Cladding defect evolution analysis method based on finite element software and cluster dynamics

Abstract

The present invention discloses a cladding defect evolution analysis method based on finite element software and cluster dynamics, comprising the following steps: (1) starting commercial finite element software, establishing rate equations for defects and their clusters in the cladding material of nuclear fuel elements, and obtaining a corresponding parameterized script file; (2) expanding the rate equations in the script file to obtain a rate equation group; (3) setting relevant physical property parameters of the rate equations corresponding to the defects and their clusters; (4) setting initial conditions; (5) setting solver parameters and running the script file; (6) post-processing the calculation results to obtain the changes in the defects in the cladding with the irradiation dose and the changes in the number of defects in the clusters and the cluster size. Compared with the traditional method of developing a cluster dynamics program in a programming language to simulate the defect evolution process, this method can save time and cost in the simulation process.

Description

Technical Field

[0001] The present invention relates to the technical field of nuclear material simulation, and in particular to a cladding defect evolution analysis method based on finite element software and cluster dynamics. Background Art

[0002] During their service life, nuclear materials in reactors are irradiated by a variety of high-energy particles generated by nuclear reactions, which can alter the material's microstructure and macroscopic properties. Point defects, dislocation loops, and solute clusters are common material defects during irradiation. Cluster dynamics has higher temporal and spatial scales than microscopic simulation methods such as molecular dynamics, capable of reaching the irradiation depths found in experimental and reactor environments while describing the accumulation and evolution of defects under varying neutron doses. Cluster dynamics, based on mean-field rate theory, solves the diffusion-reaction kinetic rate equation to obtain the temporal evolution and spatial distribution of the concentration of various defects. This requires establishing a corresponding physical model and incorporating it into a program for solution.

[0003] Cluster dynamics methods are mesoscopic simulation methods that can analyze the dynamic time-dependent evolution of defects in metastable material systems. They effectively combine microscopic irradiation damage with macroscopic physical properties, and have broad applications in the field of nuclear material irradiation. Currently, cluster dynamics programs are developed using programming languages. These require not only the development of relevant models and theoretical foundations for rate equations, but also a thorough understanding of software technology areas such as solvers, program architecture, and model interfaces. This is labor-intensive and resource-intensive, and can only be applied to specific fields, resulting in limited versatility. Summary of the Invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a cladding defect evolution analysis method based on finite element software and cluster dynamics, which is used to analyze the dynamic evolution behavior of defects in the metastable system of materials over time. This method can save time and cost in simulating the evolution process of nuclear fuel element cladding defects, and is universal and can be applied to other physical problems that require solving large sets of partial differential equations.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A cladding defect evolution analysis method based on finite element software and cluster dynamics includes the following steps:

[0007] (1) Launch the commercial finite element software COMSOL Multiphysics, establish the rate equations for defects and their clusters in the nuclear fuel element cladding material, and obtain the corresponding parameterized script file;

[0008] (2) Expanding the rate equation in the script file using MATLAB software to obtain a rate equation group;

[0009] (3) Setting the relevant physical property parameters of the rate equation corresponding to defects and their clusters;

[0010] (4) Setting initial conditions;

[0011] (5) Set the solver parameters and run the script file in MATLAB;

[0012] (6) The calculation results are post-processed to obtain the changes in the defects in the cladding with the irradiation dose and the changes in the number of defects in the clusters and the size of the clusters.

[0013] A further improvement of the technology of the present invention is that in step (1), the defect types in the nuclear fuel element cladding material include vacancies and interstitial atoms or precipitated phase atoms, and the rate equation of cluster dynamics is constructed by the PDE module in the finite element software COMSOL Multiphysics.

[0014] A further improvement of the technology of the present invention is that: in step (2), the cluster dynamics rate equation is expanded by MATLAB software and a parametric modeling method to obtain a rate equation group. The mathematical form of the rate equation group is a partial differential equation group. The grouping approximation method is used in the process of establishing the rate equation group. The main function of this method is to group a preset number of rate equations corresponding to adjacent larger-sized clusters, and each group is described by only two characteristic partial differential equations, thereby reducing the number of partial differential equation groups and reducing the consumption of computing resources.

[0015] A further improvement of the present invention is that in step (3), the relevant physical property parameters of the rate equation of the defects and their clusters include the diffusion coefficient, migration energy, formation energy, generation rate, radius, binding energy between defect clusters, temperature, dislocation density and defect trap absorption efficiency of the defects and their clusters, which are set by MATLAB software.

[0016] A further improvement of the present invention is that in step (4), the initial conditions set include the initial concentration distribution of defects, which are set by MATLAB software.

[0017] A further improvement of the present invention is that: in step (5), a transient solver is selected in the finite element software COMSOL Multiphysics for calculation, and the solver parameters are set based on the solver and parameter setting method provided in the finite element software COMSOL Multiphysics and are set through MATLAB software.

[0018] A further improvement of the present invention is that in step (6), the operation results are batch processed and exported by a parametric design method in an APP developer of the finite element software COMSOL Multiphysics.

[0019] Compared with the prior art, the present invention has the following outstanding features:

[0020] (1) This method can reduce the burden on professional designers and shorten the research cycle. It can operate the commercial finite element software COMSOL Multiphysics through parametric commands, combining the advantages of the maturity of the commercial software COMSOL Multiphysics and the flexibility of the programming language.

[0021] (2) The group approximation method is used in the rate equation group, which helps to reduce the number of partial differential equations and reduce the consumption of computing resources.

[0022] (3) Based on the commercial software COMSOL Multiphysics, the cluster dynamics method is used to simulate the evolution of defects in nuclear fuel elements. Compared with existing technologies, this method greatly saves the time and cost of the simulation process and is universal and reliable. It promotes the establishment of multi-scale design methods in nuclear material analysis, achieves theoretical guidance for the design of nuclear materials, and is of great significance to the development and application of new nuclear materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of the cladding defect evolution analysis method based on finite element software and cluster dynamics of the present invention;

[0024] Figure 2 Schematic diagram of the dose dependence of defect clusters of different sizes in an embodiment of the present invention;

[0025] Figure 3 is the evolution of the average cluster concentration of all clusters with neutron irradiation dose in the embodiment of the present invention;

[0026] Figure 4 This is the growth process of the average radius of all clusters in the embodiment of the present invention as the neutron irradiation dose increases. DETAILED DESCRIPTION

[0027] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the following examples are given of the cluster dynamics simulation method using COMSOL Multiphysics software and MATLAB software as the actual finite element software and parametric modeling software, and the implementation methods of the present invention are specifically described in conjunction with the accompanying drawings.

[0028] See attached Figures 1 to 4 .

[0029] A cladding defect evolution analysis method based on finite element software and cluster dynamics, the flow diagram is as follows Figure 1 , specifically including the following steps:

[0030] (1) Start COMSOL Multiphysics software, add a one-dimensional component to the software, add a PDE module to the component, and establish the rate equation of defects and their clusters in the nuclear fuel element cladding material in the module. Taking FeCu alloy as an example, for the precipitation phase clusters in FeCu alloy material, the rate equation is in the form of

[0031]

[0032] Where:

[0033] C i (t) — the concentration of clusters with size i at time t;

[0034] β i ——the absorption coefficient of a cluster with cluster size i;

[0035] α i ——The emission coefficient of the cluster with cluster size i.

[0036] Convert to a script file that can be edited by MATLAB program;

[0037] (2) Start the COMSOL Multiphysics with MATLAB module and MATLAB software, expand the rate equations in MATLAB software, and obtain a rate equation group containing 50,000 clusters. The group approximation method is used in the establishment of the rate equation group. The main function of this method is to group a certain number of rate equations corresponding to adjacent larger-sized clusters. Each group is described by only two characteristic partial differential equations. These two characteristic partial differential equations represent the average value and slope of each group of clusters, respectively. Their forms are

[0038]

[0039]

[0040] Where:

[0041] L i,0 (t)—the average value of cluster concentration in the i-th cluster group at time t;

[0042] L i,1 (t)—the slope of the cluster concentration versus size distribution in the i-th cluster group at time t;

[0043] x i ——cluster size of the last cluster in the i-th cluster group;

[0044] Δx i ——The number of clusters contained in the i-th cluster group;

[0045] J(x i ,t)——the cluster size at time t is x i The cluster size is x i The net flux of cluster transformation concentration of +1;

[0046] ——the average value of the net flux of concentration of all clusters of size x in the i-th cluster group transforming into clusters of size x+1;

[0047] ——the variance of all cluster sizes in the i-th cluster group;

[0048] The concentration of a cluster C in each cluster group is determined by L i,1 (t) and L i,2 (t) is expressed as

[0049] C(x i-1 +x,t)=L 0,i (t)+L 1,i (t)(x- <x> i ) (4)

[0050] This can reduce the number of partial differential equations and the consumption of computing resources.

[0051] (3) The diffusion coefficient, migration energy, formation energy, generation rate, radius, binding energy between defect clusters, temperature, dislocation density, defect trap absorption efficiency and other parameters of the Cu precipitation phase clusters are set in MATLAB. These parameters are obtained through experimental data and molecular simulation and are set in a parameterized script file.

[0052] (4) Set the initial concentration of Cu precipitation phase in MATLAB.

[0053] (5) Establish a transient segregated solver and select an appropriate solver type. The solver parameters are set from the solver and parameter setting method provided by COMSOL Multiphysics software and are set in a parameterized script file. In this example, the MUMPS solver is selected, the maximum time step is set to 0.1 s, the relative tolerance is 0.001, and the solution time is set to 10^{range(log10(0.001),0.1,log10(1000000))}s.

[0054] (6) With the COMSOL Multiphysics software and the COMSOL Multiphysics with MATLAB module running, open the corresponding .mph file in MATLAB, and then run the script file through MATLAB.

[0055] (7) Open the corresponding .mph file and perform batch processing and export of the results using the parametric design method in the COMSOL Multiphysics software app developer. Summarize the calculation results using Origin and Excel software, and draw trend charts and distribution graphs to display the results. In this example, a set of rate equations for defect clusters with a cluster size of 1 to 50,000 was established, and the evolution of defect clusters with neutron irradiation dose was calculated. Figure 2 The figure represents the dose dependence of Cu precipitate phase clusters of different sizes, that is, the evolution of defect clusters with neutron irradiation dose calculated by the cladding defect evolution analysis method based on COMSOL Multiphysics software and cluster dynamics, under the premise of keeping the temperature, grain size and alloying elements unchanged. Figure 3 It represents the evolution of the average cluster concentration of all Cu precipitation phase clusters with neutron irradiation dose under the same environment. Figure 4 It shows the growth process of the average radius of all Cu precipitation phase clusters with neutron irradiation dose under the same environment. Figure 3 and Figure 4 The results are close to the experimental results, and the errors are within a reasonable range, which shows the reliability of the method of the present invention.

[0056] The above content is merely illustrative of the principles and effects of the present invention and is not intended to limit the present invention. Those skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concepts disclosed herein shall be encompassed by the claims of the present invention.< / x>

Claims

1. A cladding defect evolution analysis method based on finite element software and cluster dynamics, characterized in that: The following steps are involved: (1) Start the finite element software, establish the rate equation of defects and their clusters in the nuclear fuel element cladding material, and obtain the corresponding parameterized script file; the details are as follows: Start COMSOL Multiphysics software, add a one-dimensional component to the software, add the PDE module to the component, and establish the rate equation of defects and their clusters in the nuclear fuel element cladding material in the module. For the precipitation phase clusters in the FeCu alloy material, the rate equation is in the form of Where: C i (t) — the concentration of clusters with size i at time t; β i ——the absorption coefficient of a cluster with cluster size i; α i ——the emission coefficient of the cluster with cluster size i; Convert to a script file that can be edited by MATLAB program; (2) The rate equation is expanded in the script file by MATLAB software to obtain a rate equation group; specifically: the cluster dynamics rate equation is expanded by MATLAB software and a parametric modeling method to obtain a rate equation group. The mathematical form of the rate equation group is a partial differential equation group. The grouping approximation method is used in the process of establishing the rate equation group. The main function of this method is to group a preset number of rate equations corresponding to adjacent larger-sized clusters. Each group is described by only two characteristic partial differential equations, thereby reducing the number of partial differential equation groups and reducing the consumption of computing resources. (3) Setting the relevant physical property parameters of the rate equation corresponding to defects and their clusters; The relevant physical property parameters of the rate equations of defects and their clusters include the diffusion coefficient, migration energy, formation energy, generation rate, radius, binding energy between defect clusters, temperature, dislocation density and defect trap absorption efficiency of defects and their clusters, which are set using MATLAB software; (4) Set initial conditions; (5) Set the solver parameters and run the script file in MATLAB; (6) The calculation results are post-processed to obtain the changes in the defects in the cladding with the irradiation dose and the changes in the number of defects in the clusters and the size of the clusters.

2. The cladding defect evolution analysis method based on finite element software and cluster dynamics according to claim 1, characterized in that: In the step (1), the defect types in the nuclear fuel element cladding material include vacancies and interstitial atoms or precipitated phase atoms, and the rate equation of cluster dynamics is constructed by the PDE module in the finite element software COMSOL Multiphysics.

3. The cladding defect evolution analysis method based on finite element software and cluster dynamics according to claim 1, characterized in that: In the step (4), the initial conditions set include the initial concentration distribution of defects, which are set through MATLAB software.

4. The cladding defect evolution analysis method based on finite element software and cluster dynamics according to claim 1, characterized in that: In the step (5), a transient solver is selected in the finite element software COMSOL Multiphysics for calculation, and the solver parameters are set based on the solver and parameter setting method provided in the finite element software COMSOL Multiphysics and are set through MATLAB software.

5. The cladding defect evolution analysis method based on finite element software and cluster dynamics according to claim 1, characterized in that: In the step (6), the running results are batch processed and exported by parametric design method in the APP developer of the finite element software COMSOL Multiphysics.

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