A method for optimizing a hexagonal silicon carbide ceramic core structure

Abstract

A hexagonal silicon carbide ceramic core structure optimization method, the method is suitable for the hexagonal core structure involved in space nuclear power reactor, accelerator driven subcritical nuclear energy system, modular small reactor and other advanced reactors. The structure optimization method comprises the following steps: 1. Establishing a geometric model: setting the geometric size of the hexagonal silicon carbide ceramic core, setting the size, number and position of the fuel element or the coolant channel; 2. Adding a multi-physics field calculation module: according to the service condition, adding the irradiation field, temperature field, flow field and solid stress-strain field of the hexagonal silicon carbide ceramic core; 3. Setting the calculation domain boundary: setting the neutron flux density and irradiation time in the core, the coolant inlet temperature, the core volume heat source input, the coolant inlet velocity, and the material properties of silicon carbide; 4. Setting and parallel solving parameters: setting the number of parallel jobs and the number of cores occupied by a single job; 5. Carrying out the structure optimization design of the hexagonal silicon carbide ceramic core.

Description

Technical Field

[0001] This invention belongs to the field of hexagonal prism core structure optimization technology, specifically relating to a method for optimizing a hexagonal prism silicon carbide ceramic core structure. Background Technology

[0002] Unlike the square core structure used in most existing reactors, hexagonal prism cores typically employ a prism-shaped porous matrix as the core structural component, with fuel elements or coolant channels filled within the pores. Each coolant channel is independent, resulting in advantages such as small size, high structural stability, good neutron economy, high heat transfer efficiency, and strong scalability. This makes them widely applicable in various advanced reactor types, including space nuclear power reactors, accelerator-driven subcritical nuclear energy systems, and modular small modular reactors. Meanwhile, traditional in-core structural support materials such as zirconium alloys and stainless steel cannot meet the technical requirements of higher service temperatures and greater service doses in next-generation nuclear energy systems. Silicon carbide (SiC) ceramics, due to their excellent high-temperature resistance (service temperatures up to 1000-1300℃), high radiation stability (maximum radiation dose up to 150-200 dPa), excellent high-temperature chemical inertness and high-temperature strength, and strong structural stability, have become a research hotspot for novel core structural materials.

[0003] To achieve efficient and scientific design of a hexagonal prism-shaped silicon carbide ceramic reactor core, it is first necessary to conduct coupled analysis of physical fields such as irradiation field, temperature field, flow field, and solid stress-strain field. Secondly, based on the established nuclear / thermal / fluid / solid multiphysics model and solution method for the hexagonal prism fuel assembly, and using core structure optimization methods, under the condition that specific characteristic functions remain constant, a suitable normalized objective function is selected to obtain the optimal combination of design schemes for the hexagonal prism-shaped silicon carbide ceramic reactor core.

[0004] Domestic and international research

[0005] In the field of nuclear engineering, optimization of nuclear fuel has mostly focused on the nuclear fuel cycle and the loading and arrangement of nuclear fuel in the reactor, while research on optimization of reactor core components is relatively limited.

[0006] For example, in the U.S. Department of Energy’s published report, “Transformational Challenge Reactor Design Characteristics, USD Department of Energy, 2020,” the authors conducted relevant analysis and calculations on a hexagonal prism silicon carbide core structure used in space reactors using numerical simulation. However, the design approach they adopted still followed the traditional “modeling-calculation-analysis” process. For core designs with different power and structures, they only obtained simple parameter comparisons and did not conduct optimization analysis on the core structure.

[0007] In the paper "Jaehyeok Doh, Young Doo Kwon, Jongsoo Lee. Approximate Multi-Objective Optimization of Gap Size of PWR Annular Nuclear Fuels, Journal of the Korean Society for Precision Engineering, 2015", the authors used the fast non-dominated sorting algorithm NSGA-II and generated response surface models of the objective and constraint functions using surrogate model-based central combinatorial design of experiments (CCD) and optimal design to perform multi-objective optimization of the gap size of the annular fuel in a pressurized water reactor. However, this method uses a large number of theoretical assumptions and surrogate models to simplify the problem, resulting in lower accuracy compared to directly performing numerical simulations to calculate the objective function values.

[0008] For example, in the paper "Mohamed E. Wahed, Wesam Z. Ibrahim. Neural network and genetic algorithms for optimizing the plate element of Egyptian research reactor problems, Nuclear engineering and design, 2010," the authors used a genetic algorithm to optimize the cross-sectional dimensions of the plate fuel element in the Egyptian research reactor ET-RR-2. Using minimizing fuel plate mass and deformation as the objective function, and with the constraints of maximizing normal stress to meet strength requirements and ensuring non-negativity of cross-sectional dimensions, a simplified model was used for basic design optimization. However, the geometric model was relatively coarse, and it failed to achieve parametric modeling and parallel computation of the optimization algorithm.

[0009] In summary, research on engineering design optimization of reactor core structures is limited both domestically and internationally. Current optimization designs mostly rely on simple parametric analysis and comparison of results. These methods often only consider the impact of a single factor on the core structure and performance at a time, failing to simultaneously account for the combined effects of multiple structural parameters or factors on core performance. Therefore, to improve the fidelity and reliability of the objective function calculation results during core design, it is essential to develop a structural optimization method for hexagonal prism-shaped silicon carbide ceramic reactor core structures. Summary of the Invention

[0010] To address the problems existing in the prior art, the present invention aims to provide an optimization method for hexagonal prism-shaped silicon carbide ceramic core structure. This method is applicable to hexagonal prism-shaped core structures involved in advanced reactors such as space nuclear power reactors, accelerator-driven subcritical nuclear energy systems, and modular small reactors.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] An optimization method for hexagonal prism-shaped silicon carbide ceramic core structures is disclosed. This method is applicable to hexagonal prism-shaped silicon carbide ceramic core structures involved in space nuclear power reactors, accelerator-driven subcritical nuclear energy systems, and modular small modular reactors. The optimization method utilizes accurate and efficient models and multiphysics field settings, considering multi-directional coupling and global variable transfer between various physics fields. Combining fully coupled numerical solution methods and multi-objective structural optimization algorithms, it achieves structural optimization of the hexagonal prism-shaped silicon carbide ceramic core, obtaining the optimal set of schemes for the selected objective function. The steps are as follows:

[0013] 1. Establish a geometric model: Based on the actual geometry of the hexagonal prism-shaped silicon carbide ceramic reactor core, establish a geometric model of the core and set its geometric dimensions. 2. Add a multiphysics calculation module: Based on the actual service conditions of the environment in which the hexagonal prism-shaped silicon carbide ceramic reactor core is located, add a physical field calculation domain for the irradiation field, temperature field, flow field, and solid stress-strain field of the core. 3. Set the calculation domain boundary: Set the core neutron flux density and irradiation time; coolant inlet temperature, core volume heat source input; coolant inlet velocity; assign material properties to silicon carbide. 4. Set parallel solution parameters: Set the number of parallel case kernels, the number of kernels per job, and allocate the number of kernels for each job. 5. Conduct structural optimization design of the hexagonal prism-shaped silicon carbide ceramic reactor core.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. Methodological Innovation. The multi-objective optimization algorithm developed in this invention integrates competing or conflicting key objective functions to extract key factors and features in structural design. With the help of scientific algorithms, it forms an accurate and efficient quantitative optimization method to achieve the optimization analysis of hexagonal prism silicon carbide ceramic core structure design.

[0016] 2. Independent Model. The hexagonal prism-shaped silicon carbide ceramic reactor core in this invention adopts parametric modeling, which does not limit the size and form of the core, the material, or the size, number, and location of fuel elements or coolant channels. Appropriate multi-objective optimization algorithms can be selected according to design requirements. The optimization method is highly versatile and offers a large degree of freedom.

[0017] 3. The structural optimization method involved in this invention is applicable to the hexagonal prism core structure involved in advanced reactors such as space nuclear power reactors, accelerator-driven subcritical nuclear energy systems, and modular small reactors, and has wide applicability.

[0018] 4. In the optimization process, the present invention can perform parallel computer solution as needed. Compared with the serial solution used in the traditional optimization process, it greatly reduces the time to obtain the objective function value. In addition, the objective function is normalized during the optimization process, which directly improves the efficiency of the entire multi-objective optimization process. Attached Figure Description

[0019] Figure 1 Flowchart of the optimization method for hexagonal prism-shaped silicon carbide ceramic core structure;

[0020] Figure 2 This is a schematic diagram of the results obtained by using the example settings in the operation steps of this invention (maximum shear stress of SiC - maximum circumferential stress of SiC - Pareto front of the highest core temperature). Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings.

[0022] like Figure 1 As shown, the process of the optimization method for the hexagonal prism-shaped silicon carbide ceramic core structure proposed in this invention is as follows:

[0023] Step 1: Establish the geometric model. Based on the actual geometry of the hexagonal prism-shaped silicon carbide ceramic reactor core, establish a geometric model of the hexagonal prism-shaped silicon carbide ceramic reactor core and set its geometric dimensions, including but not limited to: the height of the hexagonal prism-shaped silicon carbide ceramic reactor core, the distance between opposite sides of the cross-section of the regular hexagon; and the size, number, and location of the fuel elements or coolant channels.

[0024] Step 2: Add a multiphysics calculation module. Based on the actual service conditions of the hexagonal prism-shaped silicon carbide ceramic reactor core, add a multiphysics calculation module to simulate the service behavior of the hexagonal prism-shaped silicon carbide ceramic reactor core. Taking into account the complexity of the operating environment within the nuclear power system and the structural characteristics of the hexagonal prism-shaped silicon carbide ceramic reactor core, and considering the operating conditions, irradiation effects, and fuel characteristics, add physical field calculation domains for irradiation field, temperature field, flow field, and solid stress-strain field based on the geometric model established in Step 1.

[0025] Step 3: Setting the computational domain boundary. Steps 1 and 2 respectively determined the geometric model and physical field computational domain of the hexagonal prism-shaped silicon carbide ceramic core. Based on Steps 1 and 2, Step 3 further sets the boundary of the physical field computational domain, including but not limited to: setting the core neutron flux density and irradiation time in the irradiation field; setting the coolant inlet temperature and core volume heat source input in the temperature field; and setting the flow field...

[0026] The coolant inlet velocity is set in the middle; the material properties of silicon carbide are imparted in the solid stress-strain field.

[0027] Step 4: Set Parallel Solving Parameters. After completing Steps 1 through 3, simulation calculations can be performed on the hexagonal prism-shaped silicon carbide ceramic core. To improve solving efficiency, it is necessary to set computer parallel solving parameters, including but not limited to: allocating the number of parallel instance kernels and setting the number of kernels per job.

[0028] Steps 1 to 4 completed the geometric modeling of the hexagonal prism-shaped silicon carbide ceramic core, the addition of the multiphysics calculation module, the setting of the computational domain boundary, and the setting of parallel solution parameters, respectively. A performance evaluation method for the hexagonal prism-shaped silicon carbide ceramic core was developed using numerical simulation, providing a foundation for the optimized design of the hexagonal prism-shaped silicon carbide ceramic core structure.

[0029] Step 5: Structural optimization design of the hexagonal prism-shaped silicon carbide ceramic core. Further, step 5 specifically involves:

[0030] Step 5.1: Modeling and Standardization of the Multi-Objective Optimization Problem. The optimization problem of the hexagonal prism-shaped silicon carbide ceramic core structure is considered as a multi-objective optimization problem, consisting of n decision variables, m objective functions, and p constraints. The meanings and values ​​of each parameter are as follows:

[0031] minF(X)=[f1(X),f2(X),……f m (X)] (1)

[0032] X = (x1, x2, ..., x) n (2)

[0033] g i (X)≤0, i=1,2……p (3)

[0034] In the formula:

[0035] minF(X) represents minimizing the objective function;

[0036] f i (X) represents the i-th objective function, where i takes the values ​​1, 2, ..., m;

[0037] X represents the decision variable consisting of n optimization variables;

[0038] g i (X) represents the i-th constraint, where i can be 1, 2, ..., p.

[0039] The criteria for multi-objective optimization follow Pareto dominance, meaning that the decision variables are U = (u1, u2, ..., u3). n ) and decision variables V = (v1, v2, ..., v n If the following conditions are met:

[0040]

[0041]

[0042] In the formula:

[0043] f i (U) — Represents the i-th objective function composed of decision variables U;

[0044] f i (V) — Represents the i-th objective function composed of decision variables V;

[0045] f j (U) represents the j-th objective function composed of decision variables U;

[0046] f j (V) represents the j-th objective function composed of decision variables V.

[0047] If decision variable U is superior to decision variable V, then U is said to dominate V, denoted as U < V. If there is no decision variable that can dominate U, then decision variable U is a Pareto optimal solution.

[0048] Step 5.2: Set the initial parameters of the optimization algorithm, including but not limited to: a suitable multi-objective optimization algorithm, the number of populations, the number of generations of population evolution, the number of optimization objective functions and variables.

[0049] Step 5.3: Using standard genetic algorithms, perform selection, crossover, and mutation operations on the population and its individuals. Using existing standard genetic algorithms, select high-performing individuals from the current population as parents to generate the next generation. Mimic the gene recombination process of natural reproduction, passing on the original superior genotypes to the offspring while maintaining as much diversity as possible within the population and preventing premature convergence.

[0050] Step 5.4: Genetic operations generate a new generation of individuals in the population, obtain the objective function values ​​of the individuals, and screen for the normalized optimal solution. Set the member functions required for the optimization result analysis, including but not limited to: the number of optimization variables, the upper and lower limits of the optimization variables, and the encoding method.

[0051] Step 5.5: Determine whether the convergence condition is met. The determination criteria are as follows:

[0052]

[0053] In the formula:

[0054] ε n —This represents the result of the nth iteration;

[0055] ε n-1 —This represents the settlement result of the (n-1)th iteration;

[0056] a — indicates the absolute error set.

[0057] Step 5.6: Stop optimization when the convergence condition is met, and output the optimization results, including but not limited to: the set of optimal combination schemes of optimization variables obtained from core structure optimization and the corresponding objective function values.

[0058] The following is combined with Figure 2 The process of this invention will be further described in detail with specific examples, and typical results will be explained:

[0059] 1. Set the dimensional parameters of the hexagonal silicon carbide ceramic core: height is 50cm, and the distance between opposite sides of the cross-section is 20cm; set the size, number and location of fuel element or coolant channels: the diameter of the fuel element or coolant channel is 12mm, the number of reserved channels for fuel elements is 12, the number of reserved channels for coolant channels is 12, and the fuel element or coolant channels are evenly distributed in the cross-section of the core.

[0060] 2. Add a multiphysics calculation module for simulating the service behavior of hexagonal prism silicon carbide ceramic reactor cores, and add physical field calculation domains for irradiation field, temperature field, flow field, and solid stress-strain field respectively.

[0061] 3. The neutron flux density in the reactor core is set at 10-1 in the irradiation field. 18 n / m 2 •s, irradiation time is 3 years; the coolant inlet temperature in the temperature field is set at 300K, and the core volume heat source is 1×10⁹ W / m². 3 The coolant inlet velocity in the flow field is set to 5 m / s; the density of the silicon carbide ceramic in the solid stress-strain field is set to 3000 kg / m³. 3 It has a Poisson's ratio of 0.23, a Young's modulus of 650 GPa, a thermal conductivity of 8 W / m·K, and a porosity of 0.98.

[0062] 4. Set the number of parallel jobs to 30 and the number of kernels per job to 2, meaning that a single computation will use 30 × 2 = 60 kernels.

[0063] 5. Set the number of optimization objective functions to 3, where the first optimization objective function is the maximum shear stress of SiC, the second optimization objective function is the maximum circumferential stress of SiC, and the third optimization objective function is the highest core temperature.

[0064] Set the initial parameters of the optimization algorithm: the multi-objective optimization algorithm is the NSGAII algorithm, the population size is 30, and the population evolution generation is 15.

[0065] Set the number of optimization variables to 5; set the upper and lower limits of the optimization variables: limit the core height to 0.5 to 2 times the initial height, the diameter range of fuel element or coolant channel is 12 to 14 mm, the number of reserved holes for fuel element is 10 to 12, and the number of reserved holes for coolant channel is 10 to 12.

[0066] Obtain the objective function values ​​for individual populations; set the absolute error value to 10. -5 The Pareto front, composed of the three optimization objective functions—maximum shear stress of SiC, maximum circumferential stress of SiC, and highest core temperature—is as follows: Figure 2 As shown in the figure, each point represents the calculated optimal combination of hexagonal prism-shaped silicon carbide ceramic cores, i.e., the optimal structure of the hexagonal prism-shaped silicon carbide ceramic core.

[0067] The structural optimization method involved in this invention can quickly provide the optimal set of structural parameters that meet the engineering design requirements for hexagonal prism silicon carbide ceramic core structures under multi-physics field environments and core assembly scale conditions, with different optimization objectives and constraints.

[0068] The above content is a further detailed description of the present invention in conjunction with specific optimized embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A method of hexagonal silicon carbide ceramic core structure optimization, characterized by: The method is suitable for the six-prism type silicon carbide ceramic core structure involved in a space nuclear power reactor, an accelerator driven subcritical nuclear energy system and a modular small reactor advanced reactor; the optimization method considers multi-directional coupling and global variable transmission among various physical fields through an accurate and efficient model and multi-physical field setting, combines a full-coupling numerical solving method and a multi-objective structure optimization algorithm, realizes structure optimization of the six-prism type silicon carbide ceramic core, and obtains a best scheme set of a selected target function; the steps are as follows: Step 1: establishing a geometric model: according to the real geometry of the six-prism type silicon carbide ceramic core, a geometric model of the six-prism type silicon carbide ceramic core is established, and the geometric size of the six-prism type silicon carbide ceramic core is set; Step 2: adding a multi-physical field calculation module: according to the real service condition of the environment where the six-prism type silicon carbide ceramic core is located, a multi-physical field calculation module for simulating the service behavior of the six-prism type silicon carbide ceramic core is added; considering the complexity of the running environment in the nuclear power system and the special structure of the six-prism type silicon carbide ceramic core, the physical field calculation domain including the irradiation field, the temperature field, the flow field and the solid stress and strain field is added on the basis of the geometric model established in step 1 according to the running condition, the irradiation effect and the fuel characteristics; Step 3: setting the calculation domain boundary: the geometric model and the physical field calculation domain of the six-prism type silicon carbide ceramic core are determined in steps 1 and 2 respectively; on the basis of steps 1 and 2, the physical field calculation domain boundary is further set in step 3; Step 4: setting parallel solving parameters: after steps 1 to 3 are completed, the simulation calculation of the six-prism type silicon carbide ceramic core is carried out; in order to improve the solving efficiency, the computer parallel solving parameters need to be set, including the number of parallel calculation cores and the number of single job cores; Step 5: structure optimization design of the six-prism type silicon carbide ceramic core: specifically including the following steps: Step 5.1, modeling and standard establishment of the multi-objective optimization problem: the six-prism type silicon carbide ceramic core structure optimization problem is regarded as a multi-objective optimization problem, which is composed of n decision variables, m objective functions and p constraint conditions; the meanings and values of the parameters are as follows: In the formula: minF(X) = [fl(X), f2(X)... f m (X)] (1) X = (x1, x2... x n ) (2) g i (X)≤0,i = 1,2...p (3) minF(X) represents the minimization objective function; X represents the decision variable composed of n optimization variables; f i (X) - denotes the i-th objective function, i takes 1, 2, …, m; In the formula: g i (X) - denotes the i-th constraint condition, i takes 1, 2, …, p; The standard for multi-objective optimization follows the Pareto dominance, i.e. respectively the decision variables U = (u1, u2... u n ) and the decision variables V = (v1, v2... v n ) satisfy: u1 < v1 and u2 > v2 and... and un > vn If the decision variable U is superior to the decision variable V, it is called that U dominates V, and is recorded as U f i (U) - denotes the i-th group of objective functions of which the decision variable U is composed; f i (V) - denotes the i-th group of objective functions of which the decision variable V is composed; f j (U) - denotes the jth group of objective functions of which the decision variable U is a component; f j (V) - denotes the jth group of objective functions in which the decision variables V are involved. Step 5.2, setting the initial parameters of the multi-objective optimization algorithm, including the population size, the population evolution algebra, the number of optimization objective functions and the variables; Step 5.3, referring to the standard genetic algorithm, the selection, crossover and mutation operations are carried out on the population and the individuals in the population; through the standard genetic algorithm, the individuals with excellent performance in the current population are selected as the parents to generate a new generation of population, and the gene recombination process in the natural reproduction is imitated to inherit the original excellent genotype to the offspring, while the individual diversity in the population is maintained as much as possible to prevent premature convergence; ​ Step 5.4, genetic operation generates new generation of population individuals, obtains population individual objective function values, screens normalized optimal solution; set member functions required for optimization result analysis. Step 5.5, determine whether the convergence condition is met, the determination criterion is: In the formula: ε n - indicates the settlement result of the nth iteration; ε n-1 - indicates the result of the settlement of the (n-1)th iteration; a represents the set absolute error. Step 5.6, stop optimization when the convergence condition is met, and output the optimization result, including the optimized variable optimal combination scheme set obtained by the core structure optimization and the corresponding objective function value.

2. The hexagonal silicon carbide ceramic core structure optimization method of claim 1, wherein: The geometric size of the hexagonal prism type silicon carbide ceramic core set in step 1 includes the height of the hexagonal prism type silicon carbide ceramic core, the distance between opposite sides of the cross-section regular hexagon; the size, number and position of the fuel element or the coolant channel.

3. The hexagonal silicon carbide ceramic core structure optimization method of claim 1, wherein: The boundary of the physical field calculation domain is set in step 3, including the setting of the neutron flux density in the core and the irradiation time in the irradiation field; the setting of the coolant inlet temperature, the core volume heat source input in the temperature field; the setting of the coolant inlet velocity in the flow field; the setting of the material properties of silicon carbide in the solid stress-strain field.

4. The hexagonal silicon carbide ceramic core structure optimization method of claim 1, wherein: The multi-objective optimization algorithm in step 5.2 is the NSGAII algorithm.

5. The hexagonal silicon carbide ceramic core structure optimization method of claim 1, wherein: In step 5, the number of optimization objective functions is set to 3, wherein the first optimization objective function is the maximum shear stress of SiC, the second optimization objective function is the maximum hoop stress of SiC, and the third optimization objective function is the highest temperature of the core.

6. The hexagonal silicon carbide ceramic core structure optimization method of claim 1, wherein: In step 5.4, the member functions required for optimization result analysis are set, including the number of optimization variables, the upper and lower limits of optimization variables and the encoding mode.

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