A method for optimizing the geometry and spatial distribution of additive phases in a composite pellet

Abstract

The application discloses a kind of composite briquette adding phase geometric structure and space distribution optimization method, adopt ellipsoid equation to simultaneously describe round ball type, whisker type, sheet type filling method, realize the optimization design of different geometric shapes;Specific steps are as follows:1, give the relevant condition of briquette;2, establish the r-θ2D section analysis model of briquette;3, given the discrete geometric number of adding phase;4, generate corresponding ellipse in model using random algorithm;5, determine whether the ellipse generated in 4 has problem, if there is problem, repeat 4;6, repeat steps 4, 5, generate M sets of data containing random geometry, space distribution;7, carry out mesh division;8, use numerical analysis method and solve in parallel, obtain M groups of key variables;9, based on the result in 8, using genetic algorithm and other optimization means, evaluate the pros and cons of M groups of design, then generate M groups of data again in combination with steps 4-6;10, repeat steps 4-9 until the optimization algorithm convergence condition is reached;11, output optimization result.

Description

Technical Field

[0001] This invention belongs to the field of composite fuel pellet optimization technology, specifically involving a method for optimizing the geometric structure and spatial distribution of added phases in composite pellets. Background Technology

[0002] UO2 is an excellent nuclear fuel due to its good radiation stability, low thermal neutron absorption cross-section, high temperature resistance, and non-reactivity with water, and is widely used in commercial nuclear power plants. However, UO2's very low thermal conductivity results in poor heat transfer from fuel to coolant, leading to a high temperature gradient, which increases the risk of fuel cracking and radioactive leakage, thus limiting further improvements in reactor parameters. Since the Fukushima accident, the importance of fuels with high thermal conductivity for reactor safety has become even more apparent.

[0003] To improve the average thermal conductivity of fuel pellets, a typical design approach involves incorporating high thermal conductivity materials into the UO2 matrix to create composite UO2 pellets. Common composite UO2 pellets, such as UO2-BeO, UO2-Mo, and UO2-SiC whiskers, largely retain the advantages of UO2 pellets and are expected to significantly improve the average thermal conductivity of the pellets. This, in turn, reduces the fuel pellet center temperature, fission gas release, and cracking effects, thereby enhancing the in-core performance of fuel elements.

[0004] Finding suitable geometric and spatial distributions of additive phases to improve composite pellet design is crucial for enhancing pellet service performance. Currently, additive phases in composite pellets exhibit various geometric designs, such as spherical, whisker-like, and lamellar shapes, and their spatial distributions vary. Obtaining a reliable relationship between structure and performance requires extensive experimental and numerical simulation work. Simultaneously, to ensure reactor efficiency, the content of additive phases in the composite material should be as low as possible. Therefore, a key challenge in composite pellet design is maximizing the average thermal conductivity of the pellet at high UO2 content. This problem involves the relationship between pellet structure and performance, encompassing numerous complex physical processes that are difficult to model accurately. Exploring global optimization solutions using existing experimental methods and traditional optimization techniques is time-consuming, costly, and difficult to optimize geometric and spatial distributions, thus hindering improvements in composite pellets.

[0005] For example, the paper "Multi-Objective Optimization Design of Plate-type Fuel via Co-simulation Method." Annals of Nuclear Energy 169(2022):108914. details the establishment of a 2D plate assembly thermo-coupling analysis model using COMSOL, and the optimization of the number of plate fuel assemblies, plate thickness, and flow channel width using a multi-objective algorithm based on genetic algorithms. However, this work does not involve the optimization of the spatial distribution of the optimization objects.

[0006] The paper "Thermal Optimization of UO2-Mo Fuel Using Sensitivity Analysis and Genetic Algorithms" (TopFuel 2022, October 9–13, Raleigh, North Carolina, 2022) introduces two optimization schemes for the thermal conductivity of UO2-Mo fuel. One scheme optimizes the Mo structure with a rod-disc design using a global sensitivity technique based on the cumulative distribution function of temperature peaks, while the other scheme optimizes the Mo structure with a fine-line design using a genetic algorithm. Although this study initially achieved optimization of the spatial location of the added phase, it did not achieve optimization of the geometry of the added phase. Summary of the Invention

[0007] To overcome the problems existing in the prior art, the present invention aims to provide a method for optimizing the geometric structure and spatial distribution of the added phase in a composite core by combining numerical simulation methods and optimization algorithms such as genetic algorithms. The optimization algorithm uses a small ellipsoid to fit the geometric structure of the added phase in the core and simulates its spatial distribution. The optimal added phase geometry and spatial distribution are explored in the entire parameter space to achieve structural optimization of the composite core.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for optimizing the geometry and spatial distribution of added phases in composite cores is proposed. The method uses ellipsoids to describe spherical, whisker, flake, and irregular filling methods. It combines numerical simulation and genetic algorithms to achieve optimized design of added phases with different geometries and spatial distributions.

[0010] The method includes the following steps:

[0011] Step 1: Given the volume fraction of the added phase in the composite core, the core power, and the heat transfer conditions or wall temperature of the outer wall surface;

[0012] Step 2: Given the core radius and inner diameter, establish a 1 / 4 or 1 / 2r-θ two-dimensional cross-sectional analysis model of the UO2 core, where r is the polar radius and θ is the angle;

[0013] Step 3: Taking into account the added phase technology level, computational resources, ease of mesh generation, and optimization objective factors, determine the number of discrete geometries N for the added phase;

[0014] Step 4: Based on the discrete geometric number N of the added phase determined in Step 3, a random algorithm is used to generate the added phase positions (r) in the model established in Step 2. i ,θ i ), azimuth angle α i and the major and minor axes of the cross section (a) i ,b i ), where i = 1, ..., N;

[0015] Step 5: Determine whether the ellipses generated from the N sets of data in Step 4 intersect or exceed the model area established in Step 2. If the ellipses intersect or exceed the model area established in Step 2, repeat Step 4 until N sets of data that meet the conditions are generated.

[0016] Step Six: Based on the requirements for the first generation of individuals in the optimization algorithm, repeat Steps Four and Five M times to generate M sets of data;

[0017] Step 7: Based on the cross-sectional analysis model established in Step 2 and the generated M sets of data, the geometric regions in the cross-sectional analysis model are subdivided and renumbered, the fuel phase and the additive phase are distinguished, the mesh is automatically generated using finite element software, and the mesh generation is completed.

[0018] Step 8: Using the finite element method combined with parallel computing technology, complete the M sets of data generation and analysis heat transfer models or irradiation thermo-mechanical coupling analysis models in Step 7 and solve them to obtain the key variables of thermal conductivity distribution, temperature distribution, and maximum temperature of the models.

[0019] Step 9: Based on the calculation results in Step 8, use an optimization algorithm to evaluate the merits of the M group designs, and then regenerate the M group data in conjunction with Steps 4 to 6.

[0020] Step 10: Repeat steps 4 to 9 until the convergence condition of the optimization algorithm is met or the optimization objective is satisfied;

[0021] Step 11: Output the phase structure and spatial geometric distribution information of the optimized composite core.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] Ellipsoids are used to describe spherical, whisker, and flake filling methods, and combined with optimization techniques such as finite element method and genetic algorithm, the first optimization design of different geometries is realized. Attached Figure Description

[0024] Figure 1 Flowchart for model generation and optimization.

[0025] Figure 2 This is a schematic diagram of the cross-section of a fuel pellet. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0027] This invention discloses a method for optimizing the geometry and spatial distribution of added phases in composite cores. Addressing the issue that added phases in composite cores exhibit various geometric designs and spatial distributions, existing experimental methods and optimization techniques are time-consuming, costly, and difficult to implement for optimizing the geometry and spatial distribution of composite cores, thus hindering improvements. This invention uses ellipsoidal particles to fit various geometric shapes and spatial distributions of added phases and employs optimization algorithms such as genetic algorithms. This allows for a representative method to broadly describe the structures of various added phases, enabling the optimization of added phase geometry and spatial distribution using a single approach while reducing the need for prior knowledge. The model generation and optimization process is attached. Figure 1 As shown in the attached figure, the cross-section of the fuel pellet is as follows. Figure 2 As shown, the small gray elliptical parts represent the geometric shape and spatial distribution of the added phase fitted by the ellipsoidal particles, (r i ,θ i ) represents the position coordinates of the ellipsoidal particle, α i The azimuth angle of the particle is the tilt angle. The remaining white part is the UO2 matrix. The heat source Q in the core is obtained from the core power. The core boundary has a definite isothermal or convection boundary condition.

[0028] The method includes the following steps:

[0029] Step 1: Specify the volume fraction of the added phase in the composite core (not exceeding 15%), as well as the core power, external wall heat transfer conditions, or wall temperature, etc.

[0030] In the optimization calculation of the same geometry and spatial distribution, the influence of boundary temperature, power distribution, power magnitude, etc. on the thermal conductivity of composite core can be analyzed by changing the above conditions.

[0031] Step 2: Given the core radius and inner diameter, establish a cross-sectional analysis model of the UO2 core (1 / 4 or 1 / 2)r-θ2D; where r is the polar radius and θ is the angle;

[0032] By taking advantage of the symmetry of the core, establishing a 1 / 4 or 1 / 2 r-θ2D cross-section analysis model can effectively reduce the amount of computation required while analyzing the influence of geometry and spatial distribution on the thermal conductivity of the composite core.

[0033] Step 3: Taking into account the added phase technology level, computational resources, ease of mesh generation, and optimization objective factors, determine the number of discrete geometric phases N to be added, such as 10, 30, 50, etc.

[0034] Given the conditions in steps one and two, grouping calculations can be performed with different discrete geometric numbers of added phases to analyze the influence of the number of discrete sets of added phases on the thermal conductivity of the composite core.

[0035] Step 4: Based on the discrete geometric number N of the added phase determined in Step 3, a random algorithm is used to generate the added phase positions (r) in the model established in Step 2. i ,θ i ), azimuth angle α i and the major and minor axes of the cross section (a) i ,b i ), where i = 1, ..., N;

[0036] Step 5: Determine whether the ellipses generated from the N sets of data in Step 4 intersect or exceed the model area established in Step 2. If the ellipses intersect or exceed the model area established in Step 2, repeat Step 4 until N sets of data that meet the condition of not intersecting or not exceeding the model area established in Step 2 are generated.

[0037] Step Six: According to the requirements of the optimization algorithm (such as the requirements for the initial population in the genetic algorithm), repeat Step Four and Step Five M times to generate M sets of data;

[0038] When using genetic algorithms for optimization, in typical genetic algorithm terminology, each individual solution in the population is called a chromosome, and each parameter in a chromosome is called a gene. The fitness function, which measures the fitness of each chromosome in a genetic algorithm, is called the fitness function. Chromosomes with high fitness scores are selected to "reproduce," passing their genes to their offspring in the next population. Genetic algorithms require a highly diverse initial population, meaning that M sets of data need to be highly diverse.

[0039] Step 7: Based on the cross-sectional analysis model established in Step 2 and the generated M sets of data, the geometric regions in the cross-sectional analysis model are subdivided and renumbered, the fuel phase and the additive phase are distinguished, the mesh is automatically generated using finite element software, and the mesh generation is completed.

[0040] Step 8: Using numerical analysis methods such as finite element method and combined with parallel computing technology, complete the heat transfer model (or irradiation thermodynamic coupling analysis model) generated from the M sets of data in Step 7 and solve it to obtain key variables such as thermal conductivity distribution, maximum temperature and temperature distribution of the model;

[0041] The key variables calculated in this step will be used as true values ​​in subsequent steps to evaluate the quality of the added phase geometry and distribution in each region;

[0042] Step 9: Based on the calculation results in Step 8, use optimization algorithms such as genetic algorithms to evaluate the merits (or fitness) of the M group designs, retain the geometric shape and spatial distribution characteristics with high thermal conductivity, perform certain crossover and mutation, and regenerate the M group data in combination with Steps 4 to 6.

[0043] Taking genetic algorithms as an example, crossover and mutation are common genetic operators used to determine or change the genetic makeup of offspring. Crossover is a method of selecting which part of the genes are passed from the parents to the offspring. In the simplest crossover, a random number between 0 and 1 is chosen to determine which part of the gene comes from which parent. New individuals formed after the crossover operation may undergo genetic mutation, changing the values ​​of one or more genes. Like selection, mutation is also based on probability, but the probability of mutation is generally set very small.

[0044] Step 10: Repeat steps 4 to 9 until the convergence condition of the optimization algorithm is met or the optimization objective is satisfied;

[0045] Each time, the fitness of the next generation of solutions is calculated, and the best-performing solution in each generation is retained to ensure that the fitness does not decrease. Steps four through nine are repeated, and the optimization algorithm is considered to have converged when the fitness function score is high and stable across different generations.

[0046] If the fitness converges to a low level too early, it may be due to insufficient richness of the initial population. In this case, it is necessary to go back to step four when generating the initial population, increase the value of M or add a scientific sampling method to obtain an initial population with higher richness, and then proceed with the subsequent steps.

[0047] Step 11: Output the phase structure and spatial geometric distribution information of the optimized composite core.

[0048] After obtaining the calculated optimization results, they can be compared with classic composite pellet structures to compare fuel performance before and after optimization, such as thermal expansion, swelling, densification, fission gas release, burn-through depth, etc. They can also be compared in terms of pellet temperature distribution, stress distribution, etc., to demonstrate the optimization capability of the algorithm.

Claims

1. A method for optimizing the geometry and spatial distribution of added phases in a composite core, characterized in that: Ellipsoids are used to describe spherical, whisker, flake, and irregular filling methods. Combining numerical simulation and genetic algorithms, the optimized design of added phases with different geometric structures and spatial distributions is realized. The method includes the following steps: Step 1: Given the volume fraction of the added phase in the composite core, the core power, and the heat transfer conditions or wall temperature of the outer wall surface; Step 2: Given the core radius and inner diameter, establish a 1 / 4 or 1 / 2r-θ two-dimensional cross-sectional analysis model of the UO2 core, where r is the polar radius and θ is the angle; Step 3: Taking into account the added phase technology level, computational resources, ease of mesh generation, and optimization objective factors, determine the number of discrete geometries N for the added phase; Step 4: Based on the discrete geometric number N of the added phase determined in Step 3, a random algorithm is used to generate the added phase positions (r) in the model established in Step 2. i ,θ i ), azimuth angle α i and the major and minor axes of the cross section (a) i ,b i ), where i = 1, ..., N; Step 5: Determine whether the ellipses generated from the N sets of data in Step 4 intersect or exceed the model area established in Step 2. If the ellipses intersect or exceed the model area established in Step 2, repeat Step 4 until N sets of data that meet the conditions, i.e., the generated ellipses do not intersect or do not exceed the model area established in Step 2, are generated. Step Six: Based on the requirements for the first generation of individuals in the optimization algorithm, repeat Steps Four and Five M times to generate M sets of data; Step 7: Based on the cross-sectional analysis model established in Step 2 and the generated M sets of data, the geometric regions in the cross-sectional analysis model are subdivided and renumbered, the fuel phase and the additive phase are distinguished, the mesh is automatically generated using finite element software, and the mesh generation is completed. Step 8: Using the finite element numerical analysis method combined with parallel computing technology, complete the M sets of data generation and analysis heat transfer models or irradiation thermo-mechanical coupling analysis models in Step 7 and solve them to obtain the key variables of thermal conductivity distribution, temperature distribution, and maximum temperature of the model. Step 9: Based on the calculation results in Step 8, use an optimization algorithm to evaluate the merits of the M group designs, and then regenerate the M group data in conjunction with Steps 4 to 6. Step 10: Repeat steps 4 to 9 until the convergence condition of the optimization algorithm is met or the optimization objective is satisfied; Step 11: Output the phase structure and spatial geometric distribution information of the optimized composite core.

2. The method for optimizing the geometric structure and spatial distribution of added phases in a composite core according to claim 1, characterized in that: In step one, the volume fraction of the added phase in the given composite core shall not exceed 15%.

3. The method for optimizing the geometric structure and spatial distribution of added phases in a composite core according to claim 1, characterized in that: In step three, the number of discrete geometric numbers N for the added phase is determined to be 30, 50, 100, or 200.

4. The method for optimizing the geometric structure and spatial distribution of added phases in a composite core according to claim 1, characterized in that: The optimization algorithm in step six uses a genetic algorithm. In the genetic algorithm, an initial population is randomly generated, and the fitness function is used to determine the best geometric and distribution characteristics of each generation solution. The optimal solution is passed on to the next generation until the solution is converged. The fitness function is the ratio of the local peak temperature of the composite chip to the local peak temperature of the uranium dioxide chip.

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