Evolution simulation method and system for uranium dioxide heavy structure behavior

Abstract

The invention discloses an evolution simulation method and system for uranium dioxide heavy structure behaviors, and relates to the technical field of crystal evolution, and the method comprises the following steps: in a current time step, solving a pore-containing polycrystalline system evolution phase field model to obtain a vacancy concentration field variable and a grain orientation sequence parameter of the current time step; correcting the pore migration speed through the temperature distribution of the next time step; correcting grain orientation sequence parameters of the different air holes based on grain orientation and generation positions of columnar crystals generated by the different air holes; iteration is carried out on the next time step based on the corrected pore migration speed and grain orientation sequence parameters; and carrying out visualization processing on the vacancy concentration field variable and the grain orientation sequence parameter after iteration is finished to obtain the morphology evolution process of the pores and the grains in the uranium dioxide heavy structure process. According to the invention, a columnar crystal generation mechanism in a uranium dioxide heavy structure process is reflected, and simulation of an evolution process of generating columnar crystals with different orientations by migration of one or more pores is realized.

Description

Technical Field

[0001] The present invention relates to the field of crystal evolution technology, and in particular to a method and system for simulating the evolution of heavy structure behavior of uranium dioxide. Background Art

[0002] Uranium dioxide (UO2) fuel is typically produced by compacting and sintering ceramic powders. During this process, some encapsulating gas remains within the fuel, forming uniformly distributed small pores ranging in size from a few microns to more than ten microns. These pores account for approximately 5% to 10% of the fuel's total volume. Due to the low thermal conductivity of UO2 fuel, the fuel experiences steep temperature gradients during reactor operation. Experimental results show that under large temperature gradients, initial pores within the fuel migrate to higher-temperature regions, leading to complex changes in the fuel's microstructure. This process is often referred to as fuel restructuring. Pore migration is essentially an evaporation-condensation process: the UO2 matrix evaporates at the high-temperature side of the pores, passes through the pores, and condenses at the low-temperature side, tending to form a single crystal structure. Because the grains generated by pore migration differ from the original grains in orientation, they mismatch with the surrounding grains and form columnar crystals. This fuel restructuring behavior leads to significant changes in the microstructure, which in turn affects fuel performance. Therefore, in-depth research on the microstructural evolution during UO2 fuel restructuring is necessary.

[0003] Phase-field models can effectively track and describe the evolution of pore and grain boundaries and are widely used in fuel microstructure simulations. However, existing phase-field models either only consider interactions between pores and grain boundaries, failing to capture the mechanism of columnar crystal formation during uranium dioxide restructuration. Alternatively, they fail to distinguish between multiple pores, making it impossible to simulate the migration of one or more pores to form columnar crystals, and thus unable to demonstrate the evolution of columnar regions during restructuration. Summary of the Invention

[0004] Based on the above-mentioned defects in the prior art, the present invention provides a method and system for simulating the evolution of the heavy structure behavior of uranium dioxide, which solves the existing problems.

[0005] The present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for simulating the evolution of heavy structure behavior of uranium dioxide, comprising the following steps:

[0007] Setting multiple time steps, and solving the evolutionary phase field model of the porous polycrystalline system used to describe the heavy structural behavior of uranium dioxide within the current time step to obtain the vacancy concentration field variables and grain orientation order parameters of the current time step; wherein, a free energy expression of the porous polycrystalline system is constructed based on the vacancy concentration field variables and the grain orientation order parameters, and the pore migration velocity is introduced into the free energy expression to obtain the evolutionary phase field model of the porous polycrystalline system;

[0008] The vacancy concentration field variable of the current time step is input into the two-dimensional steady-state heat transfer equation to obtain the temperature distribution of the next time step, and the pore migration velocity is corrected by the temperature distribution of the next time step;

[0009] A two-dimensional image matrix for describing the pores and the uranium dioxide matrix is ​​obtained based on the vacancy concentration field variables of the current time step; the two-dimensional image matrix is ​​divided into connected regions and marked to obtain a marking matrix of different pores; the position coordinates and size information of the different pores are obtained based on the marking matrix of different pores; the orientation and generation position of the columnar crystals generated by the different pores are obtained based on the position coordinates and size information of the different pores, and the grain orientation order parameters of the different pores are corrected based on the orientation and generation position of the columnar crystals generated by the different pores;

[0010] The phase field model of the polycrystalline system with pores at the next time step is solved based on the corrected pore migration velocity and grain orientation order parameter, and the correction process of the pore migration velocity and grain orientation order parameter is iterated based on the solution until the entire iteration is completed;

[0011] The vacancy concentration field variables and grain orientation order parameters after the iteration are visualized to obtain the morphological evolution of pores and grains during the uranium dioxide restructure process.

[0012] Preferably, the free energy expression is specifically as follows:

[0013]

[0014] Where F is free energy, f(c v ,η i ) is the local free energy density function, c v is the vacancy concentration field variable, η i is the grain orientation order parameter, dΩ is the volume element, is the gradient operator, and κ η is the gradient energy coefficient.

[0015] Preferably, the phase field model of the evolution of the pore-containing polycrystalline system is specifically as follows:

[0016]

[0017] Where, v p is the stomatal migration velocity, M v is the vacancy mobility, t is the time, and L is the grain boundary mobility.

[0018] Preferably, the two-dimensional steady-state heat transfer equation is specifically as follows:

[0019]

[0020] Where T is temperature, q is the heat source constant, k(c v ) is the thermal conductivity of the system, c v is the vacancy concentration field variable, is the gradient operator.

[0021] Preferably, the pore migration velocity is corrected by the temperature distribution of the next time step, as shown below:

[0022]

[0023] Where a1, a2, a3, a4 and a5 are constants, ΔH is the enthalpy of vaporization, p0 is the pressure prefactor related to pressure and pressure gradient, R is the gas constant, r is the spatial position, and m is the uranium dioxide matrix.

[0024] Preferably, the obtaining of position coordinates and size information of different pores based on the marker matrix of different pores comprises the following steps:

[0025] The stomatal position coordinates are represented by the stomatal centroid coordinates and are calculated using the following formula:

[0026]

[0027] Where x center The x-axis coordinate of the center of mass of the pore, y center Indicates the y-axis coordinate of the centroid of the pore, P tot Indicates the total number of grid points of the pore, m k , n k Represent the x-axis coordinate and y-axis coordinate of the grid point k respectively;

[0028] The size information is the major axis length. According to the marking matrix of the pore and the coordinates of the center of mass of the pore, the coordinate point farthest from the center of mass is selected, and twice the distance between the coordinate point and the center of mass is taken as the major axis length of the pore.

[0029] Preferably, obtaining the grain orientation and generation position of columnar crystals generated by different pores based on the position coordinates and size information of different pores comprises the following steps:

[0030] Obtain the sum of the vacancy concentration field variable and the grain orientation order parameter at the current time step in the simulation area, and determine whether the sum is less than the set threshold;

[0031] If the sum is less than the set threshold, the generation position of the columnar crystal corresponding to the pore is obtained based on the position coordinates and size information of different pores in the simulation area;

[0032] The different pores are recalibrated according to their position coordinates to obtain the grain orientations of columnar crystals generated by different pores in the simulation area.

[0033] In a second aspect, the present invention provides a system for simulating the evolution of heavy structure behavior of uranium dioxide, comprising:

[0034] A setting module is used to set multiple time steps and solve the evolution phase field model of the porous polycrystalline system used to describe the heavy structural behavior of uranium dioxide in the current time step to obtain the vacancy concentration field variables and grain orientation order parameters of the current time step; wherein, a free energy expression of the porous polycrystalline system is constructed based on the vacancy concentration field variables and the grain orientation order parameters, and the pore migration velocity is introduced into the free energy expression to obtain the evolution phase field model of the porous polycrystalline system;

[0035] The first correction module is used to input the vacancy concentration field variable of the current time step into the two-dimensional steady-state heat transfer equation to obtain the temperature distribution of the next time step, and correct the pore migration velocity according to the temperature distribution of the next time step;

[0036] The second correction module is used to obtain a two-dimensional image matrix for describing the pores and the uranium dioxide matrix based on the vacancy concentration field variable of the current time step; divide the two-dimensional image matrix into connected areas and mark them to obtain a marking matrix of different pores; obtain the position coordinates and size information of the different pores based on the marking matrix of different pores; obtain the orientation and generation position of the columnar crystal grains generated by the different pores based on the position coordinates and size information of the different pores, and correct the grain orientation order parameters of the different pores based on the orientation and generation position of the columnar crystal grains generated by the different pores;

[0037] An iterative module is used to solve the evolution phase field model of the pore-containing polycrystalline system at the next time step based on the corrected pore migration velocity and grain orientation order parameter, and iterate the correction process of the pore migration velocity and grain orientation order parameter based on the solution results until the entire iteration is completed;

[0038] The evolution module is used to visualize the vacancy concentration field variables and grain orientation order parameters after the iteration, and obtain the morphological evolution process of pores and grains during the restructuring process of uranium dioxide.

[0039] Compared with the prior art, the at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0040] The present invention first proposes an evolutionary phase field model of a pore-containing polycrystalline system including phase field variables for describing the interaction between pores and grains, and simultaneously constructs an image recognition algorithm including phase field variables. Specifically, a two-dimensional image matrix for describing the pores and the uranium dioxide matrix is ​​obtained based on the vacancy concentration field variables of the current time step; the two-dimensional image matrix is ​​divided into connected areas and marked to obtain a marking matrix of different pores; the position coordinates and size information of the different pores are obtained based on the marking matrix of different pores; the grain orientation and generation position of columnar crystals generated by the different pores are obtained based on the position coordinates and size information of the different pores, and multiple pores are distinguished, thereby reflecting the columnar crystal generation mechanism during the uranium dioxide restructuration process, and realizing the simulation of the evolutionary process of one or more pores migrating to generate columnar crystals with different orientations. Finally, the grain orientation order parameters of the different pores are modified based on the orientation and location of the columnar crystals generated by the pores. The pore migration velocity is also modified based on the temperature distribution at the next time step. The phase-field model of the evolution of the pore-containing polycrystalline system at the next time step is solved based on the modified pore migration velocity and grain orientation order parameter. The final iterative results determine the microstructural evolution process of the restructuration behavior of uranium dioxide fuel.

[0041] The phase-field model of the evolution of polycrystalline systems containing pores proposed in the present invention combines image recognition methods, solving the problem that traditional phase-field models cannot distinguish and calculate multiple pores. A columnar crystal generation method based on image recognition technology combined with phase-field models is proposed, which fills the defect that the current phase-field method cannot simulate the evolution process of pore migration to generate columnar crystals during the restructuring process. It shows the pore and grain morphology during the restructuring process of uranium dioxide fuel, and provides guidance for the performance analysis and prediction of uranium dioxide fuel in piles. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 A flowchart of a method for simulating the evolution of heavy structure behavior of uranium dioxide according to the present invention;

[0044] Figure 2 Schematic diagram of the image recognition algorithm containing phase field variables of the present invention;

[0045] Figure 3A diagram showing simulation results of generating columnar crystals by migration of multiple pores according to the present invention;

[0046] in, Figure 3 (a): initial microstructure morphology, Figure 3 (b): Microstructure morphology after 20,000 time steps of evolution;

[0047] Figure 4 The grain orientation field order parameter of the present invention is Figure 3 The distribution diagram on the horizontal central axis of the simulation area shown;

[0048] Figure 5 This is the pore calibration result diagram of the image segmentation module 2 in the image recognition algorithm of the present invention;

[0049] Figure 6 Graph showing the simulation results of the evolution of columnar grains during the restructure process of the present invention;

[0050] Figure 6 (a): initial microstructure morphology, Figure 6 (b): Microstructure morphology after 20,000 time steps of evolution;

[0051] Figure 7 This is a graph showing the change in the area of ​​columnar grains generated by different pores over time during the restructure process of the present invention;

[0052] Figure 8 It is an iterative flow chart of the evolution simulation method of the heavy structure behavior of uranium dioxide of the present invention. DETAILED DESCRIPTION

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0054] The present invention discloses an evolutionary simulation method for the heavy structural behavior of uranium dioxide based on a combination of image recognition and phase field methods. An evolutionary phase field model that can describe a polycrystalline system containing pores and the interaction between pores and grains is constructed. An image recognition algorithm containing phase field variables is constructed to distinguish multiple pores, thereby simulating the evolutionary process of one or more pores migrating to generate columnar crystals with different orientations, and ultimately determining the microstructural evolution process of the heavy structural behavior of uranium dioxide fuel. In the phase field model, gas and solid phases coexist, and it is necessary to establish a free energy expression that can describe the interaction between pores and grains. Establishing a heavy structural phase field model involves the problem of pore migration, and it is necessary to establish a connection between the pore migration speed and the actual temperature field.

[0055] Based on the existing experimental results and low-scale simulation results, the physical properties of uranium dioxide materials under different working conditions are calculated, and the free energy expression of the pore-containing polycrystalline system describing the interaction between pores and grains is constructed; considering the migration behavior of pores, the phase field equation is constructed to obtain the evolution phase field model of the pore-containing polycrystalline system; the phase field model is dimensionlessly processed and differentially processed; a steady-state heat transfer equation containing phase field variables is constructed to obtain the pore migration velocity, and based on the image recognition principle, an image recognition algorithm containing phase field variables is constructed; the phase field equation is calculated, and the temperature distribution of the next time step is calculated based on the steady-state heat transfer equation, and the pore migration velocity is corrected. Based on the grain orientation order parameter and the image recognition algorithm, the pore calibration information, position, and size are obtained, and then the columnar crystal grain orientation and generation position are obtained, the grain orientation order parameter of the next time step is corrected, and the iteration is run to the specified evolution time; the phase field variables are output to obtain the microstructure evolution process, display the pore and grain morphology, and explore the law of heavy structure evolution.

[0056] A method for simulating the evolution of heavy structural behavior of uranium dioxide based on the combination of image recognition and phase field, referring to Figure 1 and Figure 8 , including the following steps:

[0057] S1: Obtain the required material properties based on experimental results and low-scale simulation results; define the phase field variables in the phase field model, including the vacancy concentration field variables used to describe the pore phase and the grain orientation order parameters used to describe the grain structure. Considering the coexistence and interaction between pores and grains, the phase field variables are used for coupling to construct the polynomial system free energy of the pore-containing polycrystalline system.

[0058] Uranium dioxide fuel physical properties include: Uranium dioxide vacancy migration energy Thermal conductivity k of uranium dioxide matrix matrix and pore thermal conductivity k pore ,in, Used to calculate the diffusion coefficient D,k matrix and k pore Used to calculate the system thermal conductivity k(c v ).

[0059] Considering the coexistence and interaction of pores and grains, the phase field variables describing the microstructural evolution of uranium dioxide heavy structure are selected, and the vacancy concentration field variable c is selected. v Used to describe the stomatal phase. When located inside the pore, c v =1.0, when located outside the pore c v = 0, and changes continuously from 0 to 1 at the interface between the pore and the uranium dioxide matrix. Select the grain orientation order parameters (η1, η2, ..., η N) is used to describe and distinguish grain structures with different orientations, where subscripts 1, 2, 3, …, N are identifiers of different grain orientations, (η1, η2, …, η N ) represents N grains with different orientations. In a grain with grain orientation i, η i =1.0, in grains with other orientations η i = 0, on the grain boundary with the surrounding grains or on the interface with the pores, η i It varies continuously from 0 to 1. Therefore, inside the grain with grain orientation i, there is η i =1.0,c v =0,η j =0, j≠i; η in pores i =0,c v =1.0, i=1,2,3,…,N, η at the interface i and c v Continuously changes from 0 to 1.

[0060] Considering the coexistence and interaction between pores and grains, the phase field variables are coupled to construct the polynomial system free energy expression of the polycrystalline system containing pore phase as follows:

[0061]

[0062] In the formula, the first term f(c v ,η i ) is the local free energy density function; v represents the integration area, i.e. the simulation area, dV is the volume element, is the gradient operator; the second and third terms are the gradient energies; and κ η is the gradient energy coefficient, in J / m. Local free energy f(c v ,η i ) is:

[0063]

[0064] Here, A1, A2, and A3 are physical parameters related to the energy and width of the material's pore surfaces and grain boundaries, calculated based on low-scale simulations. The first term in the expression is a double-well function, which reaches its minimum inside the grains and pores; the second term in parentheses is a multi-well function, which reaches its minimum inside the corresponding grains; and the last term is the interaction term between the pores and grains. This form of the expression ensures that the minimum is achieved inside each grain and pore.

[0065] S2: Based on the system free energy constructed in S1 (Equation 1), the migration behavior of pores is considered and the migration velocity term is introduced to establish the conservative Cahn-Hilliard equation for the evolution of phase field variables (Equation 3). The Allen-Cahn equation for the evolution of grain orientation field is used to describe the interaction between grains and pores, resulting in a phase field model for the evolution of polycrystalline systems containing pores.

[0066] Considering the interaction between pores and grains, a phase field model of the polycrystalline system containing pores is constructed, and a conservative phase field variable evolution Cahn-Hilliard equation is established to describe the evolution of the pore phase. Considering the pore migration behavior, the migration velocity term is introduced. The specific expression is as follows:

[0067]

[0068] Where, v p is the migration speed of stomata, M v is the vacancy mobility, which is calculated by the following formula:

[0069]

[0070] Where k B is the Boltzmann constant, T is the temperature, and D is the diffusion coefficient. Its expression is:

[0071]

[0072] Where, is the migration energy of vacancies in UO2, and D0 is the pre-factor of the vacancy diffusion coefficient.

[0073] Non-conserved phase field variable η i The dynamic equation is represented by the Allen-Cahn equation, which is used to describe the interaction between grains and pores. The specific expression is as follows:

[0074]

[0075] Where L is the grain boundary mobility.

[0076] S3: The evolution phase field model of the porous polycrystalline system constructed in step S2 is dimensionlessly processed to obtain a set of phase field equations; the phase field equations are processed by finite difference in time and space: in space, the forward difference format is used; in time, the forward Euler time stepping method is used.

[0077] The parameters in the model are dimensionless: the simulation grid spacing is Δx = l / l * , the simulation time step is τ = t / t * , the dimensionless form of the diffusion coefficient is where l * and t* are the characteristic length and characteristic time respectively. The specific expressions of the phase field equations after dimensionless processing are as follows:

[0078]

[0079] Where, is the vacancy mobility M v The dimensionless processing result of is the stomatal migration velocity v P The dimensionless processing result of is the dimensionless processing result of the grain boundary mobility L.

[0080] is the dimensionless gradient operator. The explicit finite difference method combined with the forward Euler time stepping method is used to solve the problem.

[0081] Finite difference treatment of the phase field equations in time and space: The finite difference method (FDM) is a numerical method commonly used to solve partial differential equations. The basic idea of ​​this method is to discretize the spatial and temporal regions and use the values ​​of adjacent grid points to approximate the derivatives, thereby achieving a numerical solution to the equations. For any continuous and smooth function f, the gradient operator is calculated using first-order central differences on a one-dimensional grid with grid spacing Δx, Δy. The specific expression is:

[0082]

[0083] Among them, f i Represents the function value of the grid at point i in the x-direction or y-direction.

[0084] The second-order central difference is used to calculate the Laplace operator in the phase field method. For a two-dimensional function f, the specific expression of the Laplace operator difference at point (i, j) is:

[0085]

[0086] Where f(i,j) represents the function value at the grid (i,j).

[0087] S4: Construct a two-dimensional steady-state heat transfer equation containing phase field variables (Equation 12). Based on the heat transfer equation, obtain the temperature distribution of the polycrystalline system containing pores. Based on the temperature distribution, obtain the pore migration velocity distribution (Equation 11). Based on the principle of image recognition, construct an image recognition algorithm containing phase field variables.

[0088] S41: The initial pore size in uranium dioxide fuel is controlled by the vapor transport mechanism and migrates to the high-temperature region. The specific expression of the pore migration speed is:

[0089]

[0090] Where, J A is the UO2 molecular flux, Ω is the volume of the UO2 molecule, a1~a5 are constants, ΔH is the evaporation enthalpy, and p0 is the pressure prefactor related to pressure and pressure gradient.

[0091] In order to comprehensively consider the influence of pore thermal conductivity, the following two-dimensional steady-state heat transfer equation is constructed in combination with the phase field method:

[0092]

[0093] Where q is the heat source constant, k(c v ) is the thermal conductivity of the system, which is expressed as an interpolation function of the thermal conductivity of the uranium dioxide matrix and the thermal conductivity of the pores. The specific expression is:

[0094] k(c v )=(k pore -k matrix )c v +k matrix (13);

[0095] Where k pore and k matrix are the thermal conductivity of He in the pores and the thermal conductivity of the UO2 matrix, respectively. By solving the heat transfer equation, the temperature distribution of the polycrystalline system containing pores can be obtained, and then the pore migration velocity distribution can be calculated.

[0096] S42: During the restructure process, columnar crystals are generated by pore migration, and the uranium dioxide matrix deposited on the low-temperature side of the pore is a newly oriented single crystal structure. For systems with multiple migrating pores, an image recognition algorithm with phase field variables is constructed to calibrate the pores and obtain the pore position and size. The specific structure of the algorithm Figure 2 , including an image preprocessing module 1, an image segmentation module 2, a feature extraction module 3, a grain orientation acquisition module 4 and a columnar crystal generation module 5.

[0097] The image preprocessing module 1 is used to calculate the vacancy concentration field variable based on the phase field equation of the current time step. The vacancy concentration field variable is a two-dimensional array with values ​​ranging from 0 to 1; a threshold value of the vacancy concentration field variable is set, and the two-dimensional array is processed according to the threshold value. If the value is greater than the threshold value, it is set to 1, and if the value is less than the threshold value, it is set to 0, to obtain a two-dimensional image matrix describing the pores and the uranium dioxide matrix.

[0098] The image segmentation module 2 is used to divide the connected domains and mark them based on the depth-first search (DFS) algorithm according to the two-dimensional image matrix obtained by the image preprocessing module 1, and then obtain the labeling matrix of different pores.

[0099] The feature extraction module 3 is used to calculate the properties of different pores based on the pore marker matrix obtained by the image segmentation module 2, and obtain the position coordinates and size information of different pores. The pore position coordinates are represented by the pore centroid position and are calculated using the following formula:

[0100]

[0101] Where x center The x-axis coordinate of the centroid of the stomata; y center represents the y-axis coordinate of the centroid of the stoma; P tot Indicates the total number of grid points of the pore; m k , n k The x-axis coordinate and y-axis coordinate of grid point k are respectively represented. The long axis size of the stomata is obtained based on the labeling result of the stomata obtained by the image segmentation module 2 and the coordinates of the center of mass of the stomata. The coordinate point farthest from the center of mass is selected, and twice the distance between the coordinate point and the center of mass is used as the long axis length of the stomata.

[0102] The grain orientation acquisition module 4 is used to re-mark the pores according to the pore position coordinates obtained by the feature extraction module 3. For m pores, they are marked as 1, 2,..., m from front to back according to the pore migration direction. According to the pore marking, the columnar crystal grain orientations generated by different pores are N+1, N+2,..., N+m respectively.

[0103] The columnar crystal generation module 5 is used to determine whether columnar crystals have been generated based on the vacancy concentration field variables and grain orientation field order parameters calculated by the phase field equation at the current time step. The judgment is based on the sum of the vacancy concentration field variables and grain orientation field order parameters in a certain area of ​​the array being less than 0.01. Based on the pore properties obtained by the feature extraction module 3, the columnar crystal generation position is constrained to ensure that the generation process is not affected by other areas. Based on the columnar crystal grain orientation obtained by the grain orientation acquisition module 4, the corresponding grain orientation order parameters are assigned to the columnar crystals generated by different pores, thereby obtaining the grain orientation order parameters after reconstruction.

[0104] S5: Coupled solution of morphology evolution and physical field evolution, where the calculation of pore migration velocity needs to be based on the two-dimensional steady-state heat transfer equation constructed in step S4, first solve the temperature distribution of the next time step, and obtain the pore migration velocity distribution of the next time step based on the temperature distribution of the next time step; the calculation of grain morphology evolution needs to be based on the image recognition algorithm containing phase field variables constructed in step S4, calibrate different pores, and obtain the position coordinates and sizes of different pores, obtain the orientation and generation position of columnar crystals based on the pore calibration, position and size and the grain orientation order parameter of the current time step, correct the grain orientation order parameter of the current time step based on the orientation and position of the columnar crystal grains, and iterate the phase field equation calculation for the next time step until the specified evolution time is reached.

[0105] Initial conditions and boundary conditions are set based on the evolution phase field model of the pore-containing polycrystalline system constructed in step S2 and the differential format constructed in step S3; the phase field model is calculated, and the pore migration velocity is corrected based on the heat transfer equation in step S4; the grain orientation order parameter is corrected based on the image recognition algorithm in step S4; and iteration is performed until the specified time is reached.

[0106] S51: In the current time step, based on the results of the previous time step, the phase field equation is calculated to obtain the spatial distribution of the phase field variables. The boundary conditions use the periodic boundary under the virtual grid method.

[0107] S52: According to the spatial distribution of the phase field variables obtained in S51 and the two-dimensional steady-state heat transfer equation constructed in S42, the temperature distribution result of the next time step is obtained, and according to the temperature distribution and the pore migration velocity calculation model in S41, the spatial distribution of the pore migration velocity is corrected.

[0108] S53: According to the spatial distribution of the phase field variables obtained in S52 and the image recognition algorithm constructed in S42, the spatial distribution of the grain orientation order parameter in the current time step is corrected, and according to the spatial distribution of the grain orientation order parameter and the pore migration velocity distribution obtained in S52, the phase field equation is calculated to obtain the spatial distribution of the phase field variables in the next time step.

[0109] S6: According to the calculation method of step S5, the precise values ​​of the phase field variables are output and the output results are visualized; based on the visualized microstructure, the evolution of the pores and grain morphology during the restructuring process of the uranium dioxide fuel is observed, and the evolution law of the restructuring process is explored.

[0110] S61: Output CSV files of vacancy concentration field variables and grain orientation order parameters;

[0111] S62: According to the csv file in S61, obtain the spatial distribution image of the vacancy concentration field variable and the grain orientation order parameter;

[0112] S63: Based on the visualized microstructure, observe the morphological evolution of pores and grains during the restructuring process and analyze the evolution law of the restructuring process.

[0113] like Figure 3 As shown in the figure, a single pore migrates to generate columnar crystals. These are the initial microstructure morphology and the microstructure morphology after 20,000 time steps of evolution. The red area represents the pores and the blue area represents the grains. The grain orientation of the columnar crystals generated by pore migration is different from that of the grains in the matrix. The pores located behind the migration direction will re-evaporate and condense the columnar crystals in front.

[0114] like Figure 4 As shown in Figure 3, after 20000τ evolution, the grain orientation order parameter distribution on the central axis in the x direction shows that the columnar crystals generated by different pore migration have different grain orientations.

[0115] like Figure 5 As shown in Figure 1, the image segmentation and feature extraction results of multiple pores. The values ​​of the label array inside different pores are different, and the value outside the pores is 0.

[0116] like Figure 6 As shown in the figure, the morphological evolution process of columnar crystals generated by the migration of multiple pores is shown, which are the initial microstructure morphology and the microstructure morphology after 20,000 time steps of evolution. The red area represents the pores, the blue area represents the grains, and the pores are marked as pore 1, pore 2, pore 3, and pore 4 according to the direction of migration speed. Different pores generate columnar crystals with different orientations.

[0117] like Figure 7 As shown in the figure, the columnar crystal size changes with time. The columnar crystals generated by the four pores have different grain orientations. The columnar crystal size is related to the pore size and pore migration speed.

[0118] This paper constructs a phase-field model to describe the heavy structural behavior of uranium dioxide. By combining this model with image recognition methods to determine the location and size of nuclear fuel pores, this method simulates the evolution of columnar crystals and demonstrates the morphological evolution of grains and pores during the heavy structural process. This overcomes the inability of phase-field models to distinguish between multiple pores and extract distinct pore characteristics, enabling accurate simulation of the microstructure of uranium dioxide's heavy structural behavior and promising applications in nuclear fuel performance analysis and prediction.

[0119] Based on the same concept, the present invention also provides an evolution simulation system for the heavy structure behavior of uranium dioxide, including a setting module, a first correction module, a second correction module, an iteration module and an evolution module.

[0120] The setting module is used to set multiple time steps, and within the current time step, solve the evolutionary phase field model of the porous polycrystalline system used to describe the heavy structure behavior of uranium dioxide to obtain the vacancy concentration field variables and grain orientation order parameters of the current time step; among them, the free energy expression of the porous polycrystalline system is constructed based on the vacancy concentration field variables and grain orientation order parameters, and the pore migration velocity is introduced into the free energy expression to obtain the evolutionary phase field model of the porous polycrystalline system.

[0121] The first correction module is used to input the vacancy concentration field variable of the current time step into the two-dimensional steady-state heat transfer equation to obtain the temperature distribution of the next time step, and to correct the pore migration velocity according to the temperature distribution of the next time step.

[0122] The second correction module is used to obtain a two-dimensional image matrix for describing the pores and the uranium dioxide matrix based on the vacancy concentration field variables of the current time step; divide the two-dimensional image matrix into connected areas and mark them to obtain a marking matrix of different pores; obtain the position coordinates and size information of different pores based on the marking matrix of different pores; obtain the grain orientation and generation position of the columnar crystals generated by the different pores based on the position coordinates and size information of the different pores, and correct the grain orientation order parameters of the different pores based on the grain orientation and generation position of the columnar crystals generated by the different pores.

[0123] The iterative module is used to solve the evolution phase field model of the pore-containing polycrystalline system in the next time step based on the corrected pore migration velocity and grain orientation order parameter, and iterate the correction process of the pore migration velocity and grain orientation order parameter based on the solution results until the entire iteration is completed.

[0124] The evolution module is used to visualize the vacancy concentration field variables and grain orientation order parameters after the iteration, and obtain the morphological evolution process of pores and grains during the uranium dioxide restructure process.

[0125] The present invention is a simulation method with a rigorous structure, a clear implementation process and a wide range of applications. The invention can provide theoretical and technical support for the uranium dioxide fuel restructuring process, and can determine the microstructural evolution and the morphology of pores and grains in the uranium dioxide fuel restructuring process under different working conditions.

[0126] Compared with the existing technology, the phase-field model of the evolution of pore-containing polycrystalline systems proposed in the present invention combines image recognition methods, creates an image recognition algorithm combined with phase-field methods, and solves the problem that traditional phase-field models cannot distinguish and calculate multiple pores; a columnar crystal generation method based on image recognition technology combined with phase-field models is proposed, which fills the defect that the current phase-field method cannot simulate the evolution process of pore migration to generate columnar crystals during the restructuring process, and shows the pore and grain morphology during the restructuring process of uranium dioxide fuel, providing guidance for the performance analysis and prediction of uranium dioxide fuel in piles.

[0127] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0128] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations fall within the scope of the claims and their equivalents, the present invention is intended to include such modifications and variations.

Claims

1. A method for simulating the evolution of heavy structure behavior of uranium dioxide, characterized in that: The following steps are involved: Setting multiple time steps, and solving the evolutionary phase field model of the porous polycrystalline system used to describe the heavy structural behavior of uranium dioxide within the current time step to obtain the vacancy concentration field variables and grain orientation order parameters of the current time step; wherein, a free energy expression of the porous polycrystalline system is constructed based on the vacancy concentration field variables and the grain orientation order parameters, and the pore migration velocity is introduced into the free energy expression to obtain the evolutionary phase field model of the porous polycrystalline system; The vacancy concentration field variable of the current time step is input into the two-dimensional steady-state heat transfer equation to obtain the temperature distribution of the next time step, and the pore migration velocity is corrected by the temperature distribution of the next time step; A two-dimensional image matrix for describing the pores and the uranium dioxide matrix is ​​obtained based on the vacancy concentration field variables of the current time step; the two-dimensional image matrix is ​​divided into connected regions and marked to obtain a marking matrix of different pores; the position coordinates and size information of the different pores are obtained based on the marking matrix of different pores; the orientation and generation position of the columnar crystals generated by the different pores are obtained based on the position coordinates and size information of the different pores, and the grain orientation order parameters of the different pores are corrected based on the orientation and generation position of the columnar crystals generated by the different pores; The phase field model of the polycrystalline system with pores at the next time step is solved based on the corrected pore migration velocity and grain orientation order parameter, and the correction process of the pore migration velocity and grain orientation order parameter is iterated based on the solution until the entire iteration is completed; The vacancy concentration field variables and grain orientation order parameters after the iteration are visualized to obtain the morphological evolution of pores and grains during the uranium dioxide restructure process.

2. The method for simulating the evolution of the heavy structure behavior of uranium dioxide according to claim 1, wherein: The free energy expression is specifically as follows: Where F is free energy, f(c v ,η i ) is the local free energy density function, c v is the vacancy concentration field variable, η i is the grain orientation order parameter, dΩ is the volume element, is the gradient operator, and κ η is the gradient energy coefficient.

3. The method for simulating the evolution of heavy structural behavior of uranium dioxide according to claim 2, wherein the phase field model of the evolution of the porous polycrystalline system is specifically as follows: Where, v p is the stomatal migration velocity, M v is the vacancy mobility, t is the time, and L is the grain boundary mobility.

4. The method for simulating the evolution of heavy structure behavior of uranium dioxide according to claim 1, wherein: The two-dimensional steady-state heat transfer equation is specifically as follows: Where T is temperature, q is the heat source constant, k(c v ) is the thermal conductivity of the system, c v is the vacancy concentration field variable, is the gradient operator.

5. The method for simulating the evolution of heavy structure behavior of uranium dioxide according to claim 4, characterized in that: The pore migration velocity is corrected by the temperature distribution of the next time step, as shown below: Where a1, a2, a3, a4 and a5 are constants, ΔH is the enthalpy of vaporization, p0 is the pressure prefactor related to pressure and pressure gradient, R is the gas constant, r is the spatial position, and m is the uranium dioxide matrix.

6. The method for simulating the evolution of heavy structure behavior of uranium dioxide according to claim 1, wherein: The method of obtaining the position coordinates and size information of different pores based on the marker matrix of different pores includes the following steps: The stomatal position coordinates are represented by the stomatal centroid coordinates and are calculated using the following formula: Where x center The x-axis coordinate of the center of mass of the pore, y center Indicates the y-axis coordinate of the centroid of the pore, P tot Indicates the total number of grid points of the pore, m k , n k Represent the x-axis coordinate and y-axis coordinate of the grid point k respectively; The size information is the major axis length. According to the marking matrix of the pore and the coordinates of the center of mass of the pore, the coordinate point farthest from the center of mass is selected, and twice the distance between the coordinate point and the center of mass is taken as the major axis length of the pore.

7. The method for simulating the evolution of heavy structure behavior of uranium dioxide according to claim 1, wherein: The method of obtaining the grain orientation and generation position of columnar crystals generated by different pores based on the position coordinates and size information of different pores includes the following steps: Obtain the sum of the vacancy concentration field variable and the grain orientation order parameter at the current time step in the simulation area, and determine whether the sum is less than the set threshold; If the sum is less than the set threshold, the generation position of the columnar crystal corresponding to the pore is obtained based on the position coordinates and size information of different pores in the simulation area; The different pores are recalibrated according to their position coordinates to obtain the grain orientations of columnar crystals generated by different pores in the simulation area.

8. A system for simulating the evolution of heavy structural behavior of uranium dioxide, characterized in that: include: A setting module is used to set multiple time steps and solve the evolution phase field model of the porous polycrystalline system used to describe the heavy structural behavior of uranium dioxide in the current time step to obtain the vacancy concentration field variables and grain orientation order parameters of the current time step; wherein, a free energy expression of the porous polycrystalline system is constructed based on the vacancy concentration field variables and the grain orientation order parameters, and the pore migration velocity is introduced into the free energy expression to obtain the evolution phase field model of the porous polycrystalline system; The first correction module is used to input the vacancy concentration field variable of the current time step into the two-dimensional steady-state heat transfer equation to obtain the temperature distribution of the next time step, and correct the pore migration velocity according to the temperature distribution of the next time step; The second correction module is used to obtain a two-dimensional image matrix for describing the pores and the uranium dioxide matrix based on the vacancy concentration field variable of the current time step; divide the two-dimensional image matrix into connected areas and mark them to obtain a marking matrix of different pores; obtain the position coordinates and size information of the different pores based on the marking matrix of different pores; obtain the orientation and generation position of the columnar crystal grains generated by the different pores based on the position coordinates and size information of the different pores, and correct the grain orientation order parameters of the different pores based on the orientation and generation position of the columnar crystal grains generated by the different pores; An iterative module is used to solve the evolution phase field model of the pore-containing polycrystalline system at the next time step based on the corrected pore migration velocity and grain orientation order parameter, and iterate the correction process of the pore migration velocity and grain orientation order parameter based on the solution results until the entire iteration is completed; The evolution module is used to visualize the vacancy concentration field variables and grain orientation order parameters after the iteration, and obtain the morphological evolution process of pores and grains during the restructuring process of uranium dioxide.

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