Method and device for calculating neutronics parameters of reactor core

Abstract

The embodiment of the invention provides a method and device for calculating neutronics parameters of a reactor core, and belongs to the technical field of nuclear power. The method comprises the following steps: acquiring vibration frequencies of a plurality of fuel assemblies in a reactor core when the fuel assemblies work under a preset vibration working condition; dividing the working period into M continuous time steps according to the plurality of vibration frequencies; for each time step in the M time steps, the reactor core is divided in the radial direction according to the vibration positions of the multiple fuel assemblies in the time steps, and multiple arbitrary quadrilateral segments are obtained; mapping the plurality of arbitrary quadrilateral segments to a reference coordinate system to obtain a plurality of square segments; carrying out reactor core neutronics calculation on the basis of the plurality of square segments to obtain neutronics parameters corresponding to each square segment; and mapping the neutronics parameter corresponding to each square segment to any quadrilateral segment corresponding to the square segment to obtain a target neutronics parameter corresponding to the time step. According to the embodiment of the invention, the accuracy of the neutronics calculation result of the reactor core can be improved.

Description

Technical Field

[0001] This application relates to the field of nuclear power technology, and in particular to a method and apparatus for calculating neutronics parameters in a reactor core. Background Technology

[0002] Fuel assemblies are the core components of a pressurized water reactor (PWR) core, secured within the core by locating grids, upper and lower tubes, and other structures. During reactor operation, the fuel assemblies within the core are continuously subjected to irradiation growth, high temperature, and high pressure. Combined with factors such as core inlet flow fluctuations, vibrations inevitably occur, manifesting as fluctuations in detector current and nuclear power, severely impacting the safe operation of the reactor. To quantitatively assess the impact of fuel assembly vibration, accurate core neutronics calculations under PWR fuel assembly vibration conditions are required.

[0003] To quantitatively assess the impact of fuel assembly vibration on core neutronics parameters, existing technologies generally employ a deterministic two-step numerical simulation process. Specifically, the first step involves establishing two-dimensional non-uniform physical models of different types of fuel assemblies using an assembly calculation program, performing multi-group neutron transport calculations to obtain the neutron flux density distribution, and calculating the minority-group homogenization constant using an equivalent homogenization method. The second step uses a core calculation program to construct a global core physical model, performing three-dimensional neutronics calculations based on the aforementioned minority-group homogenization constant to obtain key safety parameters such as core power distribution and effective multiplication factor. In this process, the core calculation nodes are typically divided into fixed squares radially.

[0004] However, when fuel assemblies vibrate, their radial water gap size changes dynamically, altering the neutron moderation capability and water-to-uranium ratio within the assembly, thus affecting core power distribution and power peak factor, among other safety parameters. Existing methods attempt to approximate the vibration effect by pre-creating a library of minority group homogenization constants for different water gap sizes and adjusting these constants based on real-time water gap distribution during core calculations. However, because core calculations still use the traditional square segmentation method, they cannot accurately describe the geometric changes caused by fuel assembly vibration. Especially when assembly vibration crosses segment boundaries, it causes irregular segmentation, introducing significant calculation bias and resulting in low accuracy in assessing the impact of fuel assembly vibration. Summary of the Invention

[0005] The main objective of this application is to propose a method and apparatus for calculating neutronics parameters in reactor cores, aiming to solve the problem of low accuracy in assessing the impact of fuel assembly vibration in the prior art, thereby improving the accuracy of reactor core neutronics calculation results.

[0006] To achieve the above objectives, a first aspect of this application proposes a method for calculating neutronics parameters in a reactor core, the method comprising: Obtain the vibration frequency of multiple fuel assemblies in the reactor core when they operate under preset vibration conditions; Based on the multiple vibration frequencies, the working period is divided into M consecutive time steps, where M is a positive integer greater than 2; For each of the M time steps, the core is divided radially according to the vibration position of the multiple fuel assemblies at that time step to obtain multiple arbitrary quadrilateral segments, wherein the vibration range of the fuel assemblies is located within the spatial range of the arbitrary quadrilateral segments. By mapping multiple arbitrary quadrilateral blocks onto a reference coordinate system, multiple square blocks are obtained; Based on multiple square nodes, core neutronics calculations are performed to obtain the initial neutronics parameters corresponding to each square node; The neutronics parameters corresponding to each square node are mapped to any quadrilateral node corresponding to the square node to obtain the target neutronics parameters corresponding to the time step.

[0007] In some embodiments, dividing the reactor core radially according to the vibration positions of the plurality of fuel assemblies at the time step to obtain a plurality of arbitrary quadrilateral segments includes: The multiple fuel assemblies are divided into multiple fuel assembly groups, each fuel assembly group including four adjacent fuel assemblies; For each group of fuel assemblies, the water gap size of the arbitrary quadrilateral segment corresponding to each fuel assembly is determined based on the positions of the four fuel assemblies in the group; and, Based on the center point of each fuel assembly and the midpoint of the four target corner points of the four fuel assemblies in the fuel assembly group, the core is radially divided to obtain a plurality of arbitrary quadrilateral segments. The four target corner points are the four corner points of the four fuel assemblies that are closest to the center point of the location of the four fuel assemblies.

[0008] In some embodiments, after dividing the reactor core radially according to the vibration positions of the plurality of fuel assemblies at the time step to obtain a plurality of arbitrary quadrilateral segments, and before mapping the plurality of arbitrary quadrilateral segments to a reference coordinate system to obtain a plurality of square segments, the method further includes: Obtain a functional relationship, which is used to characterize the relationship between the minority group homogenization constant and the water gap size; Based on the water gap size of each of the arbitrary quadrilateral nodes at the time step, the target minority group homogenization constant of each of the arbitrary quadrilateral nodes is calculated through the functional relationship. The core neutronics calculation based on multiple square nodes, to obtain the initial neutronics parameters corresponding to each square node, includes: Neutronics calculations are performed based on the square node corresponding to each of the arbitrary quadrilateral nodes and the minority group homogenization constant corresponding to each of the arbitrary quadrilateral nodes to obtain the neutronics parameters corresponding to each of the square nodes.

[0009] In some embodiments, the neutronics parameters include neutron flux density and effective multiplication factor; The core neutronics calculation based on multiple square nodes, to obtain the initial neutronics parameters corresponding to each square node, includes: The three-dimensional transient neutron spacetime dynamics equations for each square node are discretized in time to obtain the transient fixed source equations corresponding to the time steps. Solving the transient fixed source equation based on the target minority group homogenization constant yields the target neutron flux density and the target effective multiplication coefficient of the square nodal.

[0010] In some embodiments, solving the transient fixed source equation based on the target minority group homogenization constant to obtain the target neutron flux density and target effective multiplication coefficient of the square nodal includes: Construct the conditions for the continuity of surface neutron flux density and the conditions for the continuity of surface neutron current density; Based on the coarse mesh finite difference method, a set of coupled equations is constructed according to the continuity conditions of the surface neutron flux density and the surface neutron current density, and the set of coupled equations includes a coupling correction factor. Solving the coupled equations yields the first neutron flux density and the first effective multiplication coefficient of the square nodal. The current value of the coupling correction factor in the coupled equation system is updated using the block expansion method to obtain a temporary value of the coupling correction factor; The temporary value of the coupling correction factor is used as the current value of the coupling correction factor, and the process jumps to the step of solving the coupling equations to obtain the first neutron flux density and the first effective multiplication coefficient of the square block, until the iteration stopping condition is met. The first neutron flux density and the first effective multiplication coefficient obtained at the last time are used as the target neutron flux density and the target effective multiplication coefficient.

[0011] In some embodiments, the conditions for establishing continuous surface neutron flux density and continuous surface neutron current density include: At the boundary of any two adjacent square nodes, the surface neutron flux density at the boundary of the square node is adjusted by a discontinuity factor so that the surface neutron flux density at the boundary of the two adjacent square nodes is equal after adjustment. At the boundary of any two adjacent square nodes, the surface neutron flux density of the two adjacent square nodes is calculated based on the surface neutron flux density. If the difference in surface neutron flux density between two adjacent square segments exceeds a preset range, the surface neutron flux density between the two adjacent square segments is adjusted based on the principle of neutron flux conservation until the difference in surface neutron flux density between the two adjacent square segments is within the preset range.

[0012] In some embodiments, updating the current value of the coupling correction factor in the coupled equation system using the block expansion method to obtain a temporary value of the coupling correction factor includes: The transverse integral related parameters of the square block are obtained. The transverse integral related parameters include the transverse integral partial neutron flux density, the transverse integral leakage term and the transverse integral transient source term. The transverse integral partial neutron flux density is determined based on the first neutron flux density of the square block. Based on the aforementioned horizontal integral related parameters, a horizontal integral equation for the two-block problem is constructed; The transverse integral equation is solved using the nodal expansion method to obtain a temporary value for the coupling correction factor.

[0013] In some embodiments, the target neutronics parameters include the target neutron flux density of each of the arbitrary quadrilateral nodes and the target effective multiplication factor of the core; The step of mapping the neutronics parameters corresponding to each square node to any quadrilateral node corresponding to the square node to obtain the target neutronics parameters corresponding to the time step includes: For each square node, based on the volume ratio of the square node to the arbitrary quadrilateral node, the target neutron flux density of the square node in the reference coordinates is mapped to the arbitrary quadrilateral node in the spatial coordinates to obtain the target neutron flux density of the arbitrary quadrilateral node.

[0014] In some embodiments, the step of performing core neutronics calculations based on multiple square nodes to obtain initial neutronics parameters corresponding to each square node includes: For the Nth time step out of M time steps, where N is a positive integer greater than 1 and less than M, perform the following steps: When entering the (N+1)th time step, obtain the volume of each of the arbitrary quadrilateral blocks corresponding to the Nth and (N+1)th time steps; For each of the arbitrary quadrilateral nodes, obtain the ratio of the volume of the arbitrary quadrilateral node at the Nth time step to the volume of the arbitrary quadrilateral node at the (N+1)th time step, and map the target neutron flux density of the arbitrary quadrilateral node at the Nth time step to the first neutron flux density of the arbitrary quadrilateral node at the (N+1)th time step according to the ratio.

[0015] To achieve the above objectives, a second aspect of this application provides a reactor core neutronics parameter calculation apparatus, the apparatus comprising: The first acquisition module is used to acquire the vibration frequency of multiple fuel assemblies in the reactor core when they are working under preset vibration conditions. The first division module is used to divide the working period into M consecutive time steps according to the multiple vibration frequencies, where M is a positive integer greater than 2; The second partitioning module is used to partition the reactor core radially according to the vibration position of the multiple fuel assemblies in each of the M time steps, to obtain multiple arbitrary quadrilateral segments, wherein the vibration range of the fuel assemblies is located within the spatial range of the arbitrary quadrilateral segments. The first mapping module is used to map multiple arbitrary quadrilateral blocks onto a reference coordinate system to obtain multiple square blocks. The first calculation module is used to perform core neutronics calculations based on multiple square nodes to obtain the initial neutronics parameters corresponding to each square node. The second mapping module is used to map the neutronics parameters corresponding to each square node to any quadrilateral node corresponding to the square node, so as to obtain the target neutronics parameters corresponding to the time step.

[0016] The proposed method and apparatus for calculating core neutronics parameters involves: acquiring the vibration frequency of fuel assemblies under preset vibration conditions; dividing the core operation period into multiple consecutive time steps based on the vibration frequency; dynamically dividing the core radially into arbitrary quadrilateral segments matching the assembly contour within each time step, ensuring the vibration range of the assembly is completely contained within the segments; mapping the arbitrary quadrilateral segments to standard square segments in a reference coordinate system through isoparametric transformation, and performing core neutronics calculations based on the square segments to obtain neutronics parameters; finally, mapping the calculation results back to arbitrary quadrilateral segments in the physical domain to obtain the core state at that time step. This application, through a combination of dynamic mesh generation and isoparametric transformation, achieves an accurate description of core geometric changes under vibration conditions, solving the problem that traditional fixed mesh methods cannot accurately characterize assembly vibration. While ensuring computational efficiency, it significantly improves the calculation accuracy of key safety parameters such as neutron flux distribution and power, providing a reliable technical means for the safe operation and vibration risk assessment of pressurized water reactors. Attached Figure Description

[0017] Figure 1 This is a radial diagram of fuel assembly vibration at different times provided in the embodiments of this application; Figure 2 This is a flowchart illustrating the method for calculating neutronics parameters in a reactor core provided in an embodiment of this application. Figure 3 This is a schematic diagram of the radial division of any quadrilateral block at any time provided in the embodiments of this application; Figure 4 This is a schematic diagram of the isoparametric transformation of any quadrilateral block k into a square block according to the embodiments of this application; Figure 5 This is a logic block diagram of the core neutronics parameter calculation method provided in the embodiments of this application; Figure 6 This is a schematic diagram of arbitrary quadrilateral block division provided in the embodiments of this application; Figure 7 This is a schematic diagram of the core neutronics parameter calculation device provided in the embodiments of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0019] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0021] First, let's analyze some of the terms used in this application: Neutron flux refers to the number of neutrons passing through a unit area per unit time. It is calculated by multiplying the neutron density by the average velocity (φ = n·v), and the unit is neutrons per square centimeter per second. It is divided into thermal neutron flux and fast neutron flux. This parameter is used to calculate the fission reaction rate (∑fφ) and absorption reaction rate (∑aφ). Its distribution directly affects reactor safe operation, fuel management, and the determination of the maximum permissible power, and is directly related to the nuclear reactor power.

[0022] Core power distribution: This is a key parameter characterizing the operating status of a nuclear reactor and directly affects the safety performance and operational optimization of a nuclear power plant.

[0023] Effective multiplication factor (EMF): Also known as the effective multiplication factor, it is a key parameter describing the duration of a chain reaction in nuclear fission in a nuclear reactor. It is denoted by the symbol... k eff It is expressed as the ratio of the number of fission neutrons in the reactor at a certain moment to the number of neutrons in the previous generation. k eff When the value equals 1, the reactor is in a critical state. k eff When the value is less than 1 or greater than 1, the chain reaction tends to terminate or intensify, respectively. This parameter is measured by a device and applied to reactor safety control.

[0024] The few-group homogenization constant is an equivalent parameter used in nuclear reactor calculations to simplify the analysis of non-uniform grids. It homogenizes the neutron flux density distribution of a non-uniform system to that of a homogeneous system. In a non-uniform reactor core, the neutron flux density exhibits a spatially non-uniform distribution due to the uneven distribution of fuel assemblies and moderators. By calculating the homogenization constant, the complex non-uniform system can be transformed into a homogeneous medium model, thereby simplifying the solution process of the many-group diffusion equations and improving computational efficiency.

[0025] Power peak factor: This refers to the ratio of local power to average power within the reactor core, used to quantify the degree of power non-uniformity. This is a critical safety parameter used to ensure that there is no location within the core with excessively high power density, which could lead to fuel element damage or deviation from nucleation boiling (DNBR).

[0026] Fuel assemblies are the core components of a pressurized water reactor (PWR) core, secured within the core by locating grids, upper and lower tubes, and other structures. During reactor operation, the fuel assemblies within the core are continuously subjected to irradiation growth, high temperature, and high pressure. Combined with factors such as core inlet flow fluctuations, vibrations inevitably occur, manifesting as fluctuations in detector current and nuclear power, severely impacting the safe operation of the reactor. To quantitatively assess the impact of fuel assembly vibration, accurate core neutronics calculations under PWR fuel assembly vibration conditions are required.

[0027] In the nuclear design and fuel management of pressurized water reactors, a deterministic two-step calculation process is commonly used to complete numerical simulations in order to achieve high efficiency and high precision in industrial applications. The calculation process is as follows: First, a two-dimensional non-uniform physical model of different types of fuel assemblies is constructed using a component calculation program. The neutron flux density distribution is obtained through multi-group neutron transport calculations, and the minority group homogenization constant is calculated using an equivalent homogenization method. Second, a core physical model is established using a core calculation program. Based on the minority group homogenization constant, three-dimensional neutronics calculations of the core are performed to obtain key safety parameters such as core power distribution and effective multiplication factor. The core calculation nodes are typically divided into fixed squares radially.

[0028] The following example, using a 3×3 fuel assembly model, illustrates the impact of assembly vibration on the deterministic two-step calculation process. Figure 1 As shown, the red squares represent fuel assemblies, the blue gaps between the red squares represent the water gaps between adjacent fuel assemblies, and the dashed lines represent the neutronics-calculated square segments of the core divided according to the nominal design water gap size. From a physical model perspective, fuel assembly vibration directly causes dynamic changes in the radial water gap size of the fuel assembly. Further from a neutronics perspective, the dynamic changes in the radial water gap size of the assembly directly affect the neutron moderation capability and water-uranium ratio within the assembly, thus affecting safety parameters such as core power distribution and power peak factor. Figure 1 When the central fuel assembly vibrates upwards or downwards, the radial water gap size of this assembly and its adjacent assemblies will deviate from the nominal design value. Therefore, a corresponding minority group homogenization constant needs to be generated based on the water gap size after the assembly vibration. In addition, after the fuel assembly vibrates, the central fuel assembly will break through the square block boundary of the core calculation. The fuel assembly is irregularly divided by the square blocks, which makes the traditional square block method unable to accurately characterize the vibration state of the fuel assembly.

[0029] Based on the above analysis, it is crucial to perform core neutronics calculations under pressurized water reactor fuel assembly vibration conditions using a deterministic two-step calculation process. Simultaneously, accurate core neutronics calculations under fuel assembly vibration conditions using the deterministic two-step calculation process require consideration of two issues: first, how to account for the impact of dynamic changes in the radial water gap size of the fuel assembly on the minority group homogenization constant during assembly calculations; and second, how to divide the core into segments to accurately characterize the fuel assembly vibration state.

[0030] To quantify the impact of fuel assembly vibration on reactor core neutronics parameters, various computational programs have been used both domestically and internationally in related research. In a study based on a deterministic two-step computational process, the following simulation method was employed: First, a library of minority group homogenization constants with different water gap sizes was created using an assembly computational program. Then, assembly vibration was equated to the dynamic change in the water gap size between assemblies. Fixed square segments were used for calculation in the core computational program, and the core neutronics calculation was completed by reading the changing three-dimensional water gap distribution and adjusting the minority group homogenization constants. While existing methods can perform core neutronics calculations under fuel assembly vibration conditions, the use of traditional square segments in the core calculations fails to accurately characterize the fuel assembly vibration state, inevitably introducing biases. This reduces the accuracy and reliability of the assessment of the impact of fuel assembly vibration, making it difficult to meet the requirements of high-precision safety analysis.

[0031] Based on this, embodiments of this application provide a method and apparatus for calculating core neutronics parameters, aiming to provide a method for calculating core neutronics parameters under pressurized water reactor fuel assembly vibration conditions, so as to accurately characterize the vibration state of the fuel assembly and maintain high computational efficiency. Specifically, the core calculation employs radial division of arbitrary quadrilateral blocks to accurately characterize the vibration state of the fuel assembly, and combines the traditional core neutronics parameter calculation method based on square blocks with isoparametric transformation technology, thereby achieving high-efficiency core numerical calculation and obtaining accurate target neutronics parameters, providing technical assurance for the safe operation of pressurized water reactors.

[0032] The core neutronics parameter calculation method and apparatus provided in this application are specifically described through the following embodiments. First, the core neutronics parameter calculation method in this application embodiment is described.

[0033] The core neutronics parameter calculation method provided in this application relates to the field of nuclear power technology. This core neutronics parameter calculation method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application implementing the core neutronics parameter calculation method, but is not limited to the above forms.

[0034] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0035] Figure 2 This is a flowchart of the core neutronics parameter calculation method provided in the embodiments of this application. Figure 2 The method may include, but is not limited to, steps S100 to S600.

[0036] Step S100: Obtain the vibration frequency of multiple fuel assemblies in the reactor core when they are operating under preset vibration conditions.

[0037] In this embodiment, vibration monitoring devices (such as non-contact displacement sensors and core current detectors) arranged inside the reactor core are used to collect real-time vibration data of multiple fuel assemblies under preset vibration conditions. The collected vibration data is subjected to spectrum analysis to extract the vibration frequency of each fuel assembly (i.e., the number of vibration cycles of the assembly per unit time), ensuring that the obtained frequencies cover all vibration characteristics of the assembly under preset conditions.

[0038] Step S200: Based on the multiple vibration frequencies, the working period is divided into M consecutive time steps, where M is a positive integer greater than 2.

[0039] In this embodiment, the vibration frequencies of multiple fuel assemblies in the reactor core under preset vibration conditions are obtained, and the working period is divided into M continuous time steps (M>2) according to the vibration frequencies. Each time step corresponds to the instantaneous vibration position of the assembly.

[0040] Step S300: For each of the M time steps, the reactor core is radially divided according to the vibration position of the multiple fuel assemblies at the time step to obtain multiple arbitrary quadrilateral segments, wherein the vibration range of the fuel assemblies is located within the spatial range of the arbitrary quadrilateral segments.

[0041] In this embodiment, after setting the calculation time step according to the vibration frequency of the fuel assembly, as follows: Figure 3 As shown, at different time steps, the core segments are radially divided into arbitrary quadrilaterals based on the vibration position of the fuel assemblies, ensuring that the fuel assemblies are not segmented by the segments. Specifically, the range of the arbitrary quadrilateral water gap contained in each fuel assembly is first determined based on the midpoint of the corner points of four adjacent fuel assemblies, and then the arbitrary quadrilateral segments are divided in combination with the center point of the fuel assembly.

[0042] Step S400: Map the multiple arbitrary quadrilateral blocks to the reference coordinate system to obtain multiple square blocks.

[0043] In this embodiment, for the nth time step, an isoparametric transformation method is used to map any quadrilateral block in physical coordinates (x, y) to a square block in reference coordinates (s, t). For example... Figure 4 The figure shows a schematic diagram of the isoparametric transformation from an arbitrary quadrilateral block k to a square block. The explicit mapping relationship between the horizontal and vertical coordinates is shown in formulas (1) and (2): (1); (2); in, Let x be the x-coordinate of vertex 1 of any quadrilateral block at time step n; Let be the ordinate of vertex 1 of any quadrilateral block at time step n; Let x be the x-coordinate of vertex 2 of any quadrilateral block at time step n; Let be the ordinate of vertex 2 of any quadrilateral block at time step n; Let x be the x-coordinate of vertex 3 of any quadrilateral block at time step n; Let be the ordinate of vertex 3 of any quadrilateral block at time step n; Let x be the x-coordinate of vertex 4 of any quadrilateral block at time step n; Let be the ordinate of vertex 4 of any quadrilateral block at time step n.

[0044] Step S500: Perform core neutronics calculations based on the multiple square nodes to obtain the initial neutronics parameters corresponding to each square node.

[0045] In this embodiment, a core computation program is used to calculate the neutron flux density of each square node based on the transformed square nodes. A three-dimensional transient neutron spatiotemporal dynamics equation is established and discretized in time to obtain the transient fixed source equation at the nth time step. The conditions for continuity of neutron flux density and neutron flux density at adjacent node interfaces are satisfied. A coupled equation set is constructed using the coarse mesh finite difference method, and iteratively solved using the node expansion method to obtain the neutron flux density and effective multiplication coefficient of each square node.

[0046] The specific implementation consists of the following four steps: 1) Discretize the three-dimensional transient neutron spacetime dynamics equations of the square nodal and establish the transient fixed source equations at the nth time step, as shown in formula (3): (3); in, Let be the neutron diffusion coefficient of the g-th energy group of the square node k at time step n; Let be the neutron flux density of the g-th energy group at position r of the square node k at time step n; Let G be the macroscopic outgoing section of the g-th energy group of the square node k at time step n; G is the total number of energy groups. Let be the macroscopic scattering cross section from the h-th energy group to the g-th energy group of the square block k at time step n; Let be the neutron flux density of the h-th energy group at position r of the square node k at time step n; The transient neutron fission energy spectrum of the g-th energy group; The effective multiplication coefficient; This represents the average number of neutrons produced per fission cycle. Let h be the macroscopic fission cross section of the square node k at time step n; Let g be the transient source term of the g-th energy group of the square block k at time step n.

[0047] 2) Since the radial upper boundary of any quadrilateral node is continuous, the boundary of the transformed square node still satisfies the continuity of surface neutron flux density and surface neutron current density; for adjacent square nodes k and k+1, the continuity of surface neutron flux density and surface neutron current density are shown in Equation (4) and Equation (5), respectively: (4); (5); in, Let be the discontinuity factor of the interface of the square block k at time step n in the positive direction of the g-th energy group u. Let be the surface neutron flux density at the interface of the square node k with the g-th energy group u in the positive direction at time step n; Let be the discontinuity factor of the negative direction interface of the g-th energy group u in the square block k+1 at time step n; Let be the surface neutron flux density at the interface of the g-th energy group u in the negative direction of the square node k+1 at time n. Let be the surface neutron flux density at the interface of the square node k with the g-th energy group u in the positive direction at time step n; Let be the surface neutron flux density at the interface of the g-th energy group u in the negative direction of the square node k+1 at time step n. The surface neutron flux density and surface neutron flux density can be represented by the neutron flux density, thus constructing a structure containing only the neutron flux density and . k eff The equations are as follows. The discontinuity factor is calculated by the component calculation program. At the interface of the nodal blocks, the neutron flux density is not completely continuous, but there is a small jump. The discontinuity factor is a parameter used to describe this discontinuity.

[0048] 3) Based on the coarse mesh finite difference, construct a set of coupled equations to solve for the approximate average neutron flux density and effective multiplication coefficient (i.e., the first neutron flux density and the first effective multiplication coefficient) of each square node. The coarse mesh finite difference equation of square node k is shown in formula (6): (6); in, Let k be the length of the square block k at time step n in the u direction; Let be the coarse mesh finite difference coupling factor in the positive direction of the g-th energy group u of the square node k at time step n; The coupling correction factor for the positive direction of the g-th energy group u of the square block k at time step n is initially set to 0. Let be the coarse mesh finite difference coupling factor in the negative direction of the g-th energy group u of the square node k at time step n; The coupling correction factor in the negative direction of the g-th energy group u of the square block k at time step n is initially set to 0. Let be the average neutron flux density of the g-th energy group in the square node k+1 at time step n; The average neutron flux density of the g-th energy group in the square block k at time step n; Let be the average neutron flux density of the g-th energy group in the square node k-1 at time step n.

[0049] 4) Construct a two-block problem, update the coupling correction factor using the block expansion method, and iteratively solve it using a coarse-mesh finite difference equation system until convergence. Obtain the accurate neutron flux density and effective multiplication coefficient (i.e., target neutron flux density and target effective multiplication coefficient) of each square block; the block expansion method is based on the transverse integration technique, and the transverse integral equation of the square block k is shown in formula (7): (7); in, Let be the transverse integral partial neutron flux density in the direction of the g-th energy group u of the square block k at time step n; For the transverse integral leakage term in the direction of the g-th energy group u of the square node k at time step n; Let be the transverse integral term in the direction u of the transient source term of the g-th energy group in the square node k at time step n. The transverse integral leakage term is an algebraic term derived mathematically from the equation and is related to the neutron flux density.

[0050] Step S600: Map the neutronics parameters corresponding to each square node to any quadrilateral node corresponding to the square node to obtain the target neutronics parameters corresponding to the time step.

[0051] In this embodiment, the neutron flux density of the square node is mapped back to the arbitrary quadrilateral node based on an explicit mapping relationship, as shown in formula (8): (8); in, Let be the average neutron flux density in the direction of the g-th energy group u of any quadrilateral block k at time step n; Let k be the volume of the square node k at time step n; Let k be the volume of any quadrilateral block k at time step n.

[0052] After dividing the arbitrary quadrilateral blocks at time step n+1, the neutron flux density is first mapped based on the volume of the arbitrary quadrilateral blocks divided in the previous and next time steps. The mapped neutron flux density is then directly substituted into the coarse mesh finite difference equation in the next time step for calculation, as shown in formula (9): (9); in, Let be the average neutron flux density of the g-th energy group of any quadrilateral block k at time step n+1; Let k be the volume of any quadrilateral segment k at time step n+1. Then, the quadrilateral segment is parametrically transformed into a square segment to complete the core neutron transient calculation based on the square segment. This process is repeated for all time steps until the last time step when the core neutronics calculation under fuel assembly vibration conditions is completed, yielding the neutron flux density and effective multiplication factor.

[0053] The logic block diagram of this embodiment is as follows: Figure 5 As shown, firstly, the core blocks are radially divided into arbitrary quadrilaterals based on the vibration position of the components at different time steps. Then, a two-dimensional physical model of the components is established under different water gap sizes. The component calculation program is used to calculate the minority group homogenization constant, which is then fitted as a function of the water gap size. Based on the fitted function, the minority group homogenization constant of the arbitrary quadrilateral blocks is obtained and mapped to square blocks using isoparametric transformation. The core calculation program is used to calculate the neutron flux density of each square block and map it back to the arbitrary quadrilateral blocks. Finally, the neutron flux density is mapped based on the volume of the arbitrary quadrilateral blocks divided at previous and subsequent time steps, and then mapped to square blocks using isoparametric transformation to complete the calculation, until the last time step.

[0054] This embodiment dynamically divides arbitrary quadrilateral segments according to time steps, which can completely encompass the vibration range of the fuel assembly under vibration conditions, preventing the assembly from exceeding the segment boundaries and solving the problem that fixed square segments cannot accurately characterize the vibration state. Combined with isoparametric transformation, arbitrary quadrilateral segments are mapped to square segments, which not only adapts to mature square segment neutronics calculation algorithms (ensuring calculation stability), but also restores the real physical scene under vibration conditions through inverse mapping, eliminating the calculation deviation introduced by irregular partitioning. Dividing time steps according to the vibration frequency of the fuel assembly can track changes in vibration state in real time, ensuring that the segment division and vibration position match in each time step. It is applicable to core calculations under different preset vibration conditions, providing accurate numerical simulation support for the safe operation of pressurized water reactors.

[0055] In some embodiments, step S300 may include, but is not limited to, steps S310 to S330: Step S310: Divide the multiple fuel assemblies into multiple fuel assembly groups, each fuel assembly group including four adjacent fuel assemblies. Step S320: For each group of fuel assembly groups, determine the water gap size of the arbitrary quadrilateral block corresponding to each fuel assembly based on the location of the four fuel assemblies in the fuel assembly group. Step S330: For each group of fuel assemblies, the core is radially divided according to the center point of each fuel assembly and the midpoint of the four target corner points of the four fuel assemblies in the fuel assembly group to obtain a plurality of arbitrary quadrilateral segments. The four target corner points are the four corner points of the four fuel assemblies that are closest to the center point of the location of the four fuel assemblies.

[0056] In this embodiment, using a "2×2 adjacent assembly" in the radial plane of the reactor core as the basic unit, the multiple fuel assemblies in the core are divided into multiple fuel assembly groups, each group consisting of four adjacent fuel assemblies. For each fuel assembly group, the water gap size of the arbitrary quadrilateral segment corresponding to each fuel assembly is determined based on the vibration position of the four fuel assemblies at the stated time step. The water gap size refers to the size of the gap between adjacent fuel assemblies, and its dynamic changes directly affect the neutron moderation capability and the water-uranium ratio. The calculation of the water gap size is based on the relative positions of the four fuel assemblies and is pre-fitted as a function of the few-group homogenization constant by the assembly calculation program.

[0057] Specifically, the first step is to determine the four target corner points of the four fuel assemblies in each fuel assembly group. For example... Figure 6 As shown, these target corner points are the four corner points of the four fuel assemblies that are closest to the center point of the location of the fuel assembly. The center point can be calculated from the geometric center of the four fuel assemblies.

[0058] Then, the midpoint of the four target corner points in each fuel assembly group is used as a vertex of the arbitrary quadrilateral block. Based on the vertices determined for each fuel assembly group, multiple large arbitrary quadrilateral blocks are obtained. Then, based on the center point of each fuel assembly and the midpoint of each edge of each large arbitrary quadrilateral block, the multiple large arbitrary quadrilateral blocks are further divided into multiple arbitrary quadrilateral blocks.

[0059] This embodiment divides the components by combining the "component center point (locating the component core)" and the "target corner midpoint (locating the water gap boundary)" to ensure that the geometry of the components matches the vibration trajectory of the components. This can completely encompass all vibration positions of the components within the current time step, eliminating calculation deviations caused by missing boundaries. Since the division is based on the actual vibration position of the fuel components in each time step, the shape and size of the components can adapt to the dynamic changes of the components in real time, avoiding the irregular segmentation caused by traditional square components when the components vibrate, and accurately depicting the core geometry under vibration.

[0060] In some embodiments, after step S300 and before step S400, the steps may include, but are not limited to, the following: Obtain a functional relationship, which is used to characterize the relationship between the minority group homogenization constant and the water gap size; Based on the water gap size of each of the arbitrary quadrilateral nodes at the time step, the target minority group homogenization constant of each of the arbitrary quadrilateral nodes is calculated through the functional relationship. The step of performing core neutronics calculations based on multiple square nodes to obtain initial neutronics parameters corresponding to each square node includes: Neutronics calculations are performed based on the square node corresponding to each of the arbitrary quadrilateral nodes and the minority group homogenization constant corresponding to each of the arbitrary quadrilateral nodes to obtain the neutronics parameters corresponding to each of the square nodes.

[0061] In this embodiment, before performing transient calculations, a general functional relationship is established in advance to characterize the variation of minority group homogenization constants (such as diffusion coefficient, removal cross section, scattering cross section, fission cross section, etc.) with the water gap size.

[0062] Specifically, a series of two-dimensional fuel assembly physical models with different water gap sizes are first constructed. These models cover all possible water gap size ranges that may occur during the vibration of the fuel assembly. Then, a high-precision assembly calculation program (such as a program based on multi-group neutron transport theory) is used to calculate the above models to obtain the minority group homogenization constant for each model under different water gap sizes. Finally, the calculated series of (water gap size, minority group homogenization constant) data points are fitted with a function to obtain a continuous functional relationship, as shown in formula (10).

[0063] (10); Where Σ is the minority group homogenization constant; f is the functional relationship; and w is the water gap size.

[0064] For the nth time step, after dividing the core segment into arbitrary quadrilaterals radially, each segment k has an actual water gap size determined by its vibration position. Based on the above fitting function and the water gap size of the arbitrary quadrilateral segment, the minority group homogenization constant of each arbitrary quadrilateral segment is obtained, as shown in formula (11): (11); in, Let be the minority group homogenization constant for any quadrilateral block k at time step n; Let be the water gap size of any quadrilateral block k at time step n.

[0065] The functional relationship is pre-stored for rapid lookup and calculation of the minority group homogenization constant corresponding to any water gap size in subsequent transient calculations. The minority group homogenization constant includes: neutron diffusion coefficient (a parameter characterizing the ability of neutrons to diffuse in fuel assemblies and water gaps, directly affecting the spatial distribution range of neutrons in the reactor core), macroscopic fission cross section (characterizing the probability that a neutron in the g-th energy group will cause nuclear fission), macroscopic absorption cross section (characterizing the total probability that a neutron in the g-th energy group will be absorbed by a nucleus), macroscopic scattering cross section (characterizing the probability that a neutron will be scattered from energy group g to energy group h), macroscopic removal cross section (characterizing the total probability that a neutron will leave the current energy group g through absorption or scattering to other energy groups), fission energy spectrum (characterizing the probability that neutrons produced by fission will appear in energy group g), etc.

[0066] This embodiment achieves a precise geometric and physical description of core neutronics calculations under fuel assembly vibration conditions by dynamically acquiring a minority group homogenization constant that matches the size of the vibrating water gap, and by combining arbitrary quadrilateral segmentation and isoparametric transformation techniques. This significantly improves the calculation accuracy and engineering applicability.

[0067] In some embodiments, the neutronics parameters include neutron flux density and effective multiplication factor. Step S500 may include, but is not limited to, steps S510 to S520: Step S510: Discretize the three-dimensional transient neutron spacetime dynamics equations for each square node in time to obtain the transient fixed source equations corresponding to the time step. Step S520: Solve the transient fixed source equation based on the target minority group homogenization constant to obtain the target neutron flux density and target effective multiplication coefficient of the square nodal.

[0068] In this embodiment, since the vibration of the fuel assembly is a time-varying transient process, the present invention requires processing the three-dimensional transient neutron spacetime dynamics equations describing neutron behavior. Specifically, a time discretization method is used to divide the continuous time process into discrete time steps (i.e., the M time steps in step S200). For each time step N, the transient equation is transformed into a transient fixed-source equation that holds within that time step. Through time discretization, the complex transient problem is simplified into a steady-state problem with a definite source term within each time step, thereby making numerical solutions possible.

[0069] Since arbitrary quadrilateral nodes are continuous in physical space, square nodes obtained through isoparametric transformation also remain continuous in computational space. Therefore, the physical continuity condition at the interface between adjacent nodes must be satisfied during the solution process, namely, the continuity of surface neutron flux density and surface neutron current density. To improve computational efficiency while ensuring accuracy, a coupled set of equations is first constructed using a coarse-mesh finite difference method to quickly obtain the approximate average neutron flux density and effective multiplication coefficient of each square node. Then, a two-node problem is constructed using a node expansion method to update and iteratively solve the coupling correction factor in the coarse-mesh finite difference calculation. This method, based on transverse integration, can accurately capture the distribution pattern of neutron flux density within the nodes. The above iterative process continues until the calculation results (such as neutron flux density and effective multiplication coefficient) meet the preset convergence criteria. Once converged, the precise target neutron flux density and target effective multiplication coefficient of each square node are obtained.

[0070] This embodiment efficiently performs high-precision core neutronics calculations on regular square segments, laying a solid data foundation for subsequently mapping the results back to real arbitrary quadrilateral segments and ultimately obtaining accurate core neutronics calculation results under vibration conditions.

[0071] In some embodiments, step S520 may include, but is not limited to, steps S521 to S526: Step S521: Construct the conditions for the continuity of surface neutron flux density and the conditions for the continuity of surface neutron current density. Step S522: Based on the coarse mesh finite difference method, construct a set of coupled equations according to the continuity conditions of the surface neutron flux density and the continuity conditions of the surface neutron current density. The set of coupled equations includes a coupling correction factor. Step S523: Solve the coupled equations to obtain the first neutron flux density and the first effective multiplication coefficient of the square block; Step S524: Update the current value of the coupling correction factor in the coupled equation set using the block expansion method to obtain a temporary value of the coupling correction factor; Step S525: Take the temporary value of the coupling correction factor as the current value of the coupling correction factor, and jump to the step of solving the coupling equation set to obtain the first neutron flux density and the first effective multiplication coefficient of the square block, until the iteration stopping condition is met; Step S526: The first neutron flux density and the first effective multiplication coefficient obtained last time are used as the target neutron flux density and the target effective multiplication coefficient.

[0072] Step S521 may include, but is not limited to, the following steps: At the boundary of any two adjacent square nodes, the surface neutron flux density at the boundary of the square node is adjusted by a discontinuity factor so that the surface neutron flux density at the boundary of the two adjacent square nodes is equal after adjustment. At the boundary of any two adjacent square nodes, the surface neutron flux density of the two adjacent square nodes is calculated based on the surface neutron flux density. If the difference in surface neutron flux density between two adjacent square segments exceeds a preset range, the surface neutron flux density between the two adjacent square segments is adjusted based on the principle of neutron flux conservation until the difference in surface neutron flux density between the two adjacent square segments is within the preset range.

[0073] In this embodiment, before solving the node equations, the physical continuity of the entire reactor core must first be ensured. Since the reactor core is composed of multiple nodes, the following two fundamental physical conditions must be satisfied at the common boundary between any two adjacent square nodes k and k+1: First, the surface neutron flux density must be continuous, meaning the neutron flux density values ​​on both sides of the boundary must be equal. Second, the surface neutron flux density must be continuous, meaning the neutron flux (net neutron number) crossing the boundary from one side to the other must be conserved. These two conditions form the basis for constructing the subsequent coupled equations, ensuring the physical rationality of the numerical solution.

[0074] Specifically, in actual calculations, due to the non-uniformity within the nodes, the surface neutron flux densities on both sides of the node boundary obtained by direct calculation may not be equal. For the interface between adjacent nodes k and k+1, a discontinuity factor is introduced to adjust the calculated surface neutron flux density so that the adjusted values ​​are equal at the interface.

[0075] After ensuring the continuity of the surface neutron flux density, it is also necessary to ensure the continuity of the surface neutron current density. Based on the surface neutron flux density, the surface neutron current density at the interface of each node can be calculated. Theoretically, the surface neutron current densities of adjacent nodes at the interface should be equal in magnitude and opposite in sign. If the difference between the calculated values ​​of two surface neutron current densities exceeds a preset range, it indicates that the neutron current is not conserved. In this case, based on the principle of neutron current conservation, the surface neutron current densities of the two adjacent nodes need to be adjusted until the difference is within the preset range, thus strictly satisfying the physical continuity of the neutron current.

[0076] In this embodiment, to quickly obtain an approximate global solution, a coarse-mesh finite-difference method is first employed. Based on the boundary conditions constructed in the previous steps, a global set of coupled equations is established for all square nodes. This set of equations uses the average neutron flux density and effective multiplication coefficient of each node as unknowns. To correct for errors introduced by the coarse-mesh finite-difference method in subsequent steps, a coupling correction factor is introduced into the equations. Solving this set of coupled equations yields an approximate solution, including the first neutron flux density and the first effective multiplication coefficient for each square node.

[0077] To improve the accuracy of the solution, this embodiment introduces a nodal expansion method to correct the preliminary solution of the coarse-mesh finite difference method. Using the obtained first neutron flux density and first effective multiplication coefficient as the current values, the nodal expansion method is used to solve for the fine flux distribution within each nodal. Based on this fine solution, the neutron flux at the nodal interface is recalculated, thereby updating the current value of the coupling correction factor in the coupled equations and obtaining its temporary value. The updated temporary value of the coupling correction factor is used as the new current value and resubmitted into the coupled equations for solving. In each iteration, the coupling correction factor is continuously optimized, making the solution of the coupled equations increasingly closer to the true solution. When the iteration meets a preset iteration stopping condition (e.g., the relative change in the effective multiplication coefficient obtained from two adjacent iterations is less than a very small threshold, such as 10), the iteration stops. -5 If the calculation is complete (i.e., the first neutron flux density and the first effective multiplication factor obtained from the last iteration are taken as the final target neutron flux density and target effective multiplication factor), then the calculation is considered to have converged. At this point, the first neutron flux density and the first effective multiplication factor obtained from the last iteration are taken as the final target neutron flux density and target effective multiplication factor. These two parameters accurately reflect the impact of fuel assembly vibration on the core neutronics characteristics at the current time step.

[0078] This embodiment ensures the accuracy of the physical description of the nodal boundaries by introducing a discontinuity factor and strictly conserving the surface neutron flux density; the iterative update of the coupling correction factor systematically eliminates the coarse mesh approximation error, ultimately enabling the acquisition of high-confidence neutron parameters for security analysis even on square nodules transformed from arbitrary quadrilaterals.

[0079] In some embodiments, step S524 may also include, but is not limited to, the following steps: The transverse integral related parameters of the square block are obtained. The transverse integral related parameters include the transverse integral partial neutron flux density, the transverse integral leakage term and the transverse integral transient source term. The transverse integral partial neutron flux density is determined based on the first neutron flux density of the square block. Based on the aforementioned horizontal integral related parameters, a horizontal integral equation for the two-block problem is constructed; The transverse integral equation is solved using the nodal expansion method to obtain a temporary value for the coupling correction factor.

[0080] In this embodiment, the nodal expansion method (NEM) is a numerical computation method in the field of nuclear reactor physics, mainly used to solve the multi-group diffusion equation problem under complex geometries. Its core idea is to divide a continuous spatial region into multiple discrete nodules, and achieve efficient computation by simplifying the coupling relationship between the nodules.

[0081] Specifically, the first step is to obtain the relevant parameters of the transverse integration of the square nodal, including but not limited to: the transverse integrated partial neutron flux density, the transverse integrated leakage term, and the transverse integrated term of the transient source term. The transverse integrated partial neutron flux density is obtained by transversely integrating the first neutron flux density of the square nodal in a specific direction; the transverse integrated leakage term characterizes the net leakage rate of neutrons in a plane perpendicular to the integration direction and is obtained by integrating the neutron flux density over the corresponding surface; the transverse integrated term of the transient source term can be obtained by performing the same transverse integration operation on the transient source term in the transient fixed source equation.

[0082] Based on the obtained transverse integral parameters, a locally refined model is constructed for two adjacent square nodules. The three-dimensional neutron diffusion equation is transversely integrated in a specific direction (e.g., the x-direction) to obtain a one-dimensional transverse integral equation. This equation describes the variation of the partial neutron flux density in the main directions after considering transverse leakage and transient source terms. By constructing such equations for adjacent nodal pairs, a mathematical model that accurately describes the physical behavior of the nodal interface is formed.

[0083] The nodal expansion method is used to solve the aforementioned transverse integral equations. This method assumes that the partial neutron flux density within the nodules follows a specific expansion form, transforming the differential equations into a system of algebraic equations for solution. By solving this refined model, a more accurate neutron flux density distribution at the nodal interfaces can be obtained. This accurate distribution can then be used to inversely calculate a more precise physical quantity at the nodal interfaces, i.e., the net neutron flux. Based on this accurate net neutron flux, a more precise inter-nodal coupling relationship can be recalculated. The coupling correction factors in the coupling equations are updated according to the more accurate inter-nodal coupling relationship, resulting in temporary values ​​for the coupling correction factors.

[0084] This embodiment reduces the dimensionality of the three-dimensional problem by using lateral integration and employs the nodal expansion method to perform a precise solution on the local two-nodal problem. This ensures computational efficiency and significantly improves the accuracy of the calculation of physical quantities at the nodal interface. This enables the rapid acquisition of core neutronics parameters that meet engineering accuracy requirements under complex conditions of fuel assembly vibration, providing reliable technical support for the safe operation of the reactor.

[0085] In some embodiments, the target neutronics parameters include the target neutron flux density of each of the arbitrary quadrilateral nodes and the target effective multiplication factor of the reactor core. Step S600 may include, but is not limited to, step S610: Step S610: For each square node, based on the volume ratio of the square node to the arbitrary quadrilateral node, the target neutron flux density of the square node in the reference coordinates is mapped to the arbitrary quadrilateral node in the spatial coordinates to obtain the target neutron flux density of the arbitrary quadrilateral node.

[0086] In this embodiment, after completing the core neutronics calculations based on square nodes and obtaining the accurate target neutron flux density and target effective multiplication factor, a reverse mapping of the results is required. The target neutron flux density obtained in the reference coordinate system is an average physical quantity (neutron flux per unit volume) within the square node. However, isoparametric transformation only guarantees a one-to-one correspondence of coordinate points, not that the node volumes before and after the transformation are equal. Typically, square nodes in the reference coordinate system have a standardized unit volume, while arbitrary quadrilateral nodes in the physical coordinate system have actual volumes that vary with vibrational states. Therefore, the calculated values ​​cannot be simply assigned directly to the physical nodes.

[0087] To ensure physical conservation (i.e., maintaining the same total neutron number or power within the nodal before and after mapping), this embodiment uses a volume ratio for mapping. Specifically, for each nodal pair (a square nodal and its corresponding arbitrary quadrilateral nodal), the volume ratio between the two is calculated. This ratio is then multiplied by the target neutron flux density of the square nodal to obtain the target neutron flux density of the arbitrary quadrilateral nodal in physical space.

[0088] The target effective multiplication factor is directly used as the core's target effective multiplication factor because it is a global parameter reflecting the critical state of the entire core and does not change with the geometric transformation of the nodes. Through the above mapping process, the target neutronics parameters that accurately reflect the vibration state of the fuel assembly at the nth time step are finally obtained, including the target neutron flux density of each arbitrary quadrilateral node and the core's target effective multiplication factor.

[0089] This embodiment uses a volume conservation mapping method to accurately convert the calculation results of square blocks back to arbitrary quadrilateral blocks. This process strictly follows the physical conservation laws, ensuring the physical accuracy and reliability of the calculation results.

[0090] In some embodiments, step S300 may also include, but is not limited to, the following steps: For the Nth time step out of M time steps, where N is a positive integer greater than 1 and less than M, perform the following steps: When entering the (N+1)th time step, obtain the volume of each of the arbitrary quadrilateral blocks corresponding to the Nth and (N+1)th time steps; For each of the arbitrary quadrilateral nodes, obtain the ratio of the volume of the arbitrary quadrilateral node at the Nth time step to the volume of the arbitrary quadrilateral node at the (N+1)th time step, and map the target neutron flux density of the arbitrary quadrilateral node at the Nth time step to the first neutron flux density of the arbitrary quadrilateral node at the (N+1)th time step according to the ratio.

[0091] In this embodiment, due to the continuous vibration of the fuel assembly, its vibration position differs at different time steps. This causes the shape and volume of the arbitrarily divided quadrilateral segments to dynamically change over time. Directly using the calculation result of the Nth time step as the initial value for the N+1th time step ignores this geometric change, violates the law of conservation of physics, and may lead to difficulties in convergence or distortion of the calculation results in the N+1th step. Instead of simply replicating the neutron flux density value when entering the next time step, a smart mapping is performed based on the principle of conservation of physics. The core idea is that the total number of neutrons (or total power) within a segment should be continuous within an extremely short time interval. Therefore, by considering the change in segment volume, the initial neutron flux density for the new time step can be accurately derived.

[0092] Specifically, when transitioning from the Nth time step to the (N+1)th time step, the shape and volume of any quadrilateral segment corresponding to the same fuel assembly will change due to continuous vibration of the fuel assembly. The volume of any quadrilateral segment k at the Nth time step is obtained, as well as the volume of any quadrilateral segment k obtained after re-dividing according to the vibration position at the (N+1)th time step. For each quadrilateral segment, the volume ratio of its volume in the previous time step (Nth step) to its volume in the current time step (N+1th step) is calculated. Based on this volume ratio, the target neutron flux density calculated at the Nth time step is scaled to obtain the first neutron flux density at the (N+1)th time step.

[0093] This embodiment ensures the continuity and conservation of physical quantities during time step progression by using a mapping method based on volume conservation, thereby guaranteeing the numerical stability and physical accuracy of transient calculations.

[0094] This application's embodiments accurately characterize the vibration state by dynamically dividing the fuel assembly into arbitrary quadrilateral segments at each time step based on the vibration position of the fuel assembly. It combines isoparametric transformation technology with a mature core neutronics parameter calculation method based on square segments to achieve accurate core neutronics calculations under assembly vibration conditions, providing a numerical simulation method for fuel assembly vibration phenomena within the core. Through the principle of volume conservation, it achieves accurate spatial and temporal mapping of the calculation results, solving the problem that traditional fixed segments cannot simulate the dynamic changes in geometric and physical parameters introduced by vibration. This application's embodiments provide an accurate core neutronics parameter calculation method under fuel assembly vibration conditions, applicable to the improvement and enhancement of pressurized water reactor core design programs, further ensuring the safety of core operation.

[0095] Please see Figure 7 This application also provides a reactor core neutronics parameter calculation device 700, which can implement the above-described reactor core neutronics parameter calculation method. The device includes: The first acquisition module 10 is used to acquire the vibration frequency of multiple fuel assemblies in the reactor core when they are working under a preset vibration condition. The first division module 20 is used to divide the working period into M consecutive time steps according to the multiple vibration frequencies, where M is a positive integer greater than 2; The second partitioning module 30 is used to partition the reactor core radially according to the vibration position of the multiple fuel assemblies in each of the M time steps, to obtain multiple arbitrary quadrilateral segments, wherein the vibration range of the fuel assemblies is located within the spatial range of the arbitrary quadrilateral segments. The first mapping module 40 is used to map the multiple arbitrary quadrilateral blocks to a reference coordinate system to obtain multiple square blocks; The first calculation module 50 is used to perform core neutronics calculations based on multiple square nodes to obtain the initial neutronics parameters corresponding to each square node. The second mapping module 60 is used to map the neutronics parameters corresponding to each square node to any quadrilateral node corresponding to the square node, so as to obtain the target neutronics parameters corresponding to the time step.

[0096] In some implementations, the second partitioning module 30 may include: The first division submodule is used to divide the multiple fuel assemblies into multiple fuel assembly groups, each fuel assembly group including four adjacent fuel assemblies. The determination submodule is used to determine the water gap size of the arbitrary quadrilateral block corresponding to each fuel assembly for each group of fuel assembly groups, based on the location of the four fuel assemblies in the fuel assembly group; The second partitioning submodule is used to radially partition the reactor core according to the center point of each fuel assembly and the midpoint of the four target corner points of the four fuel assemblies in the fuel assembly group to obtain a plurality of arbitrary quadrilateral segments. The four target corner points are the four corner points of the four fuel assemblies that are closest to the center point of the location of the four fuel assemblies.

[0097] In some embodiments, the apparatus may further include: The second acquisition module is used to acquire a functional relationship, which is used to characterize the relationship between the minority group homogenization constant and the water gap size. The second calculation module is used to calculate the target minority group homogenization constant for each of the arbitrary quadrilateral nodes based on the water gap size of each arbitrary quadrilateral node at the time step and through the functional relationship. The first calculation module 50 may also include: The first calculation submodule is used to perform neutronics calculations based on the square block corresponding to each of the arbitrary quadrilateral blocks and the minority group homogenization constant corresponding to each of the arbitrary quadrilateral blocks, to obtain the neutronics parameters corresponding to each of the square blocks.

[0098] In some implementations, the first computing module 50 may further include: The discrete submodule is used to perform time discretization processing on the three-dimensional transient neutron spatiotemporal dynamics equations of each square node to obtain the transient fixed source equations corresponding to the time step. The neutron parameters include neutron flux density and effective multiplication coefficient. The solution submodule is used to solve the transient fixed source equation based on the target minority group homogenization constant to obtain the target neutron flux density and target effective multiplication coefficient of the square nodal.

[0099] In some implementations, the solver submodule may include: The first building block is used to construct the conditions for the continuity of surface neutron flux density and the conditions for the continuity of surface neutron current density. The second building unit is used to construct a set of coupled equations based on the coarse mesh finite difference method, according to the continuous condition of the surface neutron flux density and the continuous condition of the surface neutron current density, and the set of coupled equations includes a coupling correction factor. The solving unit is used to solve the coupled equations to obtain the first neutron flux density and the first effective multiplication coefficient of the square block; An update unit is used to update the current value of the coupling correction factor in the coupled equation system using the block expansion method to obtain a temporary value of the coupling correction factor. A jump unit is used to take the temporary value of the coupling correction factor as the current value of the coupling correction factor and jump to the step of solving the coupling equation set to obtain the first neutron flux density and the first effective multiplication coefficient of the square block, until the iteration stopping condition is met; The determining unit is used to take the first neutron flux density and the first effective multiplication coefficient obtained last time as the target neutron flux density and the target effective multiplication coefficient.

[0100] In some implementations, the first building unit may include: The first adjustment subunit is used to adjust the surface neutron flux density at the boundary of any two adjacent square nodes by means of a discontinuity factor, so that the surface neutron flux density at the boundary of the two adjacent square nodes is equal after adjustment. The calculation subunit is used to calculate the surface neutron flux density of the two adjacent square nodes based on the surface neutron flux density at the boundary of any two adjacent square nodes. The second adjustment subunit is used to adjust the surface neutron flux density of two adjacent square nodes based on the principle of neutron flux conservation if the difference between the surface neutron flux densities of two adjacent square nodes exceeds a preset range, until the difference between the surface neutron flux densities of the two adjacent square nodes is within the preset range.

[0101] In some implementations, the update unit may include: The acquisition sub-unit is used to acquire the transverse integral related parameters of the square block. The transverse integral related parameters include the transverse integral partial neutron flux density, the transverse integral leakage term and the transverse integral term of the transient source term. The transverse integral partial neutron flux density is determined based on the first neutron flux density of the square block. Construct sub-units to build the transverse integral equations for the two-block problem based on the transverse integral related parameters; The sub-element is used to solve the transverse integral equation using the block expansion method to obtain a temporary value for the coupling correction factor.

[0102] In some implementations, the second mapping module 60 may include: The first mapping submodule is used to map the target neutron flux density of the square node in the reference coordinate to the arbitrary quadrilateral node in the spatial coordinate based on the volume ratio of the square node to the arbitrary quadrilateral node for each square node, so as to obtain the target neutron flux density of the arbitrary quadrilateral node.

[0103] In some implementations, the second partitioning module 30 may further include: The execution submodule is used to perform the following steps for the Nth time step out of M time steps, where N is a positive integer greater than 1 and less than M; The acquisition submodule is used to acquire the volume of each of the arbitrary quadrilateral blocks corresponding to the Nth and N+1th time steps when entering the N+1th time step; The second mapping submodule is used to obtain, for each of the arbitrary quadrilateral nodes, the ratio of the volume of the arbitrary quadrilateral node at the Nth time step to the volume of the arbitrary quadrilateral node at the (N+1)th time step, and map the target neutron flux density of the arbitrary quadrilateral node at the Nth time step to the first neutron flux density of the arbitrary quadrilateral node at the (N+1)th time step according to the ratio.

[0104] The specific implementation of this core neutronics parameter calculation device is basically the same as the specific embodiment of the core neutronics parameter calculation method described above, and will not be repeated here.

[0105] The core neutronics parameter calculation method and apparatus provided in this application obtain the vibration frequency of the fuel assembly under preset vibration conditions; divide the core operation period into multiple consecutive time steps according to the vibration frequency; within each time step, based on the real-time vibration position of the assembly, the core is radially dynamically divided into arbitrary quadrilateral segments matching the assembly contour, ensuring that the vibration range of the assembly is completely contained within the segments; subsequently, the arbitrary quadrilateral segments are mapped to standard square segments in a reference coordinate system through isoparametric transformation, and core neutronics calculations are performed based on the square segments to obtain neutronics parameters; finally, the calculation results are inversely mapped back to arbitrary quadrilateral segments in the physical domain to obtain the core state of that time step. This application, through the combination of dynamic mesh generation and isoparametric transformation, achieves an accurate description of the geometric changes of the core under vibration conditions, solving the problem that traditional fixed mesh methods cannot accurately characterize assembly vibration. While ensuring computational efficiency, it significantly improves the calculation accuracy of key safety parameters such as neutron flux density and power distribution, providing a reliable technical means for the safe operation and vibration risk assessment of pressurized water reactors.

[0106] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0107] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0108] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0109] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0110] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0111] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0112] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0113] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0114] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0115] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0116] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method of calculating a core neutronics parameter, characterized by, The method comprises: obtaining vibration frequencies of a plurality of fuel assemblies in a core under a preset vibration working condition; dividing an operation period into M continuous time steps according to a plurality of vibration frequencies, M being a positive integer greater than 2; for each of the M time steps, dividing the core according to a radial direction according to vibration positions of a plurality of fuel assemblies in the time step to obtain a plurality of arbitrary quadrilateral segments, wherein a vibration range of the fuel assemblies is located in a spatial range of the arbitrary quadrilateral segment; mapping the plurality of arbitrary quadrilateral segments to a reference coordinate system to obtain a plurality of square segments; performing core neutron calculation based on the plurality of square segments to obtain initial neutron parameters corresponding to each of the square segments; and mapping the neutron parameters corresponding to each of the square segments to the arbitrary quadrilateral segment corresponding to the square segment to obtain target neutron parameters corresponding to the time step.

2. The method of claim 1, wherein, The method further comprises: dividing the plurality of fuel assemblies into a plurality of fuel assembly groups, each fuel assembly group comprising four positionally adjacent fuel assemblies; for each of the fuel assembly groups, determining a water gap size of an arbitrary quadrilateral segment corresponding to each of the fuel assemblies according to positions of the four fuel assemblies in the fuel assembly group; and dividing the core according to the radial direction according to a center point of each of the fuel assemblies and a midpoint of four target corner points of the four fuel assemblies in the fuel assembly group to obtain the plurality of arbitrary quadrilateral segments, the four target corner points being four corner points of the four fuel assemblies closest to the center point of the positions of the four fuel assemblies.

3. The method of claim 2, wherein, The method further comprises: obtaining a function relationship for representing a relationship between a few-group homogenization constant and a water gap size; calculating a target few-group homogenization constant of each of the arbitrary quadrilateral segments according to the water gap size of each of the arbitrary quadrilateral segments in the time step through the function relationship. The method further comprises: performing neutron calculation based on the square segment corresponding to each of the arbitrary quadrilateral segments and the few-group homogenization constant corresponding to each of the arbitrary quadrilateral segments to obtain the initial neutron parameters corresponding to each of the square segments.

4. The method of claim 3, wherein, The neutron parameters comprise neutron flux density and effective multiplication factor. The method further comprises: performing time-discrete processing on a three-dimensional transient neutron space-time dynamic equation of each of the square segments to obtain a transient fixed source equation corresponding to the time step. Solving the transient fixed source equation based on the target few-group homogenization constant to obtain the target neutron flux density and target effective multiplication factor of the square block.

5. The method of claim 4, wherein, The solving the transient fixed source equation based on the target few-group homogenization constant to obtain the target neutron flux density and target effective multiplication factor of the square block comprises: Constructing a condition of continuity of the surface neutron flux density and a condition of continuity of the surface neutron current density; Based on the coarse mesh finite difference method, constructing a coupling equation group according to the condition of continuity of the surface neutron flux density and the condition of continuity of the surface neutron current density, the coupling equation group comprising a coupling correction factor; Solving the coupling equation group to obtain the first neutron flux density and the first effective multiplication factor of the square block; Updating the current value of the coupling correction factor in the coupling equation group by using the block expansion method to obtain a temporary value of the coupling correction factor; Taking the temporary value of the coupling correction factor as the current value of the coupling correction factor, jumping to the step of solving the coupling equation group to obtain the first neutron flux density and the first effective multiplication factor of the square block until an iteration stopping condition is met; Taking the last obtained first neutron flux density and first effective multiplication factor as the target neutron flux density and target effective multiplication factor.

6. The method of claim 5, wherein, The constructing a condition of continuity of the surface neutron flux density and a condition of continuity of the surface neutron current density comprises: Adjusting the surface neutron flux density of the boundary of the square block by a discontinuous factor to make the adjusted surface neutron flux densities of the boundaries of the two adjacent square blocks equal; Calculating the surface neutron current densities of the two adjacent square blocks according to the surface neutron flux density; If the difference between the surface neutron current densities of the two adjacent square blocks exceeds a preset range, adjusting the surface neutron current densities of the two adjacent square blocks based on the neutron current conservation principle until the difference between the surface neutron current densities of the two adjacent square blocks is within the preset range.

7. The method of claim 5, wherein, The updating the current value of the coupling correction factor in the coupling equation group by using the block expansion method to obtain a temporary value of the coupling correction factor comprises: Obtaining the transverse integral related parameters of the square block, the transverse integral related parameters comprising a transverse integral partial neutron flux density, a transverse integral leakage term and a transverse integral item of a transient source term, the transverse integral partial neutron flux density being determined according to the first neutron flux density of the square block; Based on the transverse integral related parameters, constructing a transverse integral equation of a two-block problem; Solving the transverse integral equation by using the block expansion method to obtain the temporary value of the coupling correction factor.

8. The method of claim 4, wherein, The target neutronics parameters comprise a target neutron flux density of each of the arbitrary quadrilateral blocks and a target effective multiplication factor of the core. The method comprises the following steps: For each of the square segments, the target neutron flux density of the square segment in the reference coordinates is mapped to the arbitrary quadrilateral segment in the spatial coordinates based on the volume ratio of the square segment to the arbitrary quadrilateral segment, to obtain the target neutron flux density of the arbitrary quadrilateral segment.

9. The method of claim 5, wherein, The method comprises the following steps: For each of the square segments, the target neutron flux density of the square segment in the reference coordinates is mapped to the arbitrary quadrilateral segment in the spatial coordinates based on the volume ratio of the square segment to the arbitrary quadrilateral segment, to obtain the target neutron flux density of the arbitrary quadrilateral segment. The method comprises the following steps: For each of the square segments, the target neutron flux density of the square segment in the reference coordinates is mapped to the arbitrary quadrilateral segment in the spatial coordinates based on the volume ratio of the square segment to the arbitrary quadrilateral segment, to obtain the target neutron flux density of the arbitrary quadrilateral segment.

10. A reactor core neutronics parameter calculation device, characterized by, The device comprises: A first obtaining module is configured to obtain vibration frequencies of a plurality of fuel assemblies in a core when the fuel assemblies are working under a preset vibration condition; A first dividing module is configured to divide a working period into M continuous time steps according to the vibration frequencies, where M is a positive integer greater than 2; A second dividing module is configured to divide the core according to a radial direction to obtain a plurality of arbitrary quadrilateral segments for each of the M time steps according to vibration positions of the plurality of fuel assemblies in the time step, where the vibration range of the fuel assemblies is located in a spatial range of the arbitrary quadrilateral segment; A first mapping module is configured to map the plurality of arbitrary quadrilateral segments to a reference coordinate system to obtain a plurality of square segments; A first calculating module is configured to perform core neutron calculation based on the plurality of square segments to obtain initial neutron parameters corresponding to each of the square segments; A second mapping module is configured to map neutron parameters corresponding to each of the square segments to the arbitrary quadrilateral segment corresponding to the square segment to obtain target neutron parameters corresponding to the time step.

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