A method for optimizing the few-group energy group structure of a supercritical carbon dioxide reactor

Abstract

The application provides a supercritical carbon dioxide reactor energy group structure optimization method, and relates to the technical field of nuclear reactors, which adopts a particle swarm optimization algorithm (PSO) to optimize the neutron energy group structure of a supercritical carbon dioxide reactor, so as to improve the calculation efficiency and ensure the calculation accuracy. The method firstly constructs a one-dimensional supercomponent model, and uses a Serpent Monte Carlo program and a VI TAS deterministic neutron transport program to calculate a reference solution. Then, the PSO algorithm is used to optimize the energy group structure, the position and speed of the particles are iteratively updated, and the optimal energy group structure is searched. In the optimization process, each particle in the particle swarm represents a group of possible energy group boundaries, and the effectiveness of the optimization result is verified by comparing parameters such as keff, cross section, flux, power and the like. The method of the application can improve the accuracy of the neutron transport calculation of the supercritical carbon dioxide reactor and maintain the reasonableness of the full reactor power distribution, and provides an effective technical means for the optimization of the reactor.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear reactors, and particularly relates to a neutron transport energy group structure optimization method for a supercritical carbon dioxide reactor. BACKGROUND

[0002] In traditional supercritical carbon dioxide reactor design, 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 a balance problem between 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 of the fourth generation advanced nuclear energy system, the gas-cooled fast reactor has the advantages of high coolant outlet temperature, low investment cost, and simple system. A typical gas-cooled fast reactor usually selects helium or supercritical carbon dioxide as the 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 systems, supercritical carbon dioxide reactor (SCO2) has the advantages of efficient nuclear energy conversion and stable reaction control, and is suitable for aerospace, ocean development and other fields. It is one of the international research hotspots. In the core nuclear design, the “one-step method” of neutron calculation is relatively accurate but the calculation time is very long and it does not have the conditions for engineering application. At present, the “two-step method” is the mainstream method. It includes assembly few-group constant calculation and core diffusion / transport calculation. Among them, few-group cross-section calculation is an important content of the “two-step method” of nuclear reactor design, which is the bridge connecting assembly few-group constant calculation and core diffusion / transport calculation. The division of energy groups determines the calculation accuracy of few-group homogenization cross-section to a great extent, and greatly affects the calculation efficiency of the whole core. Few-group parameter homogenization mainly includes spatial homogenization and energy homogenization.

[0004] The energy distribution of neutrons in the core of a supercritical carbon dioxide reactor ranges widely, and each fuel assembly contains different types of cells, which makes the neutron calculation macroscopically characterized by a large neutron energy span and a complex geometric structure. The supercritical carbon dioxide reactor has a large difference in neutronics from traditional pressurized water reactors and fast neutron reactors, the reactor core arrangement is relatively complex, and there is a strong energy spectrum interference effect between assemblies. Due to the existence of the energy spectrum interference effect in the core, the energy spectrum of a single assembly is quite different from that of the assembly in a multi-assembly model, which leads to the fact that the traditional energy group division method is not suitable for this reactor type. Obviously, the probabilistic method or the deterministic method for one-time calculation of a finely described reactor is the most accurate and direct calculation method, but a large number of particles need to be sampled to reduce the calculation variance, which inevitably requires a high computational cost. In contrast, the deterministic method directly performs numerical discretization in the phase space composed of energy, space and angle and completes the solution calculation, but the memory requirement and computational cost of the one-step method for the whole core are also quite large.

[0005] A large number of in-depth studies have been conducted at home and abroad on methods for improving the accuracy of few-group cross-section data. In China, there were examples of simply applying the Monte Carlo method to calculate few-group constants in the 1970s. The China Institute of Nuclear Technology Research developed a general geometric fuel assembly group constant calculation program in 2004, which focuses on the ability of the Monte Carlo method to handle complex geometric problems and uses a multi-group cross-section library, which cannot take advantage of the high precision of continuous energy. At present, the NJOY or AMPX program is commonly used internationally to generate a wide group constant library closely related to the actual problem 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, the energy group structure of the fine group has different choices. In addition, the China Institute of Atomic Energy also developed a few-group cross-section correction sequence CREC for the characteristics of strong non-uniform effect of control rods, and conducted cross-section correction calculation research on the 12-group few-group cross-section of the safety rod and compensation rod of the China Sodium-cooled Demonstration Fast Reactor. North China Electric Power University developed the MGGC program to meet the calculation needs of fast reactor multi-group cross-sections. The program generates multi-group databases in the MATXS format based on 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 TULIP in the fast reactor neutron calculation program SARAX developed by Xi'an Jiaotong University uses the principle of combining deterministic and Monte Carlo methods to calculate multi-group cross-sections, and uses the Monte Carlo method 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-prepared continuous point cross-section database, and these databases are processed by their internal programs, which are usually not available to the outside world. SUMMARY

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

[0007] The application adopts the following technical solutions:

[0008] A method for optimizing energy group structure in a supercritical carbon dioxide reactor, characterized in that it comprises the following steps:

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

[0010] Step 2. Simulate the one-dimensional superassembly model using the Serpent Monte Carlo program to obtain 33 energy group homogenization cross-section and flux data, wherein the important processes of neutron and material interaction are considered in the simulation process, including scattering, absorption and fission, etc.

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

[0012]

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

[0014] Step 5. Fully verify the optimized energy group structure, including comparison of keff, cross-section, flux, power and other parameters to ensure calculation accuracy and reasonable full-core power distribution. Various nuclear databases are used in the verification process to evaluate the influence of different nuclear data on the optimization results.

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

[0016]

[0017] an inertia weight w with a value between 0.4 and 0.9, used to control the update of particle velocity to balance the ability of global search and local search, in the present application w = 0.8;

[0018] learning constants c1 and c2 with a value of 2, used to adjust the ability of particles to search according to their own experience and group experience, where c1 represents the ability of particles to search according to their own experience, and c2 represents the ability of particles to search according to group experience;

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

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

[0021] initializing the particle swarm, each particle represents a set of energy group boundaries, and the initial position is randomly distributed within the possible energy group boundary range, 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 swarm, 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 neutron and material interaction;

[0023] Using the VI TAS program to calculate the keff value of the energy group structure represented by each particle, where the calculation of keff value takes into account the geometric structure and material distribution of the reactor core;

[0024] updating the individual optimal solution (pbest) and global optimal solution (gbest) of each particle, where the individual optimal solution is the optimal solution found by the particle itself in its 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, update the velocity and position of the particle, where the update of velocity 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 or a predetermined error threshold is met, where the number of iterations and the error threshold are set according to the complexity of the problem and the computing resources.

[0027] Further, the comprehensive verification step includes:

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

[0029] The optimized energy group structure is applied to the full core model to calculate the power distribution, and compared with the reference solution to ensure that the maximum relative error of the power distribution is not more than 2%, to verify the applicability of the optimization method in the full core model;

[0030] The optimized energy group structure is applied to the full core model to calculate the power distribution, and compared with the reference solution to ensure that the maximum relative error of the power distribution is not more than 2%, to verify the applicability of the optimization method in the full core model;

[0031] The keff error of the optimized energy group structure in the full core model is ensured to be within an acceptable range, for example, not more than 300pcm, to meet the accuracy requirements of engineering applications;

[0032] The maximum relative error of the power distribution of the optimized energy group structure in the full core model is ensured to be within an acceptable range, for example, not more than 5%, to ensure the reasonableness of the power distribution of the core.

[0033] The beneficial effects of the present application are:

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

[0035] Figure 1 The model schematic diagram of the present application is shown in the figure;

[0036] Figure 2 The step flow chart of the present application is shown in the figure. DETAILED DESCRIPTION

[0037] To make the purpose, technical scheme and advantages of the present application clearer, the technical scheme in the present application is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor belong to the scope of protection of the present application.

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

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

[0040] 1. Model Construction

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

[0042] a. Geometric design: A superpin model containing 22 assemblies is designed, where fuel assemblies and coolant channels are arranged alternately, forming a periodic structure of the core. Each fuel assembly consists of 61 rods, including 13 moderator rods and 48 fuel rods. Coolant channels are arranged around the fuel assemblies.

[0043] b. Material property assignment: Material properties are assigned to each assembly in the model. Fuel assemblies are made of zirconium hydride (ZrH1.6) as a moderator and uranium dioxide (UO2) with 20% enrichment as fuel. Coolant channels are filled with supercritical carbon dioxide.

[0044] c. Boundary condition definition: Boundary conditions of the model are defined, 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 superpin assembly model is simulated using the Serpent Monte Carlo program to obtain homogenized cross-sections and flux data for 33 energy groups. During the simulation, the following steps are considered:

[0047] a. Physical process definition: All important processes of neutron-material interaction are defined, including elastic scattering, inelastic scattering, capture, and fission.

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

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

[0050] 3. Deterministic Neutron Transport Calculation

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

[0052] a. Data conversion: Convert the data output by Serpent into a format acceptable by 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 calculation: Run the VITAS program to perform a deterministic neutron transport calculation and obtain the keff value.

[0055] 4. Particle swarm optimization algorithm implementation

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

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

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

[0059] c. Energy group cross-section and flux calculation: Calculate the 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 global optimal solution (g_nuclear reactor est) for each particle.

[0061] e. Velocity and position update: Update the velocity and position of the particle based on the individual optimal solution and global optimal solution.

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

[0063] The present invention optimizes the energy group structure of the supercritical carbon dioxide reactor through the PSO algorithm, which effectively improves the calculation accuracy and maintains the 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 comprehensively verified, including the following steps:

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

[0067] b. Nuclear reactor cross-section, flux, and power distribution analysis: Analyze the cross-section, flux, and power distribution corresponding to the optimized energy group structure and compare it with the reference solution to ensure that the relative error is no more than 5%.

[0068] c. Full-core model application: Apply the optimized energy group structure in the full-core model to calculate the power distribution of the full-core and compare it with the reference solution to ensure that the maximum relative error of the power distribution is no more than 2%.

[0069] d. keff error verification: Ensure that the keff error of the optimized energy group structure in the full-core model is within an acceptable range, such as no more than 300 pcm.

[0070] e. Power distribution reasonableness verification: Ensure that the maximum relative error of the power distribution of the optimized energy group structure in the full-core model with the reference solution is within an acceptable range, such as no more than 5%.

[0071] In an embodiment of the present invention, a neutron transport energy group structure optimization method for supercritical carbon dioxide reactors is proposed. This method combines the construction of one-dimensional super-component models, Monte Carlo simulations, deterministic neutron transport calculations, and particle swarm optimization algorithms (PSO) to achieve efficient optimization of reactor energy group structures.

[0072] Firstly, the model takes into account the interaction of fuel assemblies, coolant channels, and reflectors, providing accurate geometric and material foundations 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 calculation accuracy. More importantly, the optimization results are comprehensively verified, including keff value comparison, cross-section and flux analysis, full-core model application, etc. These verification steps ensure the reliability and practicality of the optimization method, proving the effectiveness of the present invention in practical engineering applications.

Claims

1. A method for optimizing a cluster structure of a supercritical carbon dioxide reactor, characterized by, The method comprises the following steps: Step 1. Constructing a one-dimensional super-assembly model, which comprises at least one fuel assembly and at least one coolant channel, and at least one layer of reflector assembly, wherein the fuel assembly is composed of zirconium hydride as a moderator and uranium dioxide fuel with an enrichment of 20%, and the fuel assembly and the coolant channel are arranged alternately to form a core with a periodic structure; Step 2. Simulating the one-dimensional super-assembly model using the Serpent Monte Carlo program to obtain homogenized cross-section 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. Calculating the homogenized cross-section and flux data for the 33 energy groups using the VITAS deterministic neutron transport program to obtain an initial keff value as a reference solution, wherein the spherical harmonic expansion method is used in the calculation process to improve the accuracy and efficiency of the calculation; Step 4. Optimizing the energy group structure using the particle swarm optimization (PSO) algorithm, wherein each particle represents a set of possible energy group boundaries, and the position and velocity of the particle are iteratively updated to find the optimal energy group structure, and the influence of the energy group structure on keff and the influence on the core power distribution are considered in the optimization process; Step 5. Comprehensive verification of the optimized energy group structure, including comparison of keff, cross-section, flux, power and other parameters to ensure calculation accuracy and reasonableness of the full-core power distribution, and multiple different nuclear databases are used in the verification process to evaluate the influence of different nuclear data on the optimization results; The PSO algorithm comprises the following parameter settings: ； ； x represents the position of the particle, and the position x of each particle is an array composed of G+1 energy group boundary points selected from the initial energy group, which represents the current position of the particle in the solution space and is also a possible solution in the search process of the particle, and v represents the moving step; Inertia weight w, whose value is between 0.4 and 0.9, is used to control the update of particle velocity to balance the global search and local search capabilities, and 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 search stage; Learning constants c1 and c2, both of which are 2, are used to adjust the ability of particles to search according to their own experience and group experience, wherein c1 represents the ability of particles to search according to their own experience, and c2 represents the ability of particles to search according to group experience; Random numbers r1 and r2, with a value range of [0, 1], are used to introduce randomness when updating the particle velocity and position to avoid premature convergence to a local optimal solution, and the random numbers are regenerated in each iteration to maintain the randomness of the algorithm; The energy group structure optimization step comprises: Initializing the particle swarm, each particle representing a set of energy group boundaries, and the initial position is randomly distributed within the possible energy group boundary range, and the initial velocity is zero to avoid rapid fluctuations in the initial stage; According to the current position of each particle in the swarm, 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 neutron-material interaction; The keff value of the energy group structure represented by each particle is calculated using the VITAS program, where the calculation of keff value takes into account the geometric structure and material distribution of the reactor core; The energy group structure optimization step further includes: Updating the individual optimal solution (pbest) and global optimal solution (gbest) of each particle, where the individual optimal solution is the optimal solution found by the particle itself in its history, and the global optimal solution is the optimal solution found by all particles in the entire swarm; According to the individual optimal solution and global optimal solution, update the speed and position of the particle, where the update of speed and position takes into account the inertia of the particle, individual experience and group experience; Repeat steps 3 to 5 until a predetermined number of iterations or a predetermined error threshold is met, where the number of iterations and error threshold are set according to the complexity of the problem and the computing resources.

2. The method of claim 1, wherein, The comprehensive verification step includes: Compare the keff value of the optimized energy group structure with 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 is not more than 5% to verify the effectiveness of the optimization method; Apply the optimized energy group structure in the full-core model to calculate the power distribution of the full-core, and compare it with the reference solution to ensure that the maximum relative error of the power distribution is not more than 5% to verify the applicability of the optimization method in the full-core model.

3. The method of claim 1, wherein, The comprehensive verification step further includes: Ensure that the keff error of the optimized energy group structure in the full-core model is within an acceptable range, such as not more than 300pcm, to meet the accuracy requirements of engineering applications; Ensure that the maximum relative error of the power distribution of the optimized energy group structure in the full-core model with the reference solution is within an acceptable range, such as not more than 5%, to ensure the reasonableness of the power distribution of the reactor core.

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