Supercritical carbon dioxide reactor less group energy group structure optimization method

Abstract

The invention provides a supercritical carbon dioxide reactor energy group structure optimization method, which relates to the technical field of nuclear reactors, and adopts a particle swarm optimization (PSO) algorithm to optimize a neutron energy group structure of a supercritical carbon dioxide reactor so as to improve the calculation efficiency and ensure the calculation precision. The method comprises the following steps: firstly, constructing a one-dimensional hyper-component model, and calculating by utilizing a Serpent Monte Carlo program and a VI TAS deterministic theory neutron transport program to obtain a reference solution; secondly, optimizing the energy group structure through a PSO algorithm, iteratively updating the position and the speed of particles, and searching an optimal energy group structure; in the optimization process, each particle in the particle swarm represents a group of possible energy swarm boundaries, and the effectiveness of an optimization result is verified by comparing parameters such as keff, cross section, flux and power. According to the method, the neutron transport calculation precision of the supercritical carbon dioxide reactor can be improved, the rationality of power distribution of the whole reactor is kept, and an effective technical means is provided for optimization of the reactor of the type.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear reactors, and in particular to a method for optimizing the neutron transport energy group structure for a supercritical carbon dioxide reactor. Background Art

[0002] In the design of traditional supercritical carbon dioxide reactors, the calculation accuracy and efficiency of neutron energy spectrum are key issues. Existing neutron transport calculation methods, such as the "one-step method" and the "two-step method", have the problem of balancing efficiency and accuracy when dealing with complex core structures. Therefore, a new method is needed to optimize the energy group structure to improve the calculation efficiency and ensure the calculation accuracy.

[0003] As one of the candidate reactor types for the fourth generation of advanced nuclear energy systems, the gas-cooled fast reactor has the advantages of high coolant outlet temperature, low investment cost and simple system. Typical gas-cooled fast reactors usually use helium or supercritical carbon dioxide as coolant. Compared with helium coolant, supercritical carbon dioxide has the advantages of low core operating temperature, easy natural circulation and low cost. As one of the six types of fourth generation advanced nuclear energy system reactors, the supercritical carbon dioxide reactor (SCO2) has the advantages of being able to achieve efficient nuclear energy conversion and stable reaction control. It is suitable for aerospace, marine development and other fields and is one of the international research hotspots. In the core design, the "one-step method" of neutronics calculation is more accurate, but the calculation time is very long and it does not meet the conditions for engineering application. At present, the "two-step method" is the mainstream method. It includes component group constant calculation and core diffusion / transport calculation. Among them, the calculation of the small group cross section is an important part of the "two-step method" of nuclear reactor design. It is a bridge connecting the calculation of the small group constant of the component and the core diffusion / transport calculation. The division of the energy group determines the calculation accuracy of the small group homogenization cross section to a large extent and greatly affects the calculation efficiency of the whole core. The homogenization of the small group parameters mainly includes two parts: spatial homogenization and energy homogenization.

[0004] The energy distribution of neutrons in the core of a supercritical carbon dioxide reactor is wide, and each fuel assembly contains different types of grid elements, which makes neutron calculations have the characteristics of large neutron energy span and complex geometric structure in the macroscopic sense. Supercritical carbon dioxide reactors have great neutron differences from traditional pressurized water reactors and fast neutron reactors. The reactor core layout is relatively complex, and there is a strong spectrum interference effect between components. Due to the existence of spectrum interference effect in the core, the energy spectrum of a single component is quite different from the energy spectrum of the component in the multi-component model, which leads to the traditional energy group division method not being applicable to this type of reactor. Obviously, the most accurate and direct calculation method is to use probabilistic or deterministic methods to perform a one-time calculation on a finely described reactor. However, a large number of particles need to be sampled to reduce the calculation variance, which is bound to require expensive calculation costs. In contrast, the deterministic method directly performs numerical discretization and completes the solution calculation in the phase space composed of energy, space, and angle, but the memory requirements and calculation cost of the one-step calculation method for the whole core are also quite large.

[0005] A lot of in-depth research has been conducted at home and abroad on methods to improve the accuracy of small group cross-section data. In China, there were examples of simple application of the Monte Carlo method to calculate small group constants in the 1970s. In 2004, the China Nuclear Power Institute developed a general geometric fuel assembly group constant calculation program. The program focuses on the ability to use the Monte Carlo method to deal with complex geometric problems. It uses a multi-group cross-section library and cannot take advantage of the high accuracy of continuous energy. At present, the international community usually uses NJOY or AMPX programs to generate a wide group constant library closely related to practical problems using a three-step method. The first step is to process the continuous point cross-section to generate a fine group cross-section. Depending on the type of calculation problem, there are different choices for the energy group structure of the fine group. In addition, the China Institute of Atomic Energy has also developed a small group cross-section correction sequence CREC for the strong characteristics of the control rod non-uniform effect, and conducted cross-section correction calculations on the 12-group small group cross-sections of the safety rods and compensation rods of the Chinese sodium-cooled demonstration fast reactor. In response to the calculation needs of multi-group cross sections of fast reactors, North China Electric Power University has developed the MGGC program. This program is based on the multi-group database in MATXS format generated by the NJOY program, and generates multi-group cross sections related to the problem through the background cross section iteration method of the Bondarenko model. The multi-group cross section processing program TUL IP in the fast reactor neutronics calculation program SARAX developed by Xi'an Jiaotong University uses the principle of combining determinism with the Monte Carlo method to calculate multi-group cross sections, and the Monte Carlo method is used to generate multi-group cross sections. The above methods have one thing in common, that is, the calculation of multi-group cross sections is based on their own pre-made continuous point cross section databases, and these databases are processed by their internal programs and are usually not available to the outside world. Summary of the invention

[0006] The purpose of the present invention is to provide a method for optimizing the energy group structure in the neutron transport process of a supercritical carbon dioxide reactor, which can effectively improve the calculation accuracy and maintain a reasonable power distribution in the whole reactor.

[0007] The present invention adopts the following technical solution:

[0008] A method for optimizing the structure of a supercritical carbon dioxide reactor with a small energy group, characterized by comprising the following steps:

[0009] Step 1. construct a one-dimensional superassembly model, wherein the fuel assembly is composed of zirconium hydride as a moderator material and uranium dioxide fuel with an enrichment degree of 20%, and the fuel assembly and the coolant channels are alternately arranged to form a core with a periodic structure;

[0010] Step 2. Use the Serpent Monte Carlo program to simulate the one-dimensional supercomponent model to obtain homogenized cross sections and flux data for 33 energy groups, wherein the important processes of neutron-material interaction, including scattering, absorption and fission, are considered in the simulation process;

[0011] Step 3. Use the VI TAS deterministic neutron transport program to calculate the homogenized cross sections and flux data of the 33 energy groups, and obtain the initial keff value as a reference solution. The spherical harmonic function expansion method is used in the calculation process to improve the accuracy and efficiency of the calculation. The homogenization parameters of the few groups and the group calculation are shown in formula (1). Wherein, Σ and φ are the macroscopic cross section and neutron flux density, respectively. The subscripts x, g, and G represent the reaction type (such as fission and absorption), the fine group energy group number, and the few group energy group number, respectively.

[0012]

[0013] Step 4. Apply the particle swarm optimization (PSO) algorithm to optimize the energy group structure, where each particle represents a set of possible energy group boundaries. The optimal energy group structure is found by iteratively updating the position and velocity of the particle. The effect of the energy group structure on keff and the core power distribution are considered in the optimization process.

[0014] Step 5. Comprehensively verify the optimized energy group structure, including comparison of parameters such as keff, cross section, flux, and power, to ensure the calculation accuracy and rationality of the full-stack power distribution. A variety of different nuclear databases are used during the verification process to evaluate the impact of different nuclear data on the optimization results.

[0015] Furthermore, the PSO algorithm includes the following parameter settings:

[0016]

[0017] The inertia weight w, whose value is between 0.4 and 0.9, is used to control the update of particle velocity to balance the capabilities of global search and local search. In the present invention, w=0.8;

[0018] The learning constants c1 and c2, both of which have a value of 2, are used to adjust the ability of particles to search based on their own experience and group experience, where c1 represents the ability of particles to search based on their own experience, and c2 represents the ability of particles to search based on group experience;

[0019] The random numbers r1 and r2 have a value range of [0,1] and are used to introduce randomness when updating the particle speed and position to prevent the algorithm from converging to a local optimal solution too early. The random numbers are regenerated in each iteration to maintain the randomness of the algorithm.

[0020] Furthermore, the energy group structure optimization step includes:

[0021] Initialize the particle swarm, where each particle represents a set of energy group boundaries, and the initial positions are randomly distributed within the possible energy group boundaries, and the initial velocity is zero to avoid rapid fluctuations in the initial stage;

[0022] According to the current position of each particle in the particle group, the corresponding energy group cross section and flux are calculated, where the calculation of cross section and flux takes into account all important processes of the interaction between neutrons and materials;

[0023] The keff value of the energy group structure represented by each particle is calculated using the VI TAS program, where the calculation of the keff value takes into account the core geometry and material distribution;

[0024] Update the individual optimal solution (p nuclear reactor est) and the global optimal solution (g nuclear reactor est) of each particle, where the individual optimal solution is the optimal solution found by the particle itself in history, and the global optimal solution is the optimal solution found by all particles in the entire particle swarm;

[0025] According to the individual optimal solution and the global optimal solution, the speed and position of the particle are updated, where the update of the speed and position takes into account the inertia, individual experience and group experience of the particle;

[0026] Repeat steps 3 to 5 until a predetermined number of iterations is met or a predetermined error threshold is reached, wherein the number of iterations and the error threshold are set according to the complexity of the problem and computing resources.

[0027] Furthermore, the comprehensive verification steps include:

[0028] Compare the optimized energy group structure with the keff value of the reference solution, calculate the error, and ensure that the error is within 0.1% to verify the accuracy of the optimization method;

[0029] Analyze the cross-section, flux, and power distribution corresponding to the optimized energy group structure and compare them with the reference solution to ensure that the relative error does not exceed 5% to verify the effectiveness of the optimization method;

[0030] Apply the optimized energy group structure in the whole reactor model, calculate the power distribution of the whole reactor, and compare it with the reference solution to ensure that the maximum relative error of the power distribution does not exceed 2%, so as to verify the applicability of the optimization method in the whole reactor model;

[0031] Ensure that the keff error of the optimized energy group structure in the full-stack model is within an acceptable range, for example, no more than 300 pcm, to meet the accuracy requirements of engineering applications;

[0032] Ensure that the maximum relative error between the power distribution of the optimized energy group structure in the full reactor model and the reference solution is within an acceptable range, for example, not exceeding 5%, to ensure the rationality of the power distribution of the core.

[0033] Beneficial effects of the present invention:

[0034] The present invention optimizes the energy group structure of the supercritical carbon dioxide reactor by using the PSO algorithm, and the optimization result can effectively improve the calculation accuracy and maintain a reasonable power distribution in the whole reactor. This provides an effective method for the design and optimization of supercritical carbon dioxide reactors, breaking through the calculation efficiency bottleneck of traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of a model of the present invention;

[0036] Figure 2 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] In a specific embodiment of the present invention, each step of the method for optimizing the neutron transport energy group structure of a supercritical carbon dioxide reactor will be described in detail, including model construction, algorithm implementation, parameter setting, calculation process, result verification, etc.

[0039] In order to implement the supercritical carbon dioxide reactor neutron transport energy group structure optimization method of the present invention, the following is a detailed embodiment, including model construction, algorithm implementation, parameter setting, calculation process, result verification and other steps.

[0040] 1. Model construction

[0041] A one-dimensional supercomponent model is constructed to simulate the core part of a supercritical carbon dioxide reactor. The steps of model construction are as follows:

[0042] a. Geometric structure design: Design a super-assembly model containing 22 components, in which fuel assemblies and coolant channels are arranged alternately to form a core with a periodic structure. Each fuel assembly consists of 61 rods, including 13 moderator rods and 48 fuel rods. The coolant channels are arranged around the fuel assembly.

[0043] b. Nuclear Reactor Material Property Assignment: Assign material properties to each component in the model. The fuel assembly is composed of zirconium hydride (ZrH1.6) as a moderator and uranium dioxide (UO2) with an enrichment of 20% as fuel. The coolant channel is filled with supercritical carbon dioxide.

[0044] c. Boundary condition definition: Define the boundary conditions of the model, including vacuum boundary and total reflection boundary, to simulate the physical environment of the actual reactor.

[0045] 2. Monte Carlo Simulation

[0046] The constructed one-dimensional supercomponent model was simulated using the Serpent Monte Carlo procedure to obtain the homogenized cross sections and flux data for 33 energy groups. During the simulation, the following steps were considered:

[0047] a. Physical process definition: Define all important processes of neutron interaction with materials, including elastic scattering, inelastic scattering, capture and fission.

[0048] b. Nuclear reactor simulation parameter setting: Set the simulation parameters, including the number of particles (100,000 neutrons), number of iterations (until statistical convergence is reached), energy range (from 1E-11 to 20MeV), etc., to ensure the statistical accuracy of the simulation results.

[0049] c. Run the simulation: Run the Serpent program and collect simulation results, including neutron flux, macroscopic cross section, etc.

[0050] 3. Deterministic neutron transport calculations

[0051] The VITAS deterministic neutron transport code is used to calculate the homogenized cross section and flux data of the 33 energy group obtained from the Serpent program to obtain the initial keff value. The calculation process includes:

[0052] a. Data conversion: Convert the data output by Serpent into a format acceptable to the VITAS program.

[0053] b. Nuclear reactor calculation parameter setting: Set the calculation parameters of the VITAS program, including geometric conditions, boundary conditions, etc.

[0054] c. Run calculations: Run the VITAS program to perform deterministic neutron transport calculations and obtain the keff value.

[0055] 4. Implementation of Particle Swarm Optimization Algorithm

[0056] The particle swarm optimization (PSO) algorithm is used to optimize the energy group structure. The steps of the algorithm implementation are as follows:

[0057] a. Particle swarm initialization: Initialize the particle swarm, where each particle represents a set of possible energy group boundaries and is randomly distributed within the possible range of the energy group boundaries.

[0058] b. Nuclear reactor parameter definition: Define the parameters of the PSO algorithm, including inertia weight (w = 0.8), learning constant (c1 = c2 = 2) and random number (r1, r2 in the range [0, 1]).

[0059] c. Energy group cross section and flux calculation: Calculate the corresponding energy group cross section and flux for each particle, and use the VITAS program to calculate the keff value.

[0060] d. Optimal solution update: Update the individual optimal solution (p nuclear reactor est) and the global optimal solution (g nuclear reactor est) of each particle.

[0061] e. Speed ​​and position update: Update the speed and position of the particle according to the individual optimal solution and the global optimal solution.

[0062] f. Iteration process: Repeat steps c to e until a predetermined number of iterations (30 times) is met or a predetermined error threshold (0.1%) is reached.

[0063] The present invention optimizes the energy group structure of a supercritical carbon dioxide reactor by using a PSO algorithm, and the optimization result can effectively improve the calculation accuracy and maintain a reasonable power distribution in the whole reactor. It provides an effective method for the design and optimization of supercritical carbon dioxide reactors, breaking through the calculation efficiency bottleneck of traditional methods.

[0064] 5. Result Verification

[0065] The optimized energy group structure is fully verified, including the following steps:

[0066] a. keff value comparison: Compare the keff value of the optimized energy group structure with that of the reference solution, calculate the error, and ensure that the error is within 0.1%.

[0067] b. Analysis of nuclear reactor cross-section, flux, and power distribution: Analyze the cross-section, flux, and power distribution corresponding to the optimized energy group structure, and compare them with the reference solution to ensure that the relative error does not exceed 5%.

[0068] c. Application of the whole-stack model: Apply the optimized energy group structure in the whole-stack model, calculate the power distribution of the whole stack, and compare it with the reference solution to ensure that the maximum relative error of the power distribution does not exceed 2%.

[0069] d. keff error verification: Ensure that the keff error of the optimized energy group structure in the full stack model is within an acceptable range, for example, not exceeding 300 pcm.

[0070] e. Verification of rationality of power distribution: Ensure that the maximum relative error between the power distribution of the optimized energy group structure in the full-stack model and the reference solution is within an acceptable range, for example, not exceeding 5%.

[0071] In an embodiment of the present invention, a method for optimizing the neutron transport energy group structure for a supercritical carbon dioxide reactor is proposed. The method achieves efficient optimization of the reactor energy group structure by combining the construction of a one-dimensional supercomponent model, Monte Carlo simulation, deterministic neutron transport calculation, and particle swarm optimization (PSO) algorithm.

[0072] First, the model takes into account the interaction between fuel assemblies, coolant channels and reflectors, providing an accurate geometric and material basis for subsequent neutron transport calculations. Secondly, the application of the PSO algorithm is one of the core innovations of the present invention. By simulating the collective behavior of particle swarms, the optimal energy group structure can be effectively searched, thereby significantly improving the calculation efficiency while ensuring the calculation accuracy. More importantly, the optimization results are fully verified, including the comparison of keff values, the analysis of cross sections and fluxes, the application of the full stack model, etc. These verification steps ensure the reliability and practicality of the optimization method, and prove the effectiveness of the present invention in practical engineering applications.

Claims

1. A method for optimizing the energy group structure of a supercritical carbon dioxide reactor, characterized in that: The following steps are involved: Step 1. construct a one-dimensional superassembly model, the model comprising at least one fuel assembly and at least one coolant channel, and at least one reflector assembly, wherein the fuel assembly is composed of zirconium hydride as a moderator material and uranium dioxide fuel with an enrichment degree of 20%, and the fuel assembly and the coolant channel are alternately arranged to form a core with a periodic structure; Step 2. Use the Serpent Monte Carlo program to simulate the one-dimensional supercomponent model to obtain homogenized cross sections and flux data for 33 energy groups, wherein all important processes of neutron-material interaction are considered in the simulation process, including elastic scattering, inelastic scattering, capture and fission; Step 3. Calculate the homogenized cross sections and flux data of the 33 energy groups using the VI TAS deterministic neutron transport program to obtain an initial keff value as a reference solution, wherein the spherical harmonic function expansion method is used in the calculation process to improve the accuracy and efficiency of the calculation; Step 4. Apply the particle swarm optimization (PSO) algorithm to optimize the energy group structure, where each particle represents a set of possible energy group boundaries. The optimal energy group structure is found by iteratively updating the position and velocity of the particle. The effect of the energy group structure on keff and the core power distribution are considered in the optimization process. Step 5. Comprehensively verify the optimized energy group structure, including comparison of parameters such as keff, cross section, flux, and power, to ensure the calculation accuracy and rationality of the full-stack power distribution. A variety of different nuclear databases are used during the verification process to evaluate the impact of different nuclear data on the optimization results.

2. A supercritical carbon dioxide reactor energy group structure optimization method according to claim 1, characterized in that: The PSO algorithm includes the following parameter settings: The inertia weight w, whose value is between 0.4 and 0.9, is used to control the update of particle velocity to balance the capabilities of global search and local search. The inertia weight gradually decreases with the increase of the number of iterations to improve the local search capability of the algorithm in the later stage of the search; The learning constants c1 and c2, both of which have a value of 2, are used to adjust the ability of particles to search based on their own experience and group experience, where c1 represents the ability of particles to search based on their own experience, and c2 represents the ability of particles to search based on group experience; The random numbers r1 and r2 have a value range of [0,1] and are used to introduce randomness when updating the particle speed and position to prevent the algorithm from converging to a local optimal solution too early. The random numbers are regenerated in each iteration to maintain the randomness of the algorithm.

3. The method for optimizing the energy group structure of a supercritical carbon dioxide reactor according to claim 1, characterized in that: The energy group structure optimization step comprises: Initialize the particle swarm, where each particle represents a set of energy group boundaries, and the initial positions are randomly distributed within the possible energy group boundaries, and the initial velocity is zero to avoid rapid fluctuations in the initial stage; According to the current position of each particle in the particle group, the corresponding energy group cross section and flux are calculated, where the calculation of cross section and flux takes into account all important processes of the interaction between neutrons and materials; The VI TAS program is used to calculate the keff value of the energy group structure represented by each particle, where the calculation of the keff value takes into account the core geometry and material distribution.

4. A supercritical carbon dioxide reactor energy group structure optimization method according to claim 3, characterized in that: The energy group structure optimization step further comprises: Update the individual optimal solution (p nuclear reactor est) and the global optimal solution (g nuclear reactor est) of each particle, where the individual optimal solution is the optimal solution found by the particle itself in history, and the global optimal solution is the optimal solution found by all particles in the entire particle swarm; According to the individual optimal solution and the global optimal solution, the speed and position of the particle are updated, where the update of the speed and position takes into account the inertia, individual experience and group experience of the particle; Steps 3 to 5 are repeated until a predetermined number of iterations is met or a predetermined error threshold is reached, wherein the number of iterations and the error threshold are set according to the complexity of the problem and computing resources.

5. The method for optimizing the energy group structure of a supercritical carbon dioxide reactor according to claim 1, characterized in that: The comprehensive verification steps described include: Compare the optimized energy group structure with the keff value of the reference solution, calculate the error, and ensure that the error is within 5% to verify the accuracy of the optimization method; Analyze the cross-section, flux, and power distribution corresponding to the optimized energy group structure and compare them with the reference solution to ensure that the relative error does not exceed 5% to verify the effectiveness of the optimization method; The optimized energy group structure is applied in the full-reactor model, and the power distribution of the whole reactor is calculated and compared with the reference solution to ensure that the maximum relative error of the power distribution does not exceed 5%, so as to verify the applicability of the optimization method in the full-reactor model.

6. The method for optimizing the energy group structure of a supercritical carbon dioxide reactor according to claim 1, characterized in that: The comprehensive verification steps also include: Ensure that the keff error of the optimized energy group structure in the full-stack model is within an acceptable range, for example, no more than 300 pcm, to meet the accuracy requirements of engineering applications; Ensure that the maximum relative error between the power distribution of the optimized energy group structure in the full reactor model and the reference solution is within an acceptable range, for example, not exceeding 5%, to ensure the rationality of the power distribution of the core.

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