species density over time;
first item on the rightNumber of nuclei producing fission per unit time, f (t) fission rate, yiIs fission yield;
the second term on the right is the depletion term for the i nucleus, n (t) is the neutron fluence rate, σout(n, γ), (n,2n), (n,3n) reaction sections including the nucleus, as a spectral average disappearance section;
the third term on the right is the generation term of i nucleus, which is the contribution of other nuclei j to i nucleus through the reaction of (N, gamma), (N,2N), (N,3N), and the corresponding NjFor other product nuclei j nuclear density, σinThe corresponding average cross-section.
Further, in the method for calculating burnup of fission product nuclear in strong neutron field as described above, the subnet data file in step (2) includes ID and nuclear data of fission product nuclear with the same charge, wherein, for the charge number Z, the mass number a, the homonuclear energy state I, and its ID is ax1000 + zx 10+ I; the nuclear data include reaction cross sections of (n, γ), (n,2n), (n,3n), and independent yield Y.
Further, in the calculation method for nuclear burnup of fission products in the strong neutron field as described above, in the step (3), a change function of the nuclear density of each fission product core with time is solved by an implicit longge-kuta method, wherein the implicit longge-kuta method is realized by adopting a PERL code software package MATH-ODE and writing a cab program in PERL language.
The invention has the following beneficial effects: by adopting the calculation method, the corresponding model is established, the calculation can be rapidly carried out, and only a few minutes are needed for one calculation. The speed increase benefits from the segmentation of the entire network. The fission products are more than 1300 probably, and the differential equation set with a moment coefficient matrix of 1300x1300 needs to be solved for solving the whole network; after the division into 51 subnets, the product cores of each subnet are only dozens, and taking the subnet with Z being 58 as an example, the number of the nuclides is only 11, and the matrix is 11 × 11, which is about 14000 times of the whole network. The circulation of all 51 sub-nets was about 280 times less than the whole net. From such a rough estimate, the time can be shortened to 1/280 for the entire network event. If it takes 24 hours to solve the entire network, the time for a single subnet is about 6 seconds and the sum of the time for all 51 subnets is about 5 minutes. Therefore, the method can obviously improve the calculation efficiency of the nuclear burnup of the fission product of the strong neutron field.
Drawings
FIG. 1 is a diagram of the possible reaction paths for the generation and disappearance of any fission product nuclei in the intense neutron field;
fig. 2 is a schematic diagram of a nuclear reaction network consisting of fission product nuclei, nuclear reactions, nuclear decay, nodes representing the product nuclei, arrows representing possible nuclear reactions (see fig. 1), the network having a mass number range a of 118-;
fig. 3 is a schematic diagram of Ce (Z58, a 142-;
FIG. 4 is a flowchart of the method of the present invention implemented by writing CABAC program in PERL language;
FIG. 5 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
In the strong subfield, the differential equation of the change of the i product nuclear density is as follows:
wherein,expressed as the ith product nuclide density [ unit: b-cm]The first term on the right is the number of nuclei generating fission per unit time, f (t) is the fission rate [1/s ] as a function of time]，yiIs fission yield; the second term on the right is the depletion term of the i nucleus, n (t) is the neutron fluence rate [ 1/cm%2-s]，σout(n, γ), (n,2n), (n,3n) reaction sections of the nucleus, which are the spectral average disappearance sections; the third term on the right is the generation term of i nucleus, which is the contribution of other nuclei (j) to i nucleus, corresponding to N, through the reactions of (N, gamma), (N,2N), (N,3N), etcjNuclear density, σ, of other productsinThe corresponding average cross-section.
Each product nucleus can be generated by decay or neutron reactions of other nuclei, or can be eliminated by decay and nuclear reactions of its own, these decay and nuclear reactions include β-Decay, (n, γ), (n,2n), (n,3n), (n, p), (n, d), (n, t), (n,3he), (n, a), and the like, as shown in FIG. 1. The fission produces 1300 product nuclei whose nuclear species and reaction make up a nuclear reaction network as shown in fig. 2, with mass numbers ranging from a-66 to 172 and charge numbers Z from 22 to 72.
The duration of the strong neutron field is shorter and far shorter than the decay process, the decay process can be ignored, the decay process is eliminated by the equation (1), and other neutron reactions such as (n, p), (n, d), (n, t), (n,3the reaction cross sections of He, n, a, etc. are much smaller than the sum of the reaction cross sections of (n, gamma), (n,2n), (n,3n), and thus can be ignored. According to the assumption, the charge number of the nuclear process in which the fission product nuclear participates is unchanged, the corresponding nuclear reaction network equation can be split into subnets with the same charge number, and the whole network can be split into 51 subnets with Z being 22-72. The network range before splitting is 72-172, Z is 22-72, and FIG. 2 (schematic diagram) shows a partial network of Z54-62 (Xe-Sm). The splitting method is to transversely cut at a position where Z is 22.5, 23.5., (the dotted line with an arrow in fig. 2 is a subnet splitting line of Z58), so as to obtain a subnet with Z being 22, 23., (72), and fig. 3 is the subnet with Z being 58 after splitting, and the nuclear reactions of (n, γ), (n,2n), (n,3n) are marked; as shown in fig. 3And (3) a subnetwork composed of Ce (Z ═ 58) isotopes. The reaction subnet of the Ce isotope has a complex network with many cycles, so that the subnet is difficult to split into a single-wire network without cycles, and the time-dependent change function N (t) of the nuclear density cannot be given by an analytical method. However, since the subnet has only 11 product cores, the subnet can be solved by a numerical solution, the nuclide is few, and the problems of low speed and rigidity can be avoided. The usual implicit longge-kuta method can meet the requirements. The implicit Longge-Kutta method has ready code, and the invention adopts the public free PERL code software package MATH-ODE (http:// search. cpan. org/dist/MATH-ODE-0.07 /).
Generating a core reaction subnet which comprises a data file and a code, wherein the technical scheme of the invention is as follows (as shown in figure 4):
1) reading in the ID and nuclear data (including section and yield) of fission product nuclei of the same charge from a data file library;
a) for a certain charge Z, the mass number A, the homonuclear heteroenergetic state I, and the identity code of the homonuclear heteroenergetic state I is ID A1000 + Z10 + I;
b) nuclear data including (n, g), (n,2n) and (n,3n) cross sections, independent yield Y;
2) generating a subnet embedded code Pu239_ z.code according to the product core ID, wherein Z represents the charge number, and taking Z ═ 58 as an example, the generated code is shown as rows B1-B27 in table 1, and the information comprises ID, yield and differential code;
3) introducing subnet embedded codes by using require ("Pu 239_ $ Z.code") in the main codes, and solving;
4) and obtaining a calculation result.
Based on the above principle, the CABAC program is written in PERL language, and the flow chart is shown in FIG. 5. The method mainly comprises the following steps:
A. establishing an input data table with reference to a data format of CINDER90, wherein the file name is library;
B. establishing a subnet according to a library file and a product core with the same charge to generate a subnet data file OD-Z.dat, wherein Z is 51-72, the file comprises a reaction section and a yield;
C. generating a subnet embedded code Pu239_ Z.code, wherein Z is 51-72, the code adopts PERL language and can be embedded into a main program;
D. executing a main program Cabor.pl, and calculating, wherein codes are shown in a table 1;
E. calculating to generate an output file sum.out, see table 2;
F. and (6) ending.
The key statements are shown in table 1. Taking the solving of the Z-58, Ce133-Ce162 species density as an example, table 1 lists the core statements and modules. Line A5 inserts the subnet code (B1-B27). Lines A7-A16 initialize a system of differential equations. Lines A18-29 are loops for solving the system of differential equations, each loop completing one burn-up step and stopping when the burn-up time reaches a given time. Thus, the nuclear density at different time can be obtained, and then converted into the yield, so as to obtain the variation data of the yield, and table 2 is an example of the output.
By the method, network segmentation and numerical solution of the sub-networks are realized, and finally, yield change data are obtained.
Table 1 cabor. pl main code (a) and PU239_ z. code embedded code (B)
Table 2 Ce calculation result file sum
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is intended to include such modifications and variations.
Claims (3)
1. A method for calculating nuclear burnup of fission products of a strong neutron field comprises the following steps:
(1) splitting the nuclear reaction network of the fission-generated product nucleus into 51 subnets with charge numbers Z ranging from 22 to 72;
(2) establishing a subnet data file of the fission product nucleus;
(3) according to the subnet data file of the fission product nucleus, solving the variation function of the nuclear density of each fission product nucleus along with time, wherein the fission product nucleus i nuclear density variation differential equation is as follows:
wherein,
expressed as the ith product species density over time;
the first term on the right is the number of nuclei producing fission per unit time, f (t) is the fission rate, yiIs fission yield;
the second term on the right is the depletion term for the i nucleus, n (t) is the neutron fluence rate, σout(n, γ), (n,2n), (n,3n) reaction sections including the nucleus, as a spectral average disappearance section;
the third term on the right is the generation term of i nucleus, which is the contribution of other nuclei j to i nucleus through the reaction of (N, gamma), (N,2N), (N,3N), and the corresponding NjFor other product nuclei j nuclear density, σinThe corresponding average cross-section.
2. The method of calculating a hadron fission product nuclear burnup of claim 1, wherein: the subnet data file in the step (2) comprises ID and nuclear data of fission product nuclei with the same charge, wherein for the charge number Z, the mass number A and the homonuclear heterostate I, the ID is Ax1000 + Zx10 + I; the nuclear data include reaction cross sections of (n, γ), (n,2n), (n,3n), and independent yield Y.
3. Method for calculating the nuclear burnup of fission products of a hadron field according to claim 1 or 2, characterized in that: and (3) solving a nuclear density change function of each fission product nucleus along with time by an implicit Runge-Kutta method.
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| CN112100826B (en) * | 2020-08-27 | 2022-12-09 | 西安交通大学 | Method for special treatment of decay heat calculation in burn-up database compression process |
| CN114220580B (en) * | 2020-12-08 | 2024-08-13 | 阳江核电有限公司 | Method for predicting burn-up of damaged fuel assembly |
| 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 |
| 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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