Finite element prediction method of template method dispersion fuel pellet temperature field

Abstract

The invention relates to a finite element prediction method for a temperature field of a dispersion fuel pellet by a template method, which comprises the following steps of: establishing a three-dimensional geometric model of the dispersion fuel pellet, determining geometric parameters of the pellet and a TRISO particle structure size, and generating particle position parameters according to a random arrangement mode, a circumferential array AA arrangement mode or a hexagonal close-packed AB arrangement mode; constructing a geometric model containing TRISO particle distribution in finite element software based on the position parameters and the geometric parameters; endowing each area of the model with a material attribute, setting a heat conduction physical field and applying a boundary condition of a reactor operation condition; and finally, solving the steady-state heat conduction equation to obtain temperature field distribution in the pellet, and extracting the highest temperature and temperature cloud picture information. Compared with the prior art, the modeling method for the specific arrangement mode of the template method is provided, the problem of temperature field calculation of the dispersion fuel pellets of the template method is solved, and important technical support is provided for optimization of fuel element design.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of composite material analysis and calculation, and particularly to a finite element prediction method for temperature field of a template method dispersed fuel pellet. BACKGROUND

[0002] The dispersed fuel pellet is a new type of accident-tolerant fuel. The fuel is composed of a matrix and TRISO particles dispersed therein. According to the type of the matrix, the dispersed fuel is also different in name. When the matrix is metal zirconium, it is called zirconium-based dispersed micro-encapsulated fuel (M3 fuel); when the matrix is SiC ceramic, it is called SiC all-ceramic micro-encapsulated fuel (FCM fuel). The dispersed fuel is a typical composite material, and this form of fuel has good structural stability and fission product containment capability, and is one of the main research directions of accident-tolerant fuel. However, during the traditional sintering process of this fuel, axial shrinkage often occurs, and TRISO particles are rearranged and pressed against each other, resulting in the breakage of TRISO particles. And the breakage probability increases with the increase of the volume fraction of TRISO. Therefore, some people propose to use the template method to prepare the dispersed fuel, and to fix the position of TRISO by pre-preparing the template, to increase the distance between the particles and to reduce the contact between the particles. At present, there is less research on this template method dispersed fuel, so that the modeling and temperature prediction of the template method dispersed fuel pellet become difficult.

[0003] In the aspect of dispersed fuel performance simulation, the existing technology has obvious deficiencies. Patent CN114077796 A proposes a temperature field calculation method for multi-phase particle dispersed fuel element, which realizes macro-scale temperature field calculation through sub-region division and equivalent thermal conductivity iterative correction. However, this method does not consider the micro interaction between randomly distributed particles and the matrix, cannot simulate particle failure and its influence on thermal-mechanical-diffusion behavior, and is limited to the evaluation of thermal conductivity, lacking the ability of multi-physical field coupling analysis. Another patent CN117037963 A develops a thermal-mechanical-fission product diffusion coupling method for coated particle dispersed fuel, which can identify particle failure and perform multi-field calculation using different models, but the modeling premise of this method is that the particles are uniformly distributed, and it fails to consider the non-uniform random distribution characteristics of TRISO particles in the actual template method prepared fuel, and does not involve the problem of initial particle breakage caused by the preparation process, so it is difficult to truly reflect the microstructure characteristics and service behavior of the template method fuel.

[0004] In summary, the prior art fails to solve the problem of predicting the multi-field coupling behavior of the dispersion fuel pellets prepared by the template method due to the non-uniform random distribution structure and preparation damage, especially lacking a comprehensive analysis model that can simultaneously consider the random distribution of particles, initial damage in the preparation stage, particle failure in the reactor, and multi-physical field coupling. Therefore, developing a method that can accurately simulate the service behavior of the dispersion fuel pellets prepared by the template method under the action of thermal-mechanical-fission product diffusion multi-fields and accurately predict the temperature field, stress field and fission product release characteristics has become a key technical problem to be solved. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art and provide a finite element prediction method for the temperature field of dispersion fuel pellets prepared by the template method. The modeling method for the specific arrangement of the template method is proposed, and the temperature field calculation problem of the dispersion fuel pellets prepared by the template method is solved, providing important technical support for optimizing the design of fuel elements.

[0006] The purpose of the present application can be achieved by the following technical solutions:

[0007] The first aspect of the present application provides a finite element prediction method for the temperature field of dispersion fuel pellets prepared by the template method, comprising the following steps:

[0008] S1, a three-dimensional geometric model of the dispersion fuel pellet is established, including determining the basic geometric parameters of the pellet and the structure size of the TRISO particle, and generating corresponding position parameters according to the TRISO particle arrangement mode, the arrangement mode including one of random arrangement, circumferential array AA arrangement, and hexagonal dense AB arrangement;

[0009] S2, based on the position parameters and geometric parameters, a dispersion fuel pellet geometric model containing TRISO particle distribution is constructed in a finite element software;

[0010] S3, each region in the geometric model is assigned with corresponding material properties, a heat conduction physical field is set and boundary conditions are applied, and the temperature field distribution of the dispersion fuel under the operating condition of the reactor is simulated;

[0011] S4, based on the simulated temperature field distribution in S3, the steady-state heat conduction equation is solved and the internal temperature field distribution result of the pellet is obtained, and the highest temperature and temperature cloud picture information are extracted.

[0012] Further, in S1, the specific process of establishing the three-dimensional geometric model of the dispersion fuel pellet includes:

[0013] The geometric parameters of the fuel pellet and the structure size of each layer of the TRISO particle are set, and then the position parameters of the TRISO particle are generated according to the selected arrangement mode using the corresponding algorithm;

[0014] When the random arrangement is selected, an optimized random generation strategy is adopted, each TRISO particle position is generated and verified in a loop, so that the particle is located inside the pellet and does not overlap with the generated particles, until the preset volume fraction is reached;

[0015] When the circumferential array AA arrangement is selected, the maximum number of particles that can be accommodated in the radial and axial directions is calculated first, the particle positions on each circumference are determined by dividing concentric circles, and then the AA stacking structure is formed by arranging the particles uniformly in the axial direction;

[0016] When the hexagonal close-packed AB arrangement is selected, the plane positions of the particles in the odd and even rows are determined first, and then the AB stacking structure is formed by alternately arranging the odd and even planes in the axial direction. Finally, the particles exceeding the pellet boundary are removed and the effective position parameters are retained.

[0017] Further, the specific process of adopting the optimized random generation strategy, generating and verifying each TRISO particle position in a loop, so that the particle is located inside the pellet and does not overlap with the generated particles, until the preset volume fraction is reached, includes:

[0018] First, the random position coordinates of the ith TRISO particle are generated, and then it is judged whether the position is inside the geometric boundary of the fuel pellet;

[0019] If it is inside, it is further judged whether there is overlap with all the generated particles;

[0020] If there is no overlap, the particle position parameter is retained, and it is judged whether the current total volume fraction reaches the preset value;

[0021] If it does not reach, the next particle is generated, and the above process is repeated until the volume fraction requirement is met.

[0022] Further, the specific process of first calculating the maximum number of particles that can be accommodated in the radial and axial directions, determining the particle positions on each circumference by dividing concentric circles, and then arranging the particles uniformly in the axial direction to form the AA stacking structure includes:

[0023] First, the maximum number of particles that can be accommodated in the radial direction is calculated according to the diameter of the TRISO particle and the diameter of the pellet, and the maximum number of layers in the axial direction is calculated according to the diameter of the particle and the height of the pellet;

[0024] Then, multiple concentric circular rings are divided in the radial direction, and the number of particles that can be accommodated on each concentric circular ring and the specific position coordinates are calculated;

[0025] Finally, multiple layers are arranged at uniform intervals in the axial direction, and the positions of each layer are completely consistent, forming the AA stacking structure.

[0026] Further, the specific process of S2 includes: determining the planar positions of the odd-row and even-row particles, then arranging the odd and even planar positions in an axial ABAB alternating manner to form an AB stack structure, and finally removing the particles exceeding the pellet boundary and retaining the effective position parameters.

[0027] First, the positions of the odd-row particles are determined according to the hexagonal close packing in the plane, and then the positions of the even-row particles are calculated according to the characteristics of the hexagonal close packing;

[0028] Then, the different planar positions are arranged in an axial ABAB alternating manner, wherein the positions of the B planar particles are offset by a certain distance relative to the A planar positions.

[0029] Finally, the boundary of all generated particle positions is judged, and the particles exceeding the pellet boundary are removed, and all the effective position parameters are retained.

[0030] Further, the specific process of S2 includes: based on the position parameters and the geometric parameters, constructing a dispersed fuel pellet geometric model containing TRISO particle distribution in the finite element software.

[0031] The geometric parameters of the fuel pellet and the structure sizes of the TRISO particles are set, and then the position parameters of the TRISO particles are generated according to the selected arrangement mode and the corresponding algorithm;

[0032] When the random arrangement is selected, an optimized random generation strategy is adopted, and each TRISO particle position is generated and verified through a loop to ensure that the particle is located inside the pellet and does not overlap with the generated particles, until the preset volume fraction is reached.

[0033] When the circumferential array AA arrangement is selected, the maximum number of particles that can be accommodated in the radial and axial directions is calculated, the particle positions on each circumference are determined by dividing concentric circles, and then the AA stack structure is formed by uniformly arranging along the axial direction.

[0034] When the hexagonal close packing AB arrangement is selected, the planar positions of the odd-row and even-row particles are first determined, then the odd and even planar positions are arranged in an axial ABAB alternating manner to form an AB stack structure, and finally the particles exceeding the pellet boundary are removed and the effective position parameters are retained.

[0035] Further, the specific process of S3 includes: assigning corresponding material properties to each region in the geometric model, setting a heat conduction physical field and applying boundary conditions, and simulating the temperature field distribution of the dispersed fuel under the operating conditions of the reactor.

[0036] The TRISO particle structure and the matrix material are respectively assigned corresponding thermal physical parameters, including thermal conductivity, density, and specific heat capacity.

[0037] The steady-state heat conduction physical field is set in the finite element software, and a heat conduction differential equation control model is established.

[0038] The boundary conditions corresponding to the operating conditions of the reactor are applied, including setting a convective heat transfer boundary condition on the outer surface of the pellet to simulate the cooling environment of a pressurized water reactor, and setting a volumetric heat source inside the pellet to simulate the heat generated by fission;

[0039] The grid independence of the physical field is verified.

[0040] Further, in S4, based on the simulated temperature field distribution in S3, the steady-state heat conduction equation is solved and the internal temperature field distribution of the pellet is obtained, and the specific process of extracting the highest temperature and temperature cloud map information includes:

[0041] The finite element method is used to solve the steady-state heat conduction control equation to obtain the three-dimensional temperature field distribution inside the dispersed fuel pellet;

[0042] The temperature field data inside the pellet is extracted through the post-processing module, and the highest temperature point and its value are identified and recorded;

[0043] A temperature distribution cloud map is generated to compare and analyze the temperature field distribution characteristics of the pellets under different arrangement modes, and to evaluate the influence of the template arrangement on the heat dissipation performance.

[0044] Further, the finite element method is used to solve the steady-state heat conduction control equation to obtain the three-dimensional temperature field distribution inside the dispersed fuel pellet, and the specific process includes:

[0045] A complete finite element model containing the structure of each layer of the TRISO particle and the matrix material is established, and the corresponding thermal conductivity, heat source term and convective boundary condition parameters are set;

[0046] An appropriate solver and convergence criterion are selected to iteratively solve the steady-state heat conduction equation, and the temperature values of each node inside the pellet are obtained;

[0047] The specific process of extracting the temperature field data inside the pellet through the post-processing module, identifying and recording the highest temperature point and its value includes:

[0048] After the temperature values of each node are solved, the temperature data of all grid nodes are traversed by calling the post-processing function of the finite element software, the highest temperature point position is located by using the extreme value search algorithm, the coordinate information and temperature value of the highest temperature point position are recorded, and the temperature distribution curves along the radial and axial directions are extracted;

[0049] The specific process of generating a temperature distribution cloud map to compare and analyze the temperature field distribution characteristics of the pellets under different arrangement modes, and to evaluate the influence of the template arrangement on the heat dissipation performance includes:

[0050] Based on the temperature field data, two-dimensional and three-dimensional temperature distribution cloud maps are generated, and the temperature field characteristics of the three modes of random arrangement, circumferential array AA arrangement and hexagonal dense AB arrangement are compared and analyzed, and the differences in heat dissipation performance of different arrangement modes are evaluated by comparing the highest temperature value, temperature gradient distribution and hot spot area range.

[0051] Compared with the prior art, the present application has the following beneficial effects:

[0052] 1) The present application proposes a template method modeling method for circumferential array AA arrangement and hexagonal dense AB arrangement, which effectively overcomes the geometric distortion problem of the traditional random distribution model in describing the actual fuel pellets with regular arrangement structure. These special modeling methods can more realistically reconstruct the specific spatial distribution of fuel particles in the pellets, lay a reliable geometric model foundation for subsequent accurate thermal-physical field analysis, and significantly improve the physical authenticity of numerical simulation.

[0053] 2) Based on the established accurate geometric model, and coupled with the complete physical field describing the heat conduction, internal heat source and boundary heat exchange in the pellets, the temperature field calculation implemented by the present application can more accurately reveal the temperature distribution details and hot spot position inside the pellets under the template arrangement. Compared with the random method model, the template method shows significant differences in predicting temperature field distribution, especially the highest temperature, highlighting the importance of considering the actual arrangement mode for thermal hydraulic safety evaluation, and providing key technical support for improving the accuracy and reliability of the prediction results.

[0054] 3) The temperature field fine prediction capability and comparative analysis method provided by the present application provides a powerful tool for optimizing the design of dispersed fuel pellets and evaluating their thermal performance in the reactor. By quantifying the influence of different arrangement modes on heat dissipation effect, this method can provide important theoretical basis and decision support for guiding the microstructure design of fuel elements and improving their safety margin, and has clear engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 is a process flow chart of preparing dispersed fuel pellets by template method, which shows the arrangement and covering process of TRISO particles in the template.

[0056] Figure 2 is a flow chart of TRISO particle random distribution algorithm and a generated geometric model schematic diagram.

[0057] Figure 3 is a schematic diagram of TRISO particles arranged in circumferential array on a circular surface and arranged in AA array in the axial direction.

[0058] Figure 4 is a flow chart of TRISO particle circumferential array AA arrangement algorithm and a generated geometric model schematic diagram.

[0059] Figure 5 is a schematic diagram of TRISO particles arranged in a hexagonal close-packed manner on a circular surface, and arranged in an AB manner in the axial direction.

[0060] Figure 6 is a schematic diagram of the arrangement relationship of odd rows, even rows, odd surfaces, and even surfaces of TRISO particles arranged in a hexagonal close-packed manner.

[0061] Figure 7 is a flowchart of an AB arrangement algorithm for TRISO particles arranged in a hexagonal close-packed manner and a schematic diagram of a generated geometric model.

[0062] Figure 8 is a comparison schematic diagram of a geometric model of a dispersion fuel pellet established and a temperature distribution cloud diagram calculated.

[0063] Figure 9 is a comparison diagram of geometric models of random dispersion fuel pellets with different volume fractions (10 vol%, 20 vol%, 30 vol%).

[0064] Figure 10 is a temperature distribution cloud diagram of a random dispersion fuel pellet under a typical working condition.

[0065] Figure 11 is a geometric model diagram of dispersion fuel pellets arranged in a circumferential array AA arrangement with different volume fractions (10.83 vol%, 19.85 vol%, 31.2 vol%, 36.87 vol%).

[0066] Figure 12 is a temperature distribution cloud diagram of dispersion fuel pellets arranged in a circumferential array AA arrangement under a typical working condition.

[0067] Figure 13 is a geometric model diagram of dispersion fuel pellets arranged in a hexagonal close-packed AB arrangement with different volume fractions (10.77 vol%, 20.95 vol%, 29.78 vol%, 40.22 vol%, 50 vol%).

[0068] Figure 14 is a temperature distribution cloud diagram of dispersion fuel pellets arranged in a hexagonal close-packed AB arrangement under a typical working condition. DETAILED DESCRIPTION

[0069] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. In the technical solution, if the component model, material name, connection structure, circuit structure, control method, algorithm, and other features are not explicitly described, they are considered as common technical features disclosed in the prior art.

[0070] Example 1

[0071] The finite element prediction method for the temperature field of the dispersion fuel pellet in the template method in the embodiment comprises the following steps:

[0072] S1, a three-dimensional geometric model of the dispersion fuel pellet is established, including determining the basic geometric parameters of the pellet and the structure size of the TRISO particles, and generating corresponding position parameters according to the arrangement mode of the TRISO particles, the arrangement mode including one of random arrangement, circumferential array AA arrangement, and hexagonal dense AB arrangement;

[0073] In S1, the specific process of establishing the three-dimensional geometric model of the dispersion fuel pellet comprises:

[0074] The geometric parameters of the fuel pellet and the structure size of each layer of the TRISO particles are set, and then the position parameters of the TRISO particles are generated according to the selected arrangement mode by using the corresponding algorithm;

[0075] When the random arrangement is selected, an optimized random generation strategy is adopted, and each TRISO particle position is generated and verified through a loop, so that the particle is located inside the pellet and does not overlap with the generated particles, until the preset volume fraction is reached;

[0076] When the circumferential array AA arrangement is selected, the maximum number of particles that can be accommodated in the radial and axial directions is calculated first, the positions of the particles on each circumference are determined by dividing concentric circles, and then the AA stacking structure is formed by uniformly arranging the particles along the axial direction;

[0077] When the hexagonal dense AB arrangement is selected, the planar positions of the particles in the odd and even rows are determined first, and then the AB stacking structure is formed by alternately arranging the odd and even planes in the axial direction, and finally the particles exceeding the boundary of the pellet are removed and the effective position parameters are retained.

[0078] The specific process of adopting the optimized random generation strategy, generating and verifying each TRISO particle position through a loop, so that the particle is located inside the pellet and does not overlap with the generated particles, until the preset volume fraction is reached, comprises:

[0079] First, the random position coordinates of the i-th TRISO particle are generated, and then it is judged whether the position is inside the geometric boundary of the fuel pellet;

[0080] If it is inside, it is further judged whether there is overlap with all the generated particles;

[0081] If there is no overlap, the particle position parameter is retained, and it is judged whether the current total volume fraction reaches the preset value;

[0082] If it does not reach, the next particle is generated, and the above process is looped until the volume fraction requirement is met.

[0083] The maximum number of particles that can be accommodated in the radial and axial directions is calculated first, and the specific process of determining the positions of the particles on each circumference by dividing concentric circles and then arranging them uniformly in the axial direction to form an AA stacking structure includes:

[0084] First, the maximum number of particles that can be accommodated in the radial direction is calculated according to the diameter of the TRISO particle and the diameter of the pellet, and the maximum number of layers in the axial direction is calculated according to the diameter of the particle and the height of the pellet;

[0085] Then, a plurality of concentric circular rings are divided in the radial direction, and the number of particles that can be accommodated on each concentric circular ring and the specific position coordinates are calculated;

[0086] Finally, a plurality of layers are arranged at uniform intervals in the axial direction, and the positions of the layers are completely consistent, forming an AA stacking structure.

[0087] The specific process of determining the planar positions of the particles in the odd and even rows first, then forming an AB stacking structure by alternately arranging the odd and even planes in the axial direction, and finally removing the particles that exceed the boundary of the pellet and retaining the effective position parameters includes:

[0088] First, the positions of the particles in the odd rows are determined according to the hexagonal close packing arrangement in the plane, and then the positions of the particles in the even rows are calculated according to the characteristics of the hexagonal close packing;

[0089] Next, the different planes are arranged in the ABAB alternating manner in the axial direction, wherein the positions of the particles in the B plane are offset by a certain distance relative to the positions of the particles in the A plane;

[0090] Finally, boundary judgment is performed on all generated particle positions, and the particles that exceed the geometric boundary of the pellet are removed, and all effective position parameters are retained.

[0091] S2, based on the position parameters and the geometric parameters, constructing a dispersed fuel pellet geometric model containing a TRISO particle distribution in a finite element software;

[0092] In S2, the specific process of constructing a dispersed fuel pellet geometric model containing a TRISO particle distribution in a finite element software based on the position parameters and the geometric parameters includes:

[0093] The geometric parameters of the fuel pellet and the structure sizes of each layer of the TRISO particle are set, and then the position parameters of the TRISO particle are generated according to the selected arrangement mode using the corresponding algorithm;

[0094] When a random arrangement is selected, an optimized random generation strategy is adopted, and each TRISO particle position is generated and verified through a loop to ensure that the particle is located inside the pellet and does not overlap with the already generated particles, until a preset volume fraction is reached;

[0095] When the circumferential array AA arrangement is selected, the maximum number of particles that can be accommodated in the radial and axial directions is calculated first, the particle positions on each circumference are determined by dividing concentric circles, and then the AA stack structure is formed by uniformly arranging along the axial direction;

[0096] When the hexagonal close-packed AB arrangement is selected, the planar positions of particles in odd rows and even rows are first determined, then the AB stack structure is formed by alternately arranging odd and even surfaces in the axial direction, and finally the particles exceeding the pellet boundary are removed and the effective position parameters are retained.

[0097] S3, for each region in the geometric model, assign the corresponding material properties, set up the heat conduction physical field and apply the boundary conditions, simulate the temperature field distribution of the dispersed fuel under the operating condition of the reactor;

[0098] In S3, for each region in the geometric model, assign the corresponding material properties, set up the heat conduction physical field and apply the boundary conditions, simulate the temperature field distribution of the dispersed fuel under the operating condition of the reactor. The specific process includes:

[0099] Assign the corresponding thermal physical parameters to each layer structure of the TRISO particle and the matrix material, including thermal conductivity, density, and specific heat capacity;

[0100] Set up the steady-state heat conduction physical field in the finite element software and establish the heat conduction differential equation control model;

[0101] Apply the boundary conditions corresponding to the operating condition of the reactor, including setting the convective heat transfer boundary condition on the outer surface of the pellet to simulate the cooling environment of the pressurized water reactor, and setting the volume heat source inside the pellet to simulate the fission heat;

[0102] Verify the mesh independence of the physical field.

[0103] S4, based on the simulated temperature field distribution in S3, solve the steady-state heat conduction equation and obtain the temperature field distribution results inside the pellet, and extract the highest temperature and temperature contour information.

[0104] In S4, based on the simulated temperature field distribution in S3, solve the steady-state heat conduction equation and obtain the temperature field distribution results inside the pellet, and extract the highest temperature and temperature contour information. The specific process includes:

[0105] Solve the steady-state heat conduction control equation using the finite element method to obtain the three-dimensional temperature field distribution inside the dispersed fuel pellet;

[0106] Extract the temperature field data inside the pellet through the post-processing module, identify and record the highest temperature point and its value;

[0107] Generate a temperature distribution contour map to compare and analyze the temperature field distribution characteristics of the pellets under different arrangement methods, and evaluate the influence of the template method arrangement on the heat dissipation performance.

[0108] The specific process of obtaining the three-dimensional temperature field distribution inside the dispersion fuel pellet by solving the steady-state heat conduction control equation by the finite element method includes:

[0109] A complete finite element model containing the structure of each layer of the TRISO particle and the matrix material is established, and the corresponding thermal conductivity, heat source term and convective boundary condition parameters are set;

[0110] An appropriate solver and convergence criterion are selected to iteratively solve the steady-state heat conduction equation, and the temperature values of each node inside the pellet are obtained;

[0111] The specific process of extracting the temperature field data inside the pellet by the post-processing module, identifying and recording the highest temperature point and its value includes:

[0112] After the temperature values of each node are solved, the post-processing function of the finite element software is called to traverse the temperature data of all grid nodes, the temperature highest point position is located by the extreme value search algorithm, the coordinate information and temperature value of the temperature highest point position are recorded, and the temperature distribution curves along the radial and axial directions are extracted;

[0113] The specific process of generating temperature distribution contour maps and comparing and analyzing the temperature field distribution characteristics of the pellets under different arrangement modes to evaluate the influence of the template method arrangement on the heat dissipation performance includes:

[0114] Based on the temperature field data, two-dimensional and three-dimensional temperature distribution contour maps are generated, the temperature field characteristics of the three modes of random arrangement, circumferential array AA arrangement and hexagonal dense AB arrangement are compared and analyzed, and the differences in heat dissipation performance of different arrangement modes are evaluated by comparing the highest temperature value, temperature gradient distribution and hot spot area range.

[0115] In specific implementation, the modeling method for the template method dispersion fuel pellet in the embodiment is used to calculate the temperature field distribution of such fuel pellet under the operating condition of a pressurized water reactor. The results show that the method can perfectly model the template method dispersion fuel pellet, and the modeling method has universality. The calculated results have certain regularity. Figure 1 is a process flowchart for preparing a template method dispersion fuel pellet, showing the arrangement and covering process of TRISO particles in the template.

[0116] According to different arrangement modes: random arrangement, circumferential array AA arrangement, and hexagonal dense AB arrangement, the modeling steps are also different. Specifically as follows.

[0117] 1. Random arrangement

[0118] The modeling method of random arrangement of TRISO particles is based on the strategy of optimized randomness. This method can achieve a filling rate of TRISO particles within 30vol%. The TRISO particles are generated one by one,Figure 2 is the flow chart of the random distribution algorithm of TRISO particles and the generated geometric model diagram. The modeling steps are as follows:

[0119] (1) Set the geometric parameters of the fuel pellet, the size of each layer of TRISO particles.

[0120] (2) Set the required volume fraction.

[0121] (3) Generate the ith TRISO particle, call the random function, and generate the position (spherical center coordinates) of the TRISO particle.

[0122] (4) Determine whether the ith TRISO particle is inside the pellet. If it is, proceed to the next step. If it is not, return to step (3) and generate the position parameters of the TRISO particle again.

[0123] (5) Determine whether the ith TRISO particle overlaps with all previous particles. If it does, proceed to the next step. If it does not, return to step (3) and generate the position parameters of the TRISO particle again.

[0124] (6) Determine whether the existing TRISO particles meet the required volume fraction. If they do, proceed to the next step. If they do not, return to step (3) and generate the position parameters of the next TRISO particle.

[0125] (7) Keep all the position parameters of the TRISO particles.

[0126] (8) Generate the geometric model according to the set geometric parameters and position parameters, and assign materials.

[0127] 2. Template method - circumferential array AA arrangement

[0128] The core of the template method is that all TRISO particles have fixed positions and are not randomly generated. Therefore, for a specific template arrangement, a specific algorithm is needed to obtain the position parameters of the TRISO particles. Figure 3 is a schematic diagram of TRISO particles arranged in a circumferential array on a circular surface and arranged in an AA array in the axial direction.

[0129] Circumferential array AA arrangement refers to arranging particles in a circumferential array along the radial direction on a circular surface, with the goal of achieving the most dense arrangement on the circumference. "AA" refers to the same arrangement in the axial direction. This is to distinguish from the "AB" of hexagonal close packing. Figure 3 is a schematic diagram of TRISO particles arranged in a circumferential array on a circular surface and arranged in an AA array in the axial direction.

[0130] The modeling steps are as follows:

[0131] (1) Set the geometry parameters of fuel pellet, the size of each layer of TRISO particle.

[0132] (2) Calculate the maximum number of TRISO particles that can be filled along the diameter on the circular surface; calculate the maximum number of TRISO particles that can be filled along the axial direction of the pellet.

[0133] (3) Preliminary set the volume fraction. According to the set volume fraction, adjust the spacing of TRISO particles in the radial and axial directions.

[0134] (4) According to the number of particles that can be filled in the radial direction, divide the concentric circles.

[0135] (5) Calculate the maximum number of TRISO particles that can be filled along the circumference of each concentric circle, and calculate the position of TRISO particles on each circumference.

[0136] (6) Calculate the position of all TRISO particles on the circular surface.

[0137] (7) Calculate the position of all TRISO particles in the axial direction.

[0138] (8) Calculate the position of all TRISO particles arranged in the circumferential array AA inside the dispersion pellet.

[0139] (9) Generate a geometric model according to the set geometry parameters and position parameters, and assign materials.

[0140] Figure 4 is a flowchart of the circumferential array AA arrangement algorithm of TRISO particles and a schematic diagram of the generated geometric model.

[0141] 3. Template method - hexagonal close packing AB arrangement

[0142] Hexagonal close packing AB arrangement refers to the arrangement of particles in a hexagonal close packing on the circular surface, and the axial direction also follows the close packing mode. The purpose is to maximize the filling volume fraction of TRISO particles. Figure 5 is a schematic diagram of TRISO particles arranged in a hexagonal close packing on the circular surface and arranged in AB in the axial direction.

[0143] Modeling steps:

[0144] (1) Set the geometry parameters of fuel pellet, the size of each layer of TRISO particle.

[0145] (2) Calculate the maximum number of TRISO particles that can be filled along the diameter on the circular surface.

[0146] (3) Preliminary set the volume fraction. According to the set volume fraction, adjust the spacing of TRISO particles in the radial and axial directions.

[0147] (4) Calculate the position of TRISO particles along the diameter as the position of odd-numbered rows of TRISO particles on the odd-numbered surface.

[0148] (5) Obtain the position of even-numbered rows of TRISO particles on the odd-numbered surface according to the position of odd-numbered rows of TRISO particles on the odd-numbered surface, and further obtain the position of all TRISO particles on the odd-numbered surface.

[0149] (6) Obtain the position of all TRISO particles on the even-numbered surface according to the position of all TRISO particles on the odd-numbered surface.

[0150] (7) Calculate how many odd-numbered surfaces and even-numbered surfaces are needed according to the height of the pellet and the volume fraction.

[0151] (8) Determine whether the TRISO particles are inside the pellet according to the position of all TRISO particles. If satisfied, keep the position parameters of the TRISO particles, if not satisfied, discard.

[0152] (9) Generate a geometric model according to the set geometric parameters and position parameters, and assign materials.

[0153] Figure 6 is a schematic diagram of the arrangement relationship of odd-numbered rows, even-numbered rows, odd-numbered surfaces, and even-numbered surfaces when TRISO particles are arranged in a hexagonal close-packed arrangement.

[0154] Figure 7 is a flowchart of the AB arrangement algorithm of TRISO particles in a hexagonal close-packed arrangement and a schematic diagram of the generated geometric model.

[0155] The physical field of the pellet is set, and the temperature field of the pellet is calculated. The geometric parameters and physical field parameters of the pellet are shown in the following table:

[0156] Table 1: Geometric parameters and physical field parameters of the pellet

[0157]

[0158] The physical model for calculating the temperature field of the pellet is determined by the heat conduction differential equation and the convective heat transfer formula:

[0159]

[0160] ρ: represents the density of the material, i.e. the mass per unit volume.

[0161] Cp: represents the specific heat capacity of the material at constant pressure, i.e. the heat absorbed per unit mass to raise the temperature of the substance by one degree.

[0162] represents the rate of change of temperature with time.

[0163] k: represents the thermal conductivity of the material.

[0164] represents the net heat conduction amount per unit volume due to the temperature gradient.

[0165] Q: represents the heat source generation rate per unit volume inside the object.

[0166] h sf : represents the convective heat transfer coefficient between the cladding surface where the phase change occurs and the cooling water.

[0167] A sf : represents the cladding surface area where the phase change occurs.

[0168] T cladding : represents the temperature of the cladding material.

[0169] T water : represents the temperature of the cooling water.

[0170] -h sf A sf (T cladding -T water ): collectively represents the heat flow rate transferred through the phase change interface due to the temperature difference between the cladding and the cooling water.

[0171] Figure 8 is a schematic diagram comparing the established dispersion fuel pellet geometry model with the calculated temperature distribution contour.

[0172] Application Example 1

[0173] Temperature field calculation of SiC-FCM fuel pellets with randomly distributed TRISO particles, M3 fuel pellets.

[0174] (1) Use the random TRISO particle generation method to generate the geometry model of the dispersion fuel pellet with TRISO content of 10vol%, 20vol%, and 30vol%. Figure 9 is a comparison diagram of the geometry model of the random dispersion fuel pellet with different volume fractions (10vol%, 20vol%, 30vol%).

[0175] (2) Assign physical fields and calculate the temperature distribution of the pellets. As shown in the figure:

[0176] Figure 10 is the temperature distribution contour of the random dispersion fuel pellet under typical working conditions.

[0177] The maximum temperature of the pellets is shown in the following table:

[0178] Table 2: Temperature maximum point of random dispersion fuel pellets

[0179]

[0180] Application Example 2

[0181] TRISO particles are distributed according to the SiC-FCM fuel pellet, M3 fuel pellet temperature field calculation of the circumferential array AA.

[0182] (1) Use the TRISO particle circumferential array AA distribution generation method to generate the geometric model of the dispersion fuel pellet with TRISO content of 10.83vol%, 19.85vol%, 31.2vol%, 36.87vol%. Figure 11 is the geometric model diagram of the dispersion fuel pellet with different volume fractions (10.83vol%, 19.85vol%, 31.2vol%, 36.87vol%) arranged in circumferential array AA.

[0183] (2) Impose physical fields and calculate the temperature distribution of the pellet. Figure 12 is the temperature distribution cloud diagram of the dispersion fuel pellet arranged in circumferential array AA under typical working conditions.

[0184] The highest temperature of the pellet is shown in the following table:

[0185] Table 3: Temperature maximum point of dispersion fuel pellet arranged in circumferential array AA

[0186]

[0187] Application Example 3

[0188] TRISO particles are distributed according to the SiC-FCM fuel pellet, M3 fuel pellet temperature field calculation of the circumferential array AA.

[0189] (1) Use the TRISO particle circumferential array AA distribution generation method to generate the geometric model of the dispersion fuel pellet with TRISO content of 10.83vol%, 19.85vol%, 31.2vol%, 36.87vol%. Figure 13 is the geometric model diagram of the dispersion fuel pellet with different volume fractions (10.77vol%, 20.95vol%, 29.78vol%, 40.22vol%, 50vol%) arranged in hexagonal close packing AB.

[0190] (2) Impose physical fields and calculate the temperature distribution of the pellet. Figure 14 is the temperature distribution cloud diagram of the dispersion fuel pellet arranged in hexagonal close packing AB under typical working conditions.

[0191] The highest temperature of the pellet is shown in the following table:

[0192] Table 4: Temperature maximum point of dispersion fuel pellet arranged in hexagonal close packing AB

[0193]

[0194] The foregoing description of the embodiments has been presented for the purpose of illustration and description. It is not intended to be exhaustive or to limit the application to the precise form disclosed. Modifications and variations are possible in light of the above teachings or can be acquired from practice of the application. As well, the application has been described above with the assistance of illustrative figures and detailed descriptions. It is obvious to a person skilled in the art that variations of the application can be made and still be considered falling within the scope of the application. Accordingly, the application is not limited to that precisely as shown and described. Rather, the application is intended to cover all reasonable modifications and changes that can be made without departing from the scope of the application.

Claims

1. A finite element method for predicting the temperature field of dispersed fuel pellets using a template method, characterized in that, Includes the following steps: S1. Establish a three-dimensional geometric model of the dispersed fuel pellet, including determining the basic geometric parameters of the pellet and the size of the TRISO particle structure, and generating corresponding position parameters according to the TRISO particle arrangement. The arrangement includes one of random arrangement, circular array AA arrangement, and hexagonal close-packed AB arrangement. S2. Based on the positional and geometrical parameters, construct a geometric model of a dispersed fuel pellet containing TRISO particle distribution in finite element software; S3. Assign corresponding material properties to each region in the geometric model, set the heat conduction physical field and apply boundary conditions to simulate the temperature field distribution of dispersed fuel under reactor operating conditions. S4. Based on the simulated temperature field distribution in S3, solve the steady-state heat conduction equation and obtain the temperature field distribution inside the core, extracting the highest temperature and temperature cloud map information.

2. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 1, characterized in that, In S1, the specific process of establishing the three-dimensional geometric model of the dispersed fuel pellets includes: Set the geometric parameters of the fuel pellets and the structural dimensions of each layer of TRISO particles, and then use the corresponding algorithm to generate the TRISO particle position parameters according to the selected arrangement. When random arrangement is selected, an optimized random generation strategy is adopted. The position of each TRISO particle is generated and verified in a loop to ensure that the particles are located inside the core block and do not overlap with the generated particles until the preset volume fraction is reached. When choosing the circumferential array AA arrangement, first calculate the maximum number of particles that can be accommodated in the radial and axial directions, determine the position of particles on each circumference by dividing concentric circles, and then arrange them evenly along the axial direction to form an AA stacking structure. When choosing a hexagonal close-packed AB arrangement, first determine the planar positions of the odd-numbered and even-numbered rows of particles, then arrange the odd-numbered and even-numbered faces alternately along the axis to form an AB stacking structure, and finally remove particles that exceed the core block boundary while retaining the effective position parameters.

3. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 2, characterized in that, The optimized random generation strategy involves iteratively generating and verifying the position of each TRISO particle to ensure that the particles are located inside the core block and do not overlap with already generated particles, until a preset volume fraction is achieved. The specific process includes: First, generate the random position coordinates of the i-th TRISO particle, and then determine whether the position is located inside the geometric boundary of the fuel pellet; If it is inside, then it is further determined whether it overlaps with all the already generated particles; If there is no overlap, retain the particle position parameter and determine whether the current total integral has reached the preset value; If the volume fraction requirement is not met, the next particle is generated, and the process is repeated until the volume fraction requirement is met.

4. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 2, characterized in that, The specific process of first calculating the maximum number of particles that can be accommodated radially and axially, determining the position of particles on each circumference by dividing concentric circles, and then uniformly arranging them along the axial direction to form an AA stacked structure includes: First, calculate the maximum radial number of particles based on the TRISO particle diameter and core block diameter, and then calculate the maximum axial number of layers based on the particle diameter and core block height. Then, the radial division is divided into multiple concentric rings, and the number of particles that can be accommodated on each concentric ring and their specific position coordinates are calculated. Finally, multiple layers are arranged at uniform intervals along the axial direction, with each layer in the same position, forming an AA stacked structure.

5. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 2, characterized in that, The specific process of first determining the planar positions of the odd-numbered and even-numbered rows of particles, then forming an AB stack structure by alternating the odd and even faces along the axis, and finally removing particles that exceed the core boundary while retaining the effective position parameters includes: First, determine the positions of the odd-numbered rows of particles by arranging them in a hexagonal close-packed configuration in the plane. Then, calculate the positions of the even-numbered rows of particles based on the characteristics of the hexagonal close-packed configuration. Next, different planes are arranged in an alternating ABAB pattern along the axial direction, where the particle position on plane B is offset by a certain distance relative to plane A; Finally, boundary checks are performed on all generated particle positions, removing particles that exceed the geometric boundaries of the core block and retaining all valid position parameters.

6. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 1, characterized in that, In S2, the specific process of constructing a geometric model of a dispersed fuel pellet containing TRISO particle distribution in finite element software based on the aforementioned position and geometric parameters includes: Set the geometric parameters of the fuel pellets and the structural dimensions of each layer of TRISO particles, and then use the corresponding algorithm to generate the TRISO particle position parameters according to the selected arrangement. When random arrangement is selected, an optimized random generation strategy is adopted. By cyclically generating and verifying the position of each TRISO particle, the particle is ensured to be located inside the core block and does not overlap with the generated particles until the preset volume fraction is reached. When choosing the circumferential array AA arrangement, first calculate the maximum number of particles that can be accommodated in the radial and axial directions, determine the position of particles on each circumference by dividing concentric circles, and then arrange them evenly along the axial direction to form an AA stacking structure. When choosing a hexagonal close-packed AB arrangement, first determine the planar positions of the odd-numbered and even-numbered rows of particles, then arrange the odd-numbered and even-numbered faces alternately along the axis to form an AB stacking structure, and finally remove particles that exceed the core block boundary while retaining the effective position parameters.

7. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 1, characterized in that, In S3, the specific process of assigning corresponding material properties to each region in the geometric model, setting the heat conduction physical field and applying boundary conditions to simulate the temperature field distribution of dispersed fuel under reactor operating conditions includes: Each layer of TRISO particles and the matrix material are assigned corresponding thermophysical parameters, including thermal conductivity, density, and specific heat capacity. In finite element software, a steady-state heat conduction physical field is set up, and a heat conduction differential equation control model is established. Apply boundary conditions corresponding to reactor operating conditions, including setting convective heat transfer boundary conditions on the outer surface of the pellet to simulate the pressurized water reactor cooling environment, and setting volumetric heat sources inside the pellet to simulate fission heat generation. Verify the grid independence of the physical field.

8. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 1, characterized in that, In S4, based on the simulated temperature field distribution in S3, the steady-state heat conduction equation is solved and the internal temperature field distribution of the core is obtained. The specific process of extracting the maximum temperature and temperature contour map information includes: The steady-state heat conduction control equations were solved using the finite element method to obtain the three-dimensional temperature field distribution inside the dispersed fuel pellets. The post-processing module extracts the internal temperature field data of the core, identifies and records the highest temperature point and its value. A temperature distribution cloud map is generated, and the temperature field distribution characteristics of the core blocks under different arrangement methods are compared and analyzed to evaluate the impact of template method arrangement on heat dissipation performance.

9. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 8, characterized in that, The specific process of solving the steady-state heat conduction control equations using the finite element method to obtain the three-dimensional temperature field distribution inside the dispersed fuel pellet includes: Establish a complete finite element model that includes the structure of each layer of TRISO particles and the matrix material, and set the corresponding thermal conductivity, heat source term and convection boundary condition parameters. By selecting an appropriate solver and convergence criterion, the steady-state heat conduction equation is solved iteratively to obtain the temperature values ​​of each node inside the core. The specific process of extracting internal temperature field data of the core block through the post-processing module, and identifying and recording the highest temperature point and its value, includes: After the temperature values ​​of each node are solved, the finite element software processing function is called to traverse the temperature data of all mesh nodes. The extreme value search algorithm is used to locate the position of the highest temperature point, and the coordinate information and temperature value of the highest temperature point are recorded. At the same time, the temperature distribution curves along the radial and axial directions are extracted.

10. The finite element method for predicting the temperature field of dispersed fuel pellets using the template method according to claim 8, characterized in that, Generating temperature distribution cloud maps and comparing and analyzing the temperature field distribution characteristics of the core blocks under different arrangement methods, the specific process of evaluating the impact of template method arrangement on heat dissipation performance includes: Two-dimensional and three-dimensional temperature distribution cloud maps are generated based on temperature field data. The temperature field characteristics of three arrangements—random arrangement, circular array AA arrangement, and hexagonal dense stack AB arrangement—are compared and analyzed. The differences in heat dissipation performance of different arrangement methods are evaluated by comparing the highest temperature value, temperature gradient distribution, and hot spot area range.

Images