Nuclear fuel pore evolution simulation method and device based on phase field theory

Abstract

The invention discloses a nuclear fuel pore evolution simulation method and device based on a phase field theory, and relates to the technical field of irradiation microstructure evolution simulation. The method comprises the following steps: constructing a system free energy equation of nuclear fuel, a dynamic evolution preliminary equation of vacancy concentration changing along with time, and a dynamic equation of dislocation ring density changing along with time; according to the system free energy equation, the dynamic evolution preliminary equation of the vacancy concentration changing along with the time and the dynamic equation of the dislocation ring density changing along with the time, a phase field model of the nuclear fuel is constructed; and based on the phase field model, simulating the pore evolution process of the nuclear fuel, and analyzing the influence of fission density on the pore evolution of the nuclear fuel. The influence of the fission density on nuclear fuel pore evolution can be accurately predicted, and the problem that the cost is huge when experimental data is obtained through experimental means is solved.

Description

Technical Field

[0001] The present application relates to the technical field of irradiation microstructure evolution simulation, and in particular to a method and device for simulating nuclear fuel pore evolution based on phase field theory. Background Art

[0002] Since the Fukushima nuclear power plant accident in Japan, many accident-tolerant fuels (ATFs) have been proposed by researchers to replace traditional UO2 fuels, such as U3Si2. Compared with traditional UO2 fuels, accident-tolerant fuels have a series of unique advantages, such as higher thermal conductivity, greater uranium density, and thermal conductivity increases with temperature. These characteristics of accident-tolerant fuels help to achieve good safety under normal operating conditions and in loss of coolant accidents (LOCAs), and improve the operating efficiency of nuclear reactors.

[0003] Fuel swelling characteristics are an important part of the study of the blister failure mechanism of nuclear fuel elements. Therefore, it is of great significance to master the fuel swelling characteristics. Under irradiation, accident-resistant fuel will produce a large number of defects, including pores. The volume swelling of accident-resistant fuel is closely related to the evolution of pores.

[0004] At present, there has been no extensive safety and reliability testing of the in-pile and out-of-pile behavior of accident-resistant fuels. There is a lack of corresponding experimental data to study the effect of fission density on the pore evolution of accident-resistant fuels, and the cost of obtaining effective experimental data through experimental means is huge. Summary of the invention

[0005] In view of this, the present application provides a method and device for simulating the pore evolution of nuclear fuel based on phase field theory, which is mainly capable of accurately predicting the influence of fission density on the pore evolution of nuclear fuel and solving the problem of huge cost of obtaining experimental data through experimental means.

[0006] According to the first aspect of the present application, a method for simulating nuclear fuel pore evolution based on phase field theory is provided, the method comprising:

[0007] Construct the system free energy equation of nuclear fuel, the preliminary equation for the kinetic evolution of vacancy concentration over time, and the kinetic equation for the dislocation loop density over time;

[0008] Constructing a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time;

[0009] Based on the phase field model, the pore evolution process of the nuclear fuel is simulated, and the influence of fission density on the pore evolution of the nuclear fuel is analyzed.

[0010] According to the second aspect of the present application, a nuclear fuel pore evolution simulation device based on phase field theory is provided, the device comprising:

[0011] The first construction unit is used to construct the system free energy equation of nuclear fuel, the preliminary equation for the dynamic evolution of vacancy concentration over time, and the dynamic equation for the dislocation loop density over time;

[0012] A second construction unit is used to construct a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time;

[0013] The simulation unit is used to simulate the pore evolution process of the nuclear fuel based on the phase field model, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

[0014] According to a third aspect of the present application, a storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned nuclear fuel pore evolution simulation method based on phase field theory is implemented.

[0015] According to the fourth aspect of the present application, an electronic device is provided, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein when the processor executes the program, the above-mentioned nuclear fuel pore evolution simulation method based on phase field theory is implemented.

[0016] Through the above-mentioned technical scheme, the present application provides a method and device for simulating the pore evolution of nuclear fuel based on phase field theory. By constructing a phase field model of the pore evolution of nuclear fuel under irradiation conditions, it is possible to simulate the pore evolution process of nuclear fuel under different fission densities, thereby being able to accurately predict the influence of fission density on the pore evolution of nuclear fuel. The simulation method of the present application can replace experimental means, thereby solving the problem of the huge cost of obtaining experimental data through experimental means.

[0017] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0019] Figure 1A schematic diagram of a process flow of a nuclear fuel pore evolution simulation method based on phase field theory provided in an embodiment of the present application is shown;

[0020] Figure 2 A schematic flow chart of another method for simulating nuclear fuel pore evolution based on phase field theory provided in an embodiment of the present application is shown;

[0021] Figure 3 It shows that the fission density provided by the embodiment of the present application is 0cm -3 The pore evolution morphology of nuclear fuel at the time of

[0022] Figure 4 It shows that the fission density provided by the embodiment of the present application is 0.80×10 21 cm -3 The pore evolution morphology of nuclear fuel at the time of

[0023] Figure 5 It shows that the fission density provided by the embodiment of the present application is 0.93×10 21 cm -3 The pore evolution morphology of nuclear fuel at the time of

[0024] Figure 6 It shows that the fission density provided by the embodiment of the present application is 1.06×10 21 cm -3 The pore evolution morphology of nuclear fuel at the time of

[0025] Figure 7 A schematic diagram showing the variation of the average pore radius of the nuclear fuel provided in the embodiment of the present application with the fission density and a schematic diagram showing the size distribution of the average radius;

[0026] Figure 8 A schematic diagram showing the variation of the number of vacancies with fission density provided in an embodiment of the present application is shown;

[0027] Fig. 9 A schematic diagram showing the change of swelling rate with fission density provided in an embodiment of the present application is shown;

[0028] Fig.10 A schematic diagram showing the variation of pore concentration with fission density provided in an embodiment of the present application is shown;

[0029] Fig.11 A schematic diagram showing the change of porosity with fission density provided by an embodiment of the present application is shown;

[0030] Fig.12 A schematic structural diagram of a nuclear fuel pore evolution simulation device based on phase field theory provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0031] The present application will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

[0032] Currently, there is a lack of corresponding experimental data for studying the effect of fission density on the pore evolution of accident-resistant fuels, and the cost of obtaining effective experimental data through experimental means is enormous.

[0033] In order to solve the above problems, the embodiment of the present invention provides a nuclear fuel pore evolution simulation method based on phase field theory, such as Figure 1 As shown, the method includes:

[0034] Step 101: construct a system free energy equation for nuclear fuel, a preliminary equation for the dynamic evolution of vacancy concentration over time, and a dynamic equation for the dynamic evolution of dislocation loop density over time.

[0035] The nuclear fuel may specifically be U3Si2. In addition, it may also be other types of nuclear fuel, which is not specifically limited in the embodiment of the present invention.

[0036] The embodiment of the present invention is mainly applicable to the simulation scenario of the nuclear fuel pore evolution process. The execution subject of the embodiment of the present invention is a device or equipment that can simulate the nuclear fuel pore evolution process, which can be specifically set on the server side.

[0037] In order to construct a phase field model of nuclear fuel pore evolution under irradiation conditions, the embodiment of the present invention needs to pre-construct the system free energy equation of the nuclear fuel, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation ring density over time.

[0038] The method for constructing a free energy equation of a nuclear fuel system includes: constructing an interpolation function on field variables, a vacancy free energy density function and a double potential well function, wherein the field variables are used to describe the pore formation of the nuclear fuel; constructing a system chemical free energy density function of the nuclear fuel based on the interpolation function, the vacancy free energy density function and the double potential well function; and constructing a system free energy equation of the nuclear fuel based on the system chemical free energy density function.

[0039] The free energy equation of the system is as follows:

[0040]

[0041] Where F represents the total free energy of the nuclear fuel system; V represents the volume of the nuclear fuel; η represents the field variable, which is used to describe the pore formation of the nuclear fuel and has a value range of 0 to 1; r represents the space vector, representing the spatial position; c v represents the concentration of vacancies; κv represents the gradient energy coefficient of the vacancy; κ η represents the field variable gradient energy coefficient; G(c v ,η) represents the system chemical free energy density function of nuclear fuel. The system chemical free energy density function G(c v , n) can be specifically expressed as:

[0042] G(c v ,η)=h(η)f(c v )+φ(c v ,η) (2)

[0043] Among them, h(η) represents the interpolation function, which is in the form of h(η)=(η-1) 2 (η+1) 2 , indicating that the chemical free energy density G changes continuously from the matrix phase (h(0) = 1) to the pore phase (h(1) = 0); f(c v ) is the free energy density function of the vacancy; φ(c v ,η) is a double potential well function, which is used to represent the formation of matrix phase and pore phase.

[0044] The free energy density function of the vacancy f(c v ) can be specifically expressed as:

[0045]

[0046] in, is the vacancy thermal equilibrium concentration, is the formation energy of the vacancy; T is the temperature; k B is the Boltzmann constant; R is the gas constant; V m is the molar volume of the vacancy, N A is Avogadro's constant, is the curvature constant.

[0047] Furthermore, based on the principle of the diffusion interface model, the formation of pores is described by the non-conservative field variable η. In the pore phase, η = 1. c i =0; in the matrix phase, η=0, The field variable η changes continuously, and the interface between the pore phase and the matrix phase is a diffusion interface with a very small width. i is the interstitial atomic concentration, is the thermal equilibrium concentration of interstitial atoms.

[0048] Furthermore, the double potential well function φ(c v ,η) can be used to represent the formation of matrix phase and pore phase, specifically expressed as:

[0049]

[0050] Among them, A and B are fitting parameters, is the vacancy concentration in the pore phase.

[0051] Furthermore, for the preliminary construction process of the kinetic evolution of vacancy concentration over time, the method includes: constructing a vacancy generation function, an absorption function of vacancies by defect traps, a composite function of interstitial atoms and vacancies, and a vacancy diffusion flux; based on the vacancy generation function, the absorption function of vacancies by defect traps, the composite function of interstitial atoms and vacancies, and the vacancy diffusion flux, constructing a preliminary equation for the kinetic evolution of the vacancy concentration over time.

[0052] In addition, it is also necessary to construct a preliminary equation for the kinetic evolution of interstitial atom concentration over time. For this construction process, the method includes: constructing an interstitial atom generation function, an absorption function of interstitial atoms by defect traps, a composite function of interstitial atoms and vacancies, and an interstitial atom diffusion flux; based on the interstitial atom generation function, the absorption function of interstitial atoms by defect traps, the composite function of interstitial atoms and vacancies, and the interstitial atom diffusion flux, constructing a preliminary equation for the kinetic evolution of interstitial atom concentration over time.

[0053] When constructing the absorption function of the defect trap to the interstitial atom, the defect trap absorption intensity of the interstitial atom is determined based on the first bias factor of the grid dislocation absorption point defect, the first bias factor of the dislocation loop absorption point defect and the dislocation loop density; based on the defect trap absorption intensity of the interstitial atom, the absorption function of the defect trap to the interstitial atom is constructed.

[0054] When constructing the absorption function of the defect trap to the vacancy, the defect trap absorption intensity of the vacancy is determined based on the second bias factor of the grid dislocation absorption of point defects, the second bias factor of the dislocation loop absorption of point defects and the grid dislocation density; based on the defect trap absorption intensity of the vacancy, the absorption function of the defect trap to the vacancy is constructed.

[0055] Among them, the preliminary equations for the dynamic evolution of vacancy concentration over time and the preliminary equations for the dynamic evolution of interstitial atom concentration over time are as follows:

[0056]

[0057] Among them, equation (5) is the preliminary equation for the dynamic evolution of interstitial atom concentration over time, and equation (6) is the preliminary equation for the dynamic evolution of vacancy concentration over time. The first term K in equation (5) is i is the interstitial atom generation function, the second term is the absorption function of the vacancy trap to the interstitial atom, the third term is the composite function of the interstitial atom and the vacancy, and the fourth term ▽ is the Hamiltonian operator, J i is the interstitial atomic diffusion flux. The first term K in equation (6) v is the vacancy generation function, the second term is the absorption function of the vacancy trap to the vacancy, the third term is the composite function of the interstitial atom and the vacancy, the fourth term ▽ is the Hamiltonian operator, J v is the vacancy diffusion flux.

[0058] Furthermore, the interstitial atom generation function and the vacancy generation function can be specifically expressed as:

[0059] K i or K v =Ω0PF D (1-ε r ) (7)

[0060] Where P is the Frankel pair produced in each fission, Ω0 is the atomic volume, and F D is the fission density, ε r is the cascade relaxation efficiency.

[0061] Furthermore, D i and D v are the diffusion coefficients of interstitial atoms and vacancies, respectively, r is the recombination rate constant, and are the absorption intensity of the missing trap of the interstitial atom and the absorption intensity of the missing trap of the vacancy, which can be expressed as:

[0062]

[0063] Among them, Z Ni , Z Nv are the first bias factor and the second bias factor of point defect absorption through lattice dislocations, respectively; Z Ii , Z Iv are the first bias factor and the second bias factor of point defects absorbed by dislocation loops, respectively; ρ N is the grid dislocation density; ρ I is the dislocation loop density.

[0064] Furthermore, the dynamic equation of the change of dislocation loop density with time can be specifically expressed as:

[0065]

[0066] Among them, b v is the modulus of the Burgers vector, r i is the initial dislocation loop radius, c vLrepresents the equilibrium vacancy concentration near the dislocation loop.

[0067] The embodiment of the present invention can finely consider the influence of dislocations on irradiation defects by introducing a dynamic equation for the variation of dislocation loop density with time.

[0068] According to the above formulas, we can construct the system free energy equation of nuclear fuel (1), the preliminary equation of the dynamic evolution of vacancy concentration over time (6), and the dynamic equation of the dislocation ring density over time (10).

[0069] Step 102: construct a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the kinetic evolution of the vacancy concentration over time, and the kinetic equation of the dislocation loop density over time.

[0070] For the embodiments of the present invention, after constructing the system free energy equation (1) of the nuclear fuel, the preliminary equation (6) of the dynamic evolution of the vacancy concentration over time, and the dynamic equation (10) of the dislocation ring density over time, a phase field model of the nuclear fuel can be constructed based on the system free energy equation (1) of the nuclear fuel, the preliminary equation (6) of the dynamic evolution of the vacancy concentration over time, and the dynamic equation (10) of the dislocation ring density over time.

[0071] Step 103: Based on the phase field model, simulate the pore evolution process of the nuclear fuel, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

[0072] After the phase field model is constructed, the phase field model is used to simulate the fission density of nuclear fuel at different fission densities F D The pore evolution morphology under the condition of high fission density is analyzed, so as to analyze the relationship between the average pore radius, the number of vacancies, the swelling ratio, the pore concentration and the porosity and the fission density, and finally determine the influence of the fission density on the pore evolution of nuclear fuel.

[0073] An embodiment of the present invention provides a method for simulating the pore evolution of nuclear fuel based on phase field theory. By constructing a phase field model of the pore evolution of nuclear fuel under irradiation conditions, it is possible to simulate the pore evolution process of nuclear fuel under different fission densities, thereby being able to accurately predict the influence of fission density on the pore evolution of nuclear fuel. The simulation method of the embodiment of the present invention can replace experimental means, thereby solving the problem of the huge cost of obtaining experimental data through experimental means.

[0074] Further, as a refinement and extension of the specific implementation of the above embodiment, in order to fully illustrate the implementation of this embodiment, this embodiment also provides another nuclear fuel pore evolution simulation method based on phase field theory, such as Figure 2 As shown, the method includes:

[0075] Step 201: construct a system free energy equation for nuclear fuel, a preliminary equation for the dynamic evolution of vacancy concentration over time, and a dynamic equation for the dynamic evolution of dislocation loop density over time.

[0076] For the embodiment of the present invention, the specific process of constructing the system free energy equation of nuclear fuel, the preliminary equation of the dynamic evolution of vacancy concentration over time, and the dynamic equation of the dislocation ring density over time is exactly the same as step 101 and will not be repeated here.

[0077] Step 202: construct a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time.

[0078] For the embodiments of the present invention, after constructing the system free energy equation (1) of the nuclear fuel, the preliminary equation (6) of the dynamic evolution of the vacancy concentration over time, and the dynamic equation (10) of the dislocation ring density over time, a phase field model of the nuclear fuel can be constructed based on the system free energy equation (1) of the nuclear fuel, the preliminary equation (6) of the dynamic evolution of the vacancy concentration over time, and the dynamic equation (10) of the dislocation ring density over time.

[0079] Step 203: derive and solve the phase field model to obtain a group of dynamic control equations of the nuclear fuel.

[0080] For the embodiment of the present invention, in order to determine the kinetic control equation group of nuclear fuel, step 203 specifically includes: according to the difference between the high temperature limit and the cascade collapse, the preliminary equation of the kinetic evolution of the vacancy concentration changing with time in the phase field model is corrected to obtain the corrected preliminary equation of the kinetic evolution of the vacancy concentration changing with time; based on the system free energy equation in the phase field model, the vacancy diffusion flux in the corrected preliminary equation of the kinetic evolution of the vacancy concentration changing with time is displayed to obtain the kinetic evolution equation of the vacancy concentration changing with time; based on the system free energy equation and the migration coefficient, an equation of the field variable changing with time is constructed; according to the kinetic evolution equation of the vacancy concentration changing with time, the equation of the field variable changing with time, and the kinetic equation of the dislocation ring density changing with time, the kinetic control equation group of the nuclear fuel is determined.

[0081] Specifically, due to the diffusion coefficient D of the interstitial atoms i Much larger than the diffusion coefficient of the vacancy D v , so the interstitial atoms generated by the cascade move to the vacancy trap faster than the vacancies. In addition, at high temperatures, the concentration of interstitial atoms reaches a stable value faster than the concentration of vacancies. Considering the difference between the high temperature limit and the cascade collapse, it can be assumed that At the same time, the preliminary equation of the dynamic evolution of the interstitial atom concentration over time can be used to adjust the preliminary equation of the dynamic evolution of the vacancy concentration over time. Finally, after algebraic operations, the revised preliminary equation of the dynamic evolution of the vacancy concentration over time can be obtained. The specific formula is as follows:

[0082]

[0083] Furthermore, the vacancy diffusion flux in the modified preliminary equation of the kinetic evolution of the vacancy concentration over time is displayed to obtain the kinetic evolution equation of the vacancy concentration over time, which is as follows:

[0084]

[0085] Among them, the first migration coefficient M v =c v (1-c v )D v V m / RT

[0086] Furthermore, the equations for the field variables changing with time are constructed as follows:

[0087]

[0088] Among them, the second migration coefficient M η =D v V m / l 2 RT,

[0089] Furthermore, the dynamic equation of the change of dislocation loop density with time is mathematically converted as follows:

[0090]

[0091] After obtaining the kinetic evolution equation (12) of the vacancy concentration changing with time, the equation (13) of the field variable changing with time, and the kinetic equation (14) of the dislocation loop density changing with time, the kinetic evolution equation (12) of the vacancy concentration changing with time, the equation (13) of the field variable changing with time, and the kinetic equation (14) of the dislocation loop density changing with time are combined as a group of kinetic control equations for nuclear fuel.

[0092] Step 204: Based on the group of kinetic control equations, simulate the pore evolution process of the nuclear fuel, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

[0093] For an embodiment of the present invention, after determining the group of kinetic control equations, the group of kinetic control equations is numerically solved to obtain the pore evolution morphology of the nuclear fuel when the total free energy F is minimized, and based on the pore evolution morphology, the influence of fission density on the pore evolution of the nuclear fuel is determined.

[0094] Specifically, by consulting the references, we can find The formation energy of the vacancy is 1.69 eV, and the diffusion coefficient of the vacancy is D v 0.1nm 2 / s, the gradient energy coefficient of the vacancy κ v and field variable gradient energy coefficient κ η Both are 1.92×10 -8 J / m, molar volume of vacancy V m 0.03629nm 3 / mol. For the phase field model of the embodiment of the present invention, the simulation temperature can be selected as 1000K, and the grid dislocation density ρ N For 10 10 / cm 2 , initial dislocation loop radius r i is 5, and the fitting parameter A=B=1.

[0095] Furthermore, the relevant data of the evolution equation are dimensionless processed to obtain the following set of dynamic control equations:

[0096]

[0097] From formulas (15), (16) and (17), we can approximate κ v =κ η =0.5, M η =1.5,M v =1, α r =0.2, D i =15.

[0098] Furthermore, the Fourier spectrum method of periodic boundary is used to solve the dynamic equation. When solving the equation, the initial condition is set to c v (r,0)=10 -3 ,η(r,0)=0,ρ N (0) = ρ i (0) = 0, and the system is numerically solved on a cubic simulation unit with N × N × N grid points, the grid size is Δx = Δy = Δz = 1, the characteristic length is L = NΔL (N = 64, ΔL = 2nm), and the time step is Δt = 10 -3 , and use ParaView software to visualize the solution results.

[0099] Furthermore, in order to study the differences in pore evolution of nuclear fuel (such as U3Si2) at different fission densities, the embodiment of the present invention selects 0-1.7×10 21 cm -3 Phase field simulation is carried out for the fission density range of U3Si2 fuel in common light water reactors. The pore evolution results of the system after 20000Δt are as follows Figure 3-6 As shown, Figure 3-6 The corresponding fission densities are 0 and 0.80×10 21 , 0.93×10 21 , 1.06×10 21 cm -3 By solving the kinetic control equations, the pore evolution morphology of nuclear fuel at different fission densities when the total free energy F is minimized can be obtained.

[0100] Furthermore, when determining the influence of fission density on the pore evolution of nuclear fuel according to the pore evolution morphology, the relationship between the average pore radius, the number of vacancies, the swelling rate, the pore concentration and the porosity and the fission density are analyzed based on the pore evolution morphology, and the influence of the fission density on the pore evolution of the nuclear fuel is determined according to the relationship between the average pore radius, the number of vacancies, the swelling rate, the pore concentration and the porosity and the fission density.

[0101] Specifically, in order to quantitatively study the mathematical law of pore evolution, the embodiment of the present invention is based on Figure 3-6 The pore evolution morphology in the pores is analyzed statistically, and the distribution of the average pore radius, the number of vacancies, the swelling ratio, the pore concentration and the porosity under different fission densities are analyzed. Figure 7-11 Based on the distribution law, the embodiment of the present invention can predict the future evolution of nuclear fuel pores.

[0102] Another method for simulating the pore evolution of nuclear fuel based on phase field theory provided in an embodiment of the present invention can simulate the pore evolution process of nuclear fuel under different fission densities by constructing a phase field model of the pore evolution of nuclear fuel under irradiation conditions, thereby being able to accurately predict the influence of fission density on the pore evolution of nuclear fuel. The simulation method of the embodiment of the present invention can replace experimental means, thereby solving the problem of the huge cost of obtaining experimental data through experimental means.

[0103] Further, as Figure 1 and Figure 2 The specific implementation of the method shown in the embodiment provides a nuclear fuel pore evolution simulation device based on phase field theory, such as Fig.12 As shown, the device includes: a first building unit 31, a second building unit 32 and a simulation unit 33.

[0104] The first construction unit 31 can be used to construct the system free energy equation of nuclear fuel, the preliminary equation of the dynamic evolution of vacancy concentration over time, and the dynamic equation of the dislocation loop density over time.

[0105] The second construction unit 32 can be used to construct the phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time.

[0106] The simulation unit 33 can be used to simulate the pore evolution process of the nuclear fuel based on the phase field model, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

[0107] In some embodiments, the first construction unit 31 can be specifically used to construct an interpolation function about field variables, a vacancy free energy density function and a double potential well function, wherein the field variables are used to describe the pore formation of the nuclear fuel; based on the interpolation function, the vacancy free energy density function and the double potential well function, a system chemical free energy density function of the nuclear fuel is constructed; based on the system chemical free energy density function, a system free energy equation of the nuclear fuel is constructed.

[0108] In some embodiments, the first construction unit 31 can also be specifically used to construct a vacancy generation function, an absorption function of vacancies by defect traps, a composite function of interstitial atoms and vacancies, and a vacancy diffusion flux; based on the vacancy generation function, the absorption function of vacancies by defect traps, the composite function of interstitial atoms and vacancies, and the vacancy diffusion flux, a preliminary equation for the kinetic evolution of the vacancy concentration over time is constructed.

[0109] In some embodiments, the first construction unit 31 can also be used to construct an interstitial atom generation function, an absorption function of interstitial atoms by defect traps, a composite function of interstitial atoms and vacancies, and an interstitial atom diffusion flux; based on the interstitial atom generation function, the absorption function of interstitial atoms by defect traps, the composite function of interstitial atoms and vacancies, and the interstitial atom diffusion flux, a preliminary equation for the kinetic evolution of the interstitial atom concentration over time is constructed.

[0110] In some embodiments, the first construction unit 31 can also be specifically used to determine the defect trap absorption intensity of interstitial atoms based on the first bias factor of grid dislocation absorption point defects, the first bias factor of dislocation loop absorption point defects and the dislocation loop density; based on the defect trap absorption intensity of the interstitial atoms, construct an absorption function of the defect trap for the interstitial atoms.

[0111] In some embodiments, the first construction unit 31 can also be specifically used to determine the defect trap absorption intensity of the vacancy based on the second bias factor of the grid dislocation absorption point defect, the second bias factor of the dislocation loop absorption point defect and the grid dislocation density; based on the defect trap absorption intensity of the vacancy, construct the absorption function of the defect trap to the vacancy.

[0112] In some embodiments, the simulation unit 33 includes: a derivation module and a simulation module.

[0113] The derivation module can be used to derive and solve the phase field model to obtain the kinetic control equations of the nuclear fuel.

[0114] The simulation module can be used to simulate the pore evolution process of the nuclear fuel based on the kinetic control equations, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

[0115] In some embodiments, the derivation module can be specifically used to correct the preliminary equation of the kinetic evolution of the vacancy concentration over time in the phase field model according to the difference between the high temperature limit and the cascade collapse, so as to obtain the corrected preliminary equation of the kinetic evolution of the vacancy concentration over time; based on the system free energy equation in the phase field model, the vacancy diffusion flux in the corrected preliminary equation of the kinetic evolution of the vacancy concentration over time is displayed to obtain the kinetic evolution equation of the vacancy concentration over time; based on the system free energy equation and the migration coefficient, an equation for the field variables over time is constructed; according to the kinetic evolution equation for the vacancy concentration over time, the equation for the field variables over time, and the kinetic equation for the dislocation ring density over time, the kinetic control equation group of the nuclear fuel is determined.

[0116] In some embodiments, the simulation module includes: a solution submodule and a determination submodule.

[0117] The solving submodule can be used to solve the group of kinetic control equations to obtain the pore evolution morphology of the nuclear fuel when the total free energy is minimized.

[0118] The determination submodule can be used to determine the influence of fission density on the pore evolution of the nuclear fuel based on the pore evolution morphology.

[0119] In some embodiments, the determination submodule can be specifically used to analyze the relationship between the average pore radius, the number of vacancies, the swelling rate, the pore concentration and the porosity, and the fission density, respectively, based on the pore evolution morphology; and determine the influence of the fission density on the pore evolution of the nuclear fuel according to the relationship between the average pore radius, the number of vacancies, the swelling rate, the pore concentration and the porosity, respectively, and the fission density.

[0120] It should be noted that for other corresponding descriptions of the functional units involved in the nuclear fuel pore evolution simulation device based on phase field theory provided in this embodiment, reference can be made to Figure 1 and Figure 2 The corresponding description in will not be repeated here.

[0121] Based on the above Figure 1 and Figure 2 The method shown in the embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned Figure 1 and Figure 2 The nuclear fuel pore evolution simulation method based on phase field theory is shown.

[0122] Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), including a number of instructions for enabling an electronic device (which can be a personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of the present application.

[0123] Based on the above Figure 1 and Figure 2 The method shown, and Fig.12 In order to achieve the above-mentioned purpose, the embodiment of the present application also provides an electronic device, which can be a personal computer, a tablet computer, a server, or other network equipment, etc. The device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to achieve the above-mentioned Figure 1 and Figure 2 The nuclear fuel pore evolution simulation method based on phase field theory is shown.

[0124] Optionally, the above-mentioned physical device may also include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a WI-FI module, etc. The user interface may include a display, an input unit such as a keyboard, etc., and the optional user interface may also include a USB interface, a card reader interface, etc. The network interface may optionally include a standard wired interface, a wireless interface (such as a WI-FI interface), etc.

[0125] Those skilled in the art will appreciate that the above-mentioned physical device structure provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or a combination of certain components, or different arrangements of components.

[0126] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the above-mentioned physical device, and supports the operation of the information processing program and other software and / or programs. The network communication module is used to realize the communication between the components inside the storage medium, and the communication with other hardware and software in the information processing physical device.

[0127] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present application can be implemented by means of software plus a necessary general hardware platform, or by hardware.

[0128] The embodiment of the present invention can simulate the pore evolution process of nuclear fuel under different fission densities by constructing a phase field model of nuclear fuel pore evolution under irradiation conditions, so as to accurately predict the influence of fission density on the pore evolution of nuclear fuel. The simulation method of the embodiment of the present invention can replace experimental means, thereby solving the problem of huge cost of obtaining experimental data through experimental means.

[0129] Those skilled in the art will appreciate that the accompanying drawings are only schematic diagrams of a preferred implementation scenario, and the modules or processes in the accompanying drawings are not necessarily necessary for implementing the present application. Those skilled in the art will appreciate that the modules in the devices in the implementation scenario can be distributed in the devices of the implementation scenario according to the description of the implementation scenario, or can be changed accordingly and located in one or more devices different from the present implementation scenario. The modules of the above-mentioned implementation scenario can be combined into one module, or can be further split into multiple submodules.

[0130] The above serial numbers of this application are only for description and do not represent the advantages and disadvantages of the implementation scenarios. The above disclosure is only a few specific implementation scenarios of this application, but this application is not limited to them, and any changes that can be thought of by technicians in this field should fall within the scope of protection of this application.

Claims

1. A method for simulating nuclear fuel pore evolution based on phase field theory, characterized in that: include: Construct the system free energy equation of nuclear fuel, the preliminary equation for the kinetic evolution of vacancy concentration over time, and the kinetic equation for the dislocation loop density over time; Constructing a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time; Based on the phase field model, the pore evolution process of the nuclear fuel is simulated, and the influence of fission density on the pore evolution of the nuclear fuel is analyzed.

2. The method according to claim 1, characterized in that Construct the system free energy equation of nuclear fuel, including: constructing an interpolation function on field variables, a free energy density function of vacancies, and a double potential well function, wherein the field variables are used to describe the pore formation of the nuclear fuel; Constructing a system chemical free energy density function of the nuclear fuel based on the interpolation function, the free energy density function of the vacancy and the double potential well function; According to the chemical free energy density function of the system, a system free energy equation of the nuclear fuel is constructed.

3. The method according to claim 1, characterized in that Construct a preliminary equation for the dynamic evolution of vacancy concentration over time, including: Construct vacancy generation function, absorption function of vacancy by trap, recombination function of interstitial atoms and vacancies, and vacancy diffusion flux; Based on the vacancy generation function, the absorption function of the vacancy trap to the vacancy, the composite function of the interstitial atoms and vacancies, and the vacancy diffusion flux, a preliminary equation for the kinetic evolution of the vacancy concentration over time is constructed; The method further comprises: Construct interstitial atom generation function, interstitial atom absorption function of defect traps, interstitial atom and vacancy recombination function, and interstitial atom diffusion flux; Based on the interstitial atom generation function, the absorption function of the defect trap to the interstitial atom, the composite function of the interstitial atom and vacancy, and the interstitial atom diffusion flux, a preliminary equation for the kinetic evolution of the interstitial atom concentration over time is constructed.

4. The method according to claim 3, characterized in that Construct the absorption function of the missing trap to the interstitial atom, including: Based on the first bias factor of the grid dislocation absorption point defect, the first bias factor of the dislocation loop absorption point defect and the dislocation loop density, the defect trap absorption intensity of the interstitial atom is determined; Based on the absorption intensity of the defect trap of the interstitial atom, constructing an absorption function of the defect trap to the interstitial atom; Construct the absorption function of the missing trap to the vacancy, including: Based on the second bias factor of the lattice dislocation absorption point defect, the second bias factor of the dislocation loop absorption point defect and the lattice dislocation density, the vacancy trap absorption intensity is determined; Based on the defect trap absorption intensity of the vacancy, an absorption function of the defect trap to the vacancy is constructed.

5. The method according to claim 1, characterized in that Based on the phase field model, the pore evolution process of the nuclear fuel is simulated, and the influence of fission density on the pore evolution of the nuclear fuel is analyzed, including: Derived and solved the phase field model to obtain a group of dynamic control equations of the nuclear fuel; Based on the kinetic control equations, the pore evolution process of the nuclear fuel is simulated, and the influence of fission density on the pore evolution of the nuclear fuel is analyzed.

6. The method according to claim 5, characterized in that The phase field model is derived and solved to obtain the kinetic control equations of the nuclear fuel, including: According to the difference between the high temperature limit and the cascade collapse, the preliminary equation of the kinetic evolution of the vacancy concentration with time in the phase field model is corrected to obtain a corrected preliminary equation of the kinetic evolution of the vacancy concentration with time; Based on the system free energy equation in the phase field model, the vacancy diffusion flux in the modified preliminary equation of the kinetic evolution of the vacancy concentration over time is displayed to obtain the kinetic evolution equation of the vacancy concentration over time; Based on the free energy equation and the migration coefficient of the system, an equation for the change of field variables with time is constructed; Determining the group of kinetic control equations of the nuclear fuel according to the kinetic evolution equation of the vacancy concentration over time, the equation of the field variable over time, and the kinetic equation of the dislocation loop density over time; and / or Based on the kinetic control equations, the pore evolution process of the nuclear fuel is simulated, and the influence of fission density on the pore evolution of the nuclear fuel is analyzed, including: Solving the kinetic control equations to obtain the pore evolution morphology of the nuclear fuel when the total free energy is minimum; Based on the pore evolution morphology, the influence of fission density on the pore evolution of the nuclear fuel is determined.

7. The method according to claim 6, characterized in that Based on the pore evolution morphology, determining the influence of fission density on the pore evolution of the nuclear fuel includes: Based on the pore evolution morphology, the relationship between the average pore radius, the number of vacancies, the swelling ratio, the pore concentration and the porosity and the fission density is analyzed; The influence of the fission density on the pore evolution of the nuclear fuel is determined based on the relationship between the average pore radius, the number of vacancies, the swelling ratio, the pore concentration and the porosity, and the fission density, respectively.

8. A nuclear fuel pore evolution simulation device based on phase field theory, characterized in that: include: The first construction unit is used to construct the system free energy equation of nuclear fuel, the preliminary equation for the dynamic evolution of vacancy concentration over time, and the dynamic equation for the dislocation loop density over time; A second construction unit is used to construct a phase field model of the nuclear fuel according to the system free energy equation, the preliminary equation of the dynamic evolution of the vacancy concentration over time, and the dynamic equation of the dislocation loop density over time; The simulation unit is used to simulate the pore evolution process of the nuclear fuel based on the phase field model, and analyze the influence of fission density on the pore evolution of the nuclear fuel.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

10. An electronic device comprising a storage medium, a processor, and a computer program stored in the storage medium and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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