A phase-field simulation method for pore migration in UO2 nuclear fuel

Abstract

The present invention discloses a phase field simulation method for pore migration in UO2 nuclear fuel, by coupling temperature field T and concentration field c v As well as the non-conservative order parameter field η, the behaviors of surface diffusion and vapor transport diffusion in pore migration, as well as the distortion of temperature gradient at the pores due to the difference in thermal conductivity between pores and matrix are taken into account, thus achieving accurate prediction of pore diffusion in UO2 fuel, providing technical support for improving the service performance of UO2 fuel, and solving the problem of inaccurate and incomplete description of pore diffusion in existing technologies.

Description

Technical Field

[0001] The invention relates to the field of phase field simulation, and in particular to a phase field simulation method for pore migration in UO2 nuclear fuel. Background Art

[0002] As a commonly used oxide fuel, UO2 has a relatively low thermal conductivity. When in service, the temperature of the center can reach 2000°C, while the temperature of the surface edge is only 400-500°C. The huge temperature difference in the radial direction of the fuel rod produces a large temperature gradient. This large temperature gradient will drive the pores in the fuel to migrate to the center, forming central pores and densifying the material. At the same time, when the pores migrate, there are gaseous fission products inside. The large difference in thermal conductivity between the fission products and the UO2 matrix will also cause differences in the temperature distribution inside and outside the pores, thereby causing changes in the pore migration rate. Experimental studies have shown that not only the temperature field, but also the size changes will cause changes in the migration behavior and morphology of the pores in the fuel pellets.

[0003] At present, a lot of research reports have been conducted on the migration of UO2 pores, but there is no model that can comprehensively and accurately describe the migration of pores in UO2 nuclear fuel. Summary of the invention

[0004] The purpose of this application is to provide a phase field simulation method for pore migration in UO2 nuclear fuel, which solves the problems existing in the prior art.

[0005] The present invention is achieved through the following technical solutions:

[0006] A phase field simulation method for pore migration in UO2 nuclear fuel, comprising:

[0007] Constructing free energies of a matrix phase, a pore phase, and an interface containing vacancies, and obtaining a total free energy based on the free energies of the matrix phase, the pore phase, and the interface;

[0008] constructing a steady-state heat conduction function of the hole, and obtaining the temperature distribution in the hole according to the steady-state heat conduction function;

[0009] Obtaining the velocity of hole migration according to the temperature distribution in the hole, and obtaining a function of the evolution of vacancy concentration over time according to the velocity of hole migration;

[0010] Obtain the interface mobility, and obtain the kinetic function of the time evolution of the pore phase based on the total free energy, the function of the vacancy concentration evolving with time and the interface mobility, and complete the construction of the phase field model;

[0011] Based on the phase field model, the analysis results of pore migration in UO2 nuclear fuel are obtained, and the phase field simulation of pore migration is completed.

[0012] In a possible implementation, the total free energy F is:

[0013]

[0014]

[0015] h(η)=(η-1) 2 (η+1) 2

[0016]

[0017]

[0018] Among them, h(η) represents the interpolation function, f(c v ) represents the intermediate function, V represents the volume, represents the gradient operator, ω(c v ,η) represents the Landau-type polynomial, κ v represents the gradient coefficient of the vacancy, c v represents the vacancy concentration, κ η represents the gradient coefficient of the hole phase, and the migration and aggregation of the vacancies form holes; η represents the non-conservative field variable, represents the integration over the entire phase field model volume, represents the formation energy of the vacancy, k B represents the Boltzmann constant, T represents the absolute temperature, A represents the potential well height, represents the equilibrium vacancy concentration, B represents a constant, ln represents the logarithm with the constant e as the base, and exp represents the exponential function with the natural constant e as the base.

[0019] In a possible implementation, the steady-state heat conduction function of the hole is:

[0020]

[0021] κ(c v )=(κ pore -κ matrix )c v +κ matrix

[0022] Among them, κ(c v ) represents thermal conductivity, represents the temperature gradient in the hole, q represents the heat source constant, q(1-c v 2 ) represents the heat source term, κ pore represents the thermal conductivity of the pore, κ matrix represents the thermal conductivity of the matrix.

[0023] In a possible implementation, the velocity v of the hole migration is:

[0024]

[0025] Alternatively, the velocity function v of the hole migration is:

[0026]

[0027] Among them, D s represents the diffusion coefficient of the pore surface, Q s represents the heat transfer on the hole surface, a0 represents the lattice constant, k B represents the Boltzmann constant, represents the temperature gradient in the hole, R represents the radius of the hole, and D g represents the diffusion coefficient of the matrix molecules in the gas phase, Ω represents the volume of the solid molecules in the matrix, ΔH vap represents the heat of evaporation, ΔS vap represents the evaporation entropy, x represents the migration direction of the pore, and p represents the pore.

[0028] In one possible implementation, the function of the vacancy concentration evolving over time is:

[0029]

[0030] M v =M0(1+M1[exp(c v )-1])

[0031] in, represents the partial derivative symbol, t represents time, M v represents the mobility of the vacancy, v represents the migration speed, M0 represents the mobility of the vacancy in the matrix, and M1 represents the difference in mobility between the vacancy on the matrix surface and in the matrix.

[0032] In a possible implementation, the kinetic evolution function of the vacancy concentration is:

[0033]

[0034] Wherein, L represents the interface mobility, which is a constant.

[0035] In a possible implementation, obtaining analysis results of pore migration in UO2 nuclear fuel based on the phase field model includes:

[0036] Perform dimensionless processing on each parameter in the phase field model to obtain dimensionless parameters;

[0037] Based on the dimensionless parameters, the total free energy F is obtained;

[0038] Based on the dimensionless parameters and the steady-state heat conduction function of the hole, the temperature change around the hole is obtained;

[0039] Based on the dimensionless parameters and the temperature change around the hole, the migration speed of the hole is obtained;

[0040] Based on the dimensionless parameters, the vacancy concentration c is obtained according to the migration speed of the pores. v The evolution function of

[0041] Based on the dimensionless parameters, the evolution function of the non-conservative field variable η is obtained according to the total free energy F;

[0042] According to the vacancy concentration c v The evolution function of and the evolution function of the non-conservative field variable η are used to perform phase field model evolution calculation to obtain the vacancy concentration c v and the non-conservative field variable η, the analytical results of pore migration in UO2 nuclear fuel are obtained.

[0043] In a possible implementation, dimensionless processing is performed on each parameter in the phase field model, including:

[0044]

[0045] l * =l / l0

[0046]

[0047]

[0048]

[0049] A * =A / k B T

[0050] B * =B / k B T

[0051]

[0052] L * =Lt0k B T

[0053] Among them, t represents time, t0 represents characteristic time, t * represents the dimensionless t, l0 represents the characteristic length, l represents the size of the phase field model, and l * represents the dimensionless l, represents the dimensionless gradient operator, After non-dimensionalization represents the dimensionless κ v , A * Represents dimensionless A, B * represents the dimensionless B, M * represents the dimensionless diffusion coefficient of the pore surface, L * represents the dimensionless L.

[0054] In one possible embodiment, the vacancy concentration c v The evolution function of is:

[0055]

[0056] in, represents the equilibrium vacancy concentration.

[0057] In a possible implementation, the evolution function of the non-conservative field variable η is:

[0058]

[0059] in, represents the dimensionless κ η , h′(η) represents the interpolation function in the evolution equation of the pore phase sequence parameters.

[0060] The present application provides a phase field simulation method for pore migration in UO2 nuclear fuel, by coupling the temperature field T and the concentration field c v As well as the non-conservative order parameter field η, the behaviors such as surface diffusion and vapor transport diffusion in pore migration, as well as the distortion of temperature gradient at the pores due to the difference in thermal conductivity between the pores and the matrix are taken into account, thus achieving accurate prediction of pore diffusion in UO2 fuel, providing technical support for improving the service performance of UO2 fuel, and solving the problem of inaccurate and incomplete description of pore diffusion in the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0062] Figure 1 A flow chart of a phase field simulation method for pore migration in UO2 nuclear fuel provided in an embodiment of the present application.

[0063] Figure 2A schematic structural diagram of a phase field simulation device for pore migration in UO2 nuclear fuel provided in an embodiment of the present application.

[0064] Figure 3 A schematic structural diagram of a phase field simulation device for pore migration in UO2 nuclear fuel provided in an embodiment of the present application.

[0065] Figure 4 A schematic diagram of the temperature field distribution around the hole provided in an embodiment of the present application.

[0066] Figure 5 A schematic diagram of the morphological changes of hole migration when surface diffusion dominates at a small size (<100 nm) provided in an embodiment of the present application.

[0067] Figure 6 Schematic diagram of the migration of small-sized holes of different radii under temperature gradient provided in an embodiment of the present application.

[0068] Figure 7 A schematic diagram of the morphological changes of pore migration when vapor transport dominates at large sizes (>100 nm) provided in an embodiment of the present application.

[0069] Among them, 21-construction module, 22-first acquisition module, 23-third construction module, 24-third acquisition module, 25-analysis module, 31-memory, 32-processor, 33-bus. DETAILED DESCRIPTION

[0070] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0071] Example 1

[0072] like Figure 1 As shown, a phase field simulation method for pore migration in UO2 nuclear fuel includes:

[0073] S11. Constructing free energies of a matrix phase, a pore phase, and an interface containing vacancies, and obtaining a total free energy based on the free energies of the matrix phase, the pore phase, and the interface.

[0074] S12, constructing a steady-state heat conduction function of the hole, and obtaining the temperature distribution in the hole according to the steady-state heat conduction function.

[0075] S13. Obtain the migration speed of the pores according to the temperature distribution in the pores, and obtain the function of the evolution of the vacancy concentration over time according to the migration speed of the pores.

[0076] S14. Obtain the interface mobility, and obtain the kinetic function of the evolution of the pore phase with time based on the function of the total free energy, the vacancy concentration evolving with time and the interface mobility, and complete the construction of the phase field model.

[0077] S15. Based on the phase field model, the analysis results of pore migration in UO2 nuclear fuel are obtained to complete the phase field simulation of pore migration.

[0078] The phase field model contains a matrix phase with vacancies and a pore phase, and the vacancy concentration varies continuously at the interface. The pore model that couples conservative and non-conservative fields is used to describe the evolution of pores in space and time. v To describe the vacancy concentration distribution, a non-conservative field variable η is introduced to describe the distribution of holes. The phase field model constructed in the present invention is a heterogeneous system, and different phases occupy different regions in space. v =1, η = 1 indicates a hole; c v =0, η = 0 represents the matrix; when c v and η vary continuously between 0 and 1, indicating that at the interface between the pore and the matrix, the concentration field and phase field are continuous in space and time, representing the evolution of vacancies and the evolution of the pore microstructure, respectively. The total free energy of the system includes the free energy of the constituent phases and the free energy of the interface, and its form is:

[0079]

[0080] Among them, h(η) represents the interpolation function, f(c v ) represents the intermediate function, V represents the volume, represents the gradient operator, ω(c v ,η) represents the Landau-type polynomial, κ v represents the gradient coefficient of the vacancy, c v represents the vacancy concentration, κ η represents the gradient coefficient of the pore phase. The migration and aggregation of vacancies form pores, η represents the order parameter of the pore phase, represents the integration over the entire phase field model volume, x represents the x direction, and y represents the y direction.

[0081] f(c v ) is given by the contributions of the enthalpy and entropy of the vacancy:

[0082]

[0083] is the formation energy of the vacancy, k B represents the Boltzmann constant, T is the absolute temperature, h(η) is the interpolation function, which can be written as h(η)=(η-1) 2(η+1) 2 In the matrix phase, η = 0, h(η) = 1; in the vacancy phase, η = 1, h(η) = 0; it changes continuously at the interface between the pore and the matrix. The free energy contribution of the pore phase is always 0. is a Landau-type polynomial that maintains the stability of the entire system. represents the equilibrium concentration of vacancies, A represents the potential well height, B is a constant, ln represents the logarithm with the constant e as the base, and exp represents the exponential function with the natural constant e as the base.

[0084] The equation for the evolution of concentration over time is given by the Cahn-Hilliard equation:

[0085]

[0086] Among them, M v is the mobility of the vacancy. For holes dominated by surface diffusion mechanism, to ensure diffusion only along the surface. v Written as M v =M0(1+M1[exp(c v )-1]), M0 represents the mobility of the vacancy in the matrix, and M1 represents the difference in mobility between the vacancy on the pore surface and in the matrix.

[0087] is the advection term, which usually represents the transport of dissolved substances in flowing liquids or gases. Here, it represents the transport of molecules. In this model, it is assumed that there is a temperature gradient only in the direction of pore migration. The migration direction of the pores is opposite to the direction of the temperature gradient, so the negative sign is taken.

[0088] When the size of the hole is small (<100nm), its migration mechanism is mainly surface diffusion and volume diffusion. Considering the migration of holes with different initial radii under temperature gradient, the hole is elongated along the temperature gradient during migration; as the radius increases, the migration speed of the hole becomes slower and slower. The migration rate is positively correlated with the temperature gradient and negatively correlated with the hole radius.

[0089] The migration speed of holes dominated by surface diffusion and bulk diffusion mechanisms can be expressed as:

[0090]

[0091]

[0092] Among them, D s and D vol represent the surface diffusion and volume diffusion coefficients, Q s and Q represent the heat transfer on the hole surface and in the matrix, respectively, k Bis the Boltzmann constant, R is the radius of the hole, a0 is the lattice constant, Represents the temperature gradient in the pore. Since the surface diffusion rate is several orders of magnitude larger than the volume diffusion rate, this application only considers the effect of surface diffusion and ignores volume diffusion.

[0093] When the pore size is large (>100nm), the migration mechanism of the pore is mainly based on the vapor transport mechanism. The pore migrates in the direction opposite to the temperature gradient, and regardless of the initial morphology, the morphology will eventually evolve into a stable morphology during migration. At this time, the migration rate of the pore is independent of the size and surface morphology.

[0094] For macropore migration dominated by vapor transport mechanism, v is the velocity field of vapor transport, and the vapor molecules in the liquid fuel are transported to the inside of the pore and condensed at the other end of the pore. At this time, the vapor transport velocity of UO2 is used to represent the migration rate of the pore:

[0095]

[0096] Among them, ΔS vap and ΔH vap are the evaporation entropy and evaporation heat respectively. g represents the diffusion coefficient of gaseous matrix molecules in the pores, and Ω represents the volume of solid molecules in the matrix.

[0097] The pores often contain fission gases, which have low thermal conductivity and will increase the temperature gradient in the pores, thereby increasing the temperature non-uniformity of the fuel pellets. This temperature non-uniformity has a more significant impact on larger pores, which will change the migration rate of the pores and cause changes in the temperature field around the pores. The present application provides the following steady-state heat conduction equation:

[0098]

[0099] Among them, κ(c v )=(κ pore -κ matrix )c v +κ matrix is the thermal conductivity of the system, expressed as a linear interpolation of the thermal conductivity of the matrix phase and the pore phase, q(1-c v 2 ) represents the heat source term. By solving the heat conduction equation, the temperature distribution in the pore can be obtained, and then the migration speed of the pore can be calculated. When there is fission gas in the pore, considering the difference in thermal conductivity between the pore and the substrate, this treatment method is closer to the actual situation of pore migration.

[0100] In the phase field model, a specific driving force will cause the concentration to deviate from the equilibrium value. In this model, the introduction of the advection term makes the pore phase in the evolution process not 100% vacancies, but vacancies and solid matter advected in the pores. For pore migration dominated by the vapor transport mechanism, the process of solid phase atoms evaporating at the front end of the migration and condensing at the end is not intuitively reflected in the model, but is implicit in the migration process of the pores through the concentration transport to the surface or leaving the surface.

[0101] Therefore, the present application provides the following kinetic evolution equation:

[0102]

[0103] Where L is the interface mobility.

[0104] The simulation of pore migration under temperature gradient is carried out in two-dimensional space. Before solving the model, it is necessary to make the parameters in the model dimensionless. l * =l / l0, A * =A / k B T, B * =B / k B T, L * =

[0105] Lt0 B T. t0 and l0 are characteristic time and characteristic length respectively. Then the equation is solved by the finite difference method of the explicit Euler format as shown below. The present application uses Matlab language programming to solve the above phase field model, and outputs the results for subsequent analysis.

[0106]

[0107]

[0108] The finite difference method is a solution method that uses differences to approximate derivatives. The basic idea is to first divide the domain of the problem into a grid, and then replace the derivatives in the well-defined problem with difference quotients at the grid points according to appropriate numerical differentiation formulas, thereby discretizing the original problem into a difference format and then obtaining a numerical solution.

[0109] For a continuous and relatively smooth arbitrary function f, on a one-dimensional grid with a grid spacing of Δx, this application uses a forward difference method, and the calculation process of the finite difference method is:

[0110]

[0111] For second-order operators we have:

[0112]

[0113] If Δx=Δy, then:

[0114]

[0115] Among them, f i represents the function value of a one-dimensional grid at the i-th grid point in the x or y direction, Δx represents the spacing of the grid along the x direction, and Δy represents the spacing of the grid along the y direction. represents the second-order gradient of the function value at the two-dimensional grid (i, j), δ 2 f / δx 2 (i,j) represents the second-order gradient of the function value along the x direction at the (i, j) grid point, δ 2 f / δy 2 (i,j) represents the second-order gradient of the function value along the y direction at the (i, j) grid point, f i,j Represents the function value of function f at the point (i, j) on the two-dimensional grid.

[0116] like Figure 4 Figure 2 shows the distribution of the temperature field around the hole. Due to the difference in thermal conductivity between the hole and the substrate, the temperature field is distorted around the hole.

[0117] like Figure 5 As shown in the figure, the migration of pores when the surface diffusion is dominant at a small size (<100nm). The pores migrate from the low temperature end to the high temperature end, being elongated along the temperature gradient and compressed in the direction perpendicular to the temperature gradient.

[0118] like Figure 6 As shown in Figure 2, the migration of small-sized holes with different radii under temperature gradient. Under the surface diffusion mechanism, the migration rate gradually decreases with the increase of the hole radius.

[0119] like Figure 7 As shown in Figure 1, the migration of pores when vapor transport dominates at large sizes (>100 nm). The pores migrate in the direction opposite to the temperature gradient, and because the migration rate at the end of the pore is higher than that at the front, the pores are compressed during the migration process.

[0120] The present application provides a phase field simulation method for pore migration in UO2 nuclear fuel, by coupling the temperature field T and the concentration field c vAs well as the non-conservative order parameter field η, the behaviors such as surface diffusion and vapor transport diffusion in pore migration, as well as the distortion of temperature gradient at the pores due to the difference in thermal conductivity between the pores and the matrix are taken into account, thus achieving accurate prediction of pore diffusion in UO2 fuel, providing technical support for improving the service performance of UO2 fuel, and solving the problem of inaccurate and incomplete description of pore diffusion in the existing technology.

[0121] Example 2

[0122] like Figure 2 As shown, a phase field simulation device for pore migration in UO2 nuclear fuel includes a construction module 21, a first acquisition module 22, a second acquisition module 23, a third acquisition module 24 and an analysis module 25.

[0123] The construction module 21 is used to construct the free energy of the matrix phase, the pore phase and the interface containing vacancies, and obtain the total free energy according to the free energy of the matrix phase, the pore phase and the interface;

[0124] The first acquisition module 22 is used to construct a steady-state heat conduction function of the hole, and acquire the temperature distribution in the hole according to the steady-state heat conduction function;

[0125] The second acquisition module 23 is used to acquire the velocity of pore migration according to the temperature distribution in the pores, and acquire the function of the evolution of vacancy concentration over time according to the velocity of pore migration;

[0126] The third acquisition module 24 is used to obtain the interface mobility, and obtain the kinetic function of the evolution of the pore phase with time according to the function of the total free energy, the vacancy concentration and the interface mobility, so as to complete the construction of the phase field model;

[0127] The analysis module 25 is used to obtain the analysis results of the pore migration in the UO2 nuclear fuel based on the phase field model and complete the phase field simulation of the pore migration.

[0128] The phase field simulation device for pore migration in UO2 nuclear fuel provided in this embodiment can implement the technical solution described in Example 1. Its implementation principle and beneficial effects are similar and will not be repeated here.

[0129] Example 3

[0130] like Figure 3 As shown, this embodiment provides a phase field simulation device for pore migration in UO2 nuclear fuel, including a memory 31 and a processor 32, and the memory 31 and the processor 32 are interconnected through a bus 33.

[0131] The memory 31 stores computer-executable instructions.

[0132] The processor 32 executes the computer-executable instructions stored in the memory, so that the processor executes a phase field simulation method for pore migration in UO2 nuclear fuel as described in Example 1.

[0133] For example, the memory may include, but is not limited to, random access memory (RAM), read only memory (ROM), flash memory, first input first output (FIFO) and / or first in last out (FILO), etc. Specifically, the processor may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor may be implemented in at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). At the same time, the processor may also include a main processor and a coprocessor. The main processor is a processor for processing data in the awake state, also known as a CPU (Central Processing Unit); the coprocessor is a low-power processor for processing data in the standby state.

[0134] In some embodiments, the processor may be integrated with a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the display screen. For example, the processor may not be limited to a microprocessor of the STM32F105 series, a reduced instruction set computer (RISC) microprocessor, an X86 architecture processor, or a processor with an integrated embedded neural network processing unit (NPU); the transceiver may be, but is not limited to, a wireless fidelity (WIFI) wireless transceiver, a Bluetooth wireless transceiver, a general packet radio service technology (General Packet Radio Service, GPRS) wireless transceiver, a ZigBee protocol (a low-power LAN protocol based on the IEEE802.15.4 standard, ZigBee) wireless transceiver, a 3G transceiver, a 4G transceiver and / or a 5G transceiver, etc. In addition, the device may also include, but is not limited to, a power module, a display screen, and other necessary components.

[0135] Example 4

[0136] This embodiment provides a computer-readable storage medium, in which computer execution instructions are stored. When the computer execution instructions are executed by a processor, they are used to implement a phase field simulation method for pore migration in UO2 nuclear fuel as described in Example 1.

[0137] Example 5

[0138] The embodiment of the present application may also provide a computer program product, including a computer program, which, when executed by a processor, implements a phase field simulation method for pore migration in UO2 nuclear fuel as described in Example 1.

[0139] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A phase field simulation method for pore migration in UO2 nuclear fuel, characterized in that: include: Constructing free energies of a matrix phase, a pore phase, and an interface containing vacancies, and obtaining a total free energy based on the free energies of the matrix phase, the pore phase, and the interface; Constructing a steady-state heat conduction function of the hole, and obtaining the temperature distribution in the hole according to the steady-state heat conduction function; Obtaining the velocity of hole migration according to the temperature distribution in the hole, and obtaining a function of the evolution of vacancy concentration over time according to the velocity of hole migration; Obtain the interface mobility, and obtain the kinetic function of the time evolution of the pore phase based on the total free energy, the function of the vacancy concentration evolving with time and the interface mobility, and complete the construction of the phase field model; Based on the phase field model, the analysis results of pore migration in UO2 nuclear fuel are obtained, and the phase field simulation of pore migration is completed.

2. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 1, characterized in that: The total free energy F is: h(n)=(n-1) 2 (n+1) 2 Among them, h(η) represents the interpolation function, f(c v ) represents the intermediate function, V represents the volume, ▽ represents the gradient operator, ω(c v ,η) represents the Landau-type polynomial, κ v represents the gradient coefficient of the vacancy, c v represents the vacancy concentration, κ η represents the gradient coefficient of the hole phase, and the migration and aggregation of the vacancies form holes; η represents the non-conservative field variable, represents the integration over the entire phase field model volume, represents the formation energy of the vacancy, k B represents the Boltzmann constant, T represents the absolute temperature, A represents the potential well height, represents the equilibrium vacancy concentration, B represents a constant, ln represents the logarithm with the constant e as the base, and exp represents the exponential function with the natural constant e as the base.

3. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 2, characterized in that: The steady-state heat conduction function of the hole is: k(c v )=(k pore -k matrix )c v +k matrix Among them, κ(c v ) represents thermal conductivity, represents the temperature gradient in the hole, q represents the heat source constant, q(1-c v 2 ) represents the heat source term, κ pore represents the thermal conductivity of the pore, κ matrix represents the thermal conductivity of the matrix.

4. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 3, characterized in that: The velocity v of the hole migration is: Alternatively, the velocity function v of the hole migration is: Among them, D s represents the diffusion coefficient of the pore surface, Q s represents the heat transfer on the hole surface, a0 represents the lattice constant, k B represents the Boltzmann constant, represents the temperature gradient in the hole, R represents the radius of the hole, and D g represents the diffusion coefficient of the matrix molecules in the gas phase, Ω represents the volume of the solid molecules in the matrix, ΔH vap represents the heat of evaporation, ΔS vap represents the evaporation entropy, x represents the pore migration direction, and p represents the pore.

5. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 4, characterized in that: The function of the vacancy concentration evolution over time is: M v =M0(1+M1[exp(c v )-1]) in, represents the partial derivative symbol, t represents time, M v represents the mobility of the vacancy, v represents the migration speed, M0 represents the mobility of the vacancy in the matrix, and M1 represents the difference in mobility between the vacancy on the matrix surface and in the matrix.

6. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 5, characterized in that: The dynamic evolution function of the vacancy concentration is: Wherein, L represents the interface mobility, which is a constant.

7. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 6, characterized in that: Based on the phase field model, the analysis results of pore migration in UO2 nuclear fuel are obtained, including: Perform dimensionless processing on each parameter in the phase field model to obtain dimensionless parameters; Based on the dimensionless parameters, the total free energy F is obtained; Based on the dimensionless parameters and the steady-state heat conduction function of the hole, the temperature change around the hole is obtained; Based on the dimensionless parameters and the temperature change around the hole, the migration speed of the hole is obtained; Based on the dimensionless parameters, the vacancy concentration c is obtained according to the migration speed of the pores. v The evolution function of Based on the dimensionless parameters, the evolution function of the non-conservative field variable η is obtained according to the total free energy F; According to the vacancy concentration c v The evolution function of and the evolution function of the non-conservative field variable η are used to perform phase field model evolution calculation to obtain the vacancy concentration c v and the non-conservative field variable η, the analytical results of pore migration in UO2 nuclear fuel are obtained.

8. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 7, characterized in that: The parameters in the phase field model are dimensionless, including: l * ＝l / l0 A * =A / k B T B * =B / k B T L * =Lt0k B T Among them, t represents time, t0 represents characteristic time, t * represents the dimensionless t, l0 represents the characteristic length, l represents the size of the phase field model, and l * represents the dimensionless l, represents the dimensionless gradient operator, After non-dimensionalization represents the dimensionless κ v , A * Represents dimensionless A, B * represents the dimensionless B, M * represents the dimensionless diffusion coefficient of the pore surface, L * represents the dimensionless L.

9. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 8, characterized in that: Vacancy concentration c v The evolution function of is: in, represents the equilibrium vacancy concentration.

10. The phase field simulation method for pore migration in UO2 nuclear fuel according to claim 9, characterized in that: The evolution function of the non-conservative field variable η is: in, represents the dimensionless κ η , h′(η) represents the interpolation function in the evolution equation of the pore phase sequence parameters.

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