A method for nuclear thermal coupled transient analysis of a nuclear reactor core fuel assembly

Abstract

The application discloses a nuclear reactor core fuel assembly nuclear heat coupling transient analysis method, and steps are as follows: 1, according to the geometric structure parameters of the fuel assembly, a thermal hydraulic model and a neutron physical model are respectively established, coolant sub-channel control bodies and fuel rod control bodies are divided, and unstructured grids are divided; 2, a Monte Carlo method is used to calculate the neutron parameters of different energy groups of the actual geometric structure, and equivalent treatment is carried out according to the fuel area in the neutron physical calculation model, and a neutron parameter database of different energy groups is established; 3, a coupling parameter mapping relationship between the thermal hydraulic model and the neutron physical model is established; 4, on the basis of the initial steady-state result, transient calculation is carried out, and the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature and fuel rod power distribution in the fuel assembly are output. The method can improve the calculation stability and result precision under the strong feedback transient working condition, and provides a calculation basis for reactor design and safety analysis.

Description

Technical Field

[0001] This invention belongs to the field of multiphysics numerical simulation and safety analysis technology for nuclear reactors, specifically relating to a method for transient analysis of nuclear thermal coupling of fuel assemblies in nuclear reactor cores. Background Technology

[0002] Reactor safety analysis and refined design require an accurate description of the bidirectional feedback between neutron physics processes and thermal-hydraulic processes. The power distribution obtained from neutron transport calculations determines the heat source of each fuel rod, thus affecting the fuel cladding temperature, fuel pellet temperature, coolant temperature, and coolant flow rate. Conversely, changes in fuel cladding temperature, fuel pellet temperature, and coolant temperature and density alter the neutron parameters of different energy groups in the material, further influencing neutron flux and power distribution. Therefore, it is necessary to exchange local parameters under a consistent spatial mapping and iteratively solve for the aforementioned bidirectional feedback within a transient time step.

[0003] Existing nuclear thermal coupling analysis typically couples neutron diffusion programs with system analysis programs or subchannel programs, offering the advantage of high computational efficiency. However, the region-averaged parameters and coarse spatial discretization weaken the ability to describe the complex geometry of fuel assemblies and local feedback effects. Furthermore, if parameters are exchanged only once between adjacent time steps, the thermal-hydraulic field and the neutron physics field may not maintain consistency within the same time step, thus affecting the computational stability and accuracy under strong feedback transient conditions.

[0004] Therefore, a nuclear thermal coupling transient analysis method at the fuel assembly level is needed to obtain the fine distribution of power and thermal-hydraulic parameters within the fuel assembly through neutronics parameter databases of different energy groups, heterogeneous grid region mapping, and time-step iteration, providing a computational basis for reactor design and safety analysis. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a nuclear thermal coupling transient analysis method for nuclear reactor core fuel assemblies, thereby improving the calculation stability and result accuracy under strong feedback transient conditions, and obtaining a fine distribution of power and thermal-hydraulic parameters within the fuel assembly, providing a calculation basis for reactor design and safety analysis.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies includes the following steps: Step 1: Establish a thermal-hydraulic model and a neutron physics model based on the geometric parameters of the nuclear reactor core fuel assemblies. The thermal-hydraulic model divides the coolant region into coolant sub-channel control volumes according to the sub-channel boundaries, and divides the fuel rod region into radial fuel rod control volumes according to the fuel cladding, air gap, and fuel pellets. The neutron physics model divides the unstructured computational mesh with the fuel region boundaries as constraints. By using coolant sub-channel control volumes suitable for coolant flow and heat transfer calculations and unstructured computational meshes suitable for describing complex material boundaries, the two models can maintain their respective spatial discretization characteristics and provide a spatial basis for the corresponding transfer of local coolant parameters, fuel cladding temperature, fuel pellet temperature, and fuel rod power. Preferably, the geometric parameters of the nuclear reactor core fuel assembly include the number of fuel rods, the arrangement of fuel rods, the fuel rod spacing, the fuel pellet radius, the air gap thickness, the fuel cladding thickness, the assembly width, and the assembly height. These geometric parameters determine the coolant flow area, hydraulic diameter, the radial coordinates of the fuel rod guides, and the neutron physics fuel region boundary. Therefore, using these parameters allows the thermal-hydraulic model and the neutron physics model to be established based on the same fuel assembly geometric reference, reducing parameter mapping errors caused by inconsistent geometric definitions.

[0007] Preferably, the established thermal-hydraulic model consists of the following equations: Coolant mass conservation equation:

[0008] Coolant momentum conservation equation:

[0009] Coolant energy conservation equation:

[0010] The thermal conduction equation for fuel rods is as follows:

[0011] In the formula: — Coolant sub-channel number; ——No. i Coolant subchannel density, kg / m³ 3 ; ——No. i The flow area of ​​each coolant sub-channel is [m²]. 2 ; ——No. i Axial flow velocity of each coolant sub-channel, m / s; —Axial coordinates of the coolant subchannel, in meters; —Time, s; —Net mass exchange source term generated by lateral flow per unit length, kg / (m·s); ——No. i Pressure of each coolant sub-channel, Pa; — Friction coefficient; ——No. i Hydraulic diameter of each coolant sub-channel, m; —Axial component of gravitational acceleration, m / s 2 ; —Net momentum exchange source term generated by lateral flow per unit length, kg / s 2 ; ——No. i Specific enthalpy of each coolant sub-channel, J / kg; —Fuel rods towards the first i Heat transferred per unit axial length by each coolant sub-channel, W / m; —Net energy exchange source term from lateral flow and turbulent mixing per unit length, W / m; —Radial region numbering of fuel rods; —Radial coordinates of the fuel rod, in meters; ——No. j Layer material temperature, K; ——No. j Layer material density, kg / m 3 ; ——No. j Specific heat capacity of the layered material, J / (kg·K); ——No. j Thermal conductivity of the layer material, W / (m·K); ——No. j Volumetric heat source density of layered material, W / m 3 .

[0012] By employing the coolant mass conservation equation, momentum conservation equation, and energy conservation equation, the mass transport of coolant within each sub-channel, the flow under pressure and resistance, and the energy changes caused by fuel rod heat transfer and lateral mixing can be described, respectively. The fuel rod thermal conductivity equation can be used to describe the radial transient heat transfer process between fuel pellets, air gaps, and fuel cladding. Therefore, while satisfying the mass, momentum, and energy conservation relationships, coolant temperature, flow velocity, fuel cladding temperature, and fuel pellet temperature can be obtained simultaneously. This overcomes the difficulty in describing local flow, lateral exchange, and fuel rod thermal inertia when only regional average temperature or steady-state heat transfer relationships are used, providing physically consistent thermo-hydraulic parameters for nuclear-thermal coupling iteration.

[0013] The preferred neutron physics model is as follows: Neutron transport equations:

[0014] In the formula: —Group number; ——No. g The average velocity of neutrons in an energy group, cm / s; ——No. g Neutron angular flux of the energy group, n / (cm) 2 ·s·sr); —The unit vector of the direction of neutron motion; ——No. g The total macroscopic cross section of the energy group, cm -1 ; ——No. g Neutron source term of the energy group, n / (cm) 3 ·s·sr).

[0015] Employing the neutron transport equation as a neutron physics model, this approach simultaneously describes the temporal variations, spatial migration, material collision losses, and neutron source effects of neutrons from different energy groups. By combining neutronics parameters of different energy groups updated with the thermal-hydraulic state, the dynamic spatial distribution of neutron flux and power within the fuel assembly can be calculated. This model overcomes the limitations of coarse-grid region-averaging methods in describing complex material boundaries and local power variations, providing a computational foundation for the precise transfer of fuel rod power to the thermal-hydraulic model and the iterative updating of power distribution under temperature feedback.

[0016] Step 2: Select multiple state points for coolant temperature, fuel cladding temperature, and fuel pellet temperature, and use the Monte Carlo method to calculate the neutron parameters of different energy groups at each state point for the actual geometry of the fuel assembly. Perform equivalent processing on the neutron parameters of the different energy groups according to the fuel region in the neutron physics model, and establish a database of equivalent neutron parameters for different energy groups with coolant temperature, fuel cladding temperature, and fuel pellet temperature as three independent variables. By pre-calculating the neutron parameters of different energy groups at different state points and interpolating them during transient calculations, the repeated execution of Monte Carlo calculations in each coupling iteration can be avoided, thereby reducing the transient coupling computation load while preserving the actual geometric neutron information. Preferably, the equivalent processing method for neutronics parameters of different energy groups is as follows: The equivalent neutronics parameters of different energy groups in the overall fuel region of the neutron physics model are obtained by using an area-weighted method for the fuel rod, which consists of fuel cladding, air gap, and fuel pellets.

[0017] In the formula: —Group number; — Neutronics parameter types; —Nengqun g Neutronics parameter types in the whole fuel region x The corresponding equivalent neutronics parameters; —Area of ​​fuel cladding region, m 2 ; —Area of ​​the air gap region, m 2 ; —Area of ​​fuel pellet region, m 2 ; —Nengqun g Neutron parameters in the fuel cladding region x The corresponding neutron parameters; —Nengqun g Neutron parameters in the middle gas gap region x The corresponding neutron parameters; —Nengqun g Neutron parameters in the fuel pellet region x The corresponding neutron parameters.

[0018] Area weighting is used because the height of each axial computational layer is consistent. The area weight can reflect the relative proportion of fuel pellets, air gaps and fuel cladding in the equivalent fuel region. This allows the neutronics parameters of different material regions in the fuel region to be converted into parameter forms that match the neutron physics equivalent fuel region, avoiding repeated reconstruction of the computational mesh due to the different material region divisions in the fuel region between the thermal-hydraulic model and the neutron physics model.

[0019] Preferably, the neutronics parameters for different energy groups include total cross section, absorption cross section, transport cross section or diffusion coefficient, inter-group scattering matrix, fission neutron production cross section, and fission spectrum, and, according to the needs of the transient neutronics model, include delayed neutron fraction and precursor nuclear decay constant. Specifically, the total cross section and absorption cross section describe the collision loss and absorption process of neutrons in materials; the transport cross section or diffusion coefficient describes the spatial migration characteristics of neutrons; the inter-group scattering matrix describes the energy transfer of neutrons between different energy groups; the fission neutron production cross section and fission spectrum determine the intensity and energy distribution of the fission neutron source; and the delayed neutron fraction and delayed neutron precursor nuclear decay constant describe the delayed neutron effect during the time-varying process of fission power. By employing the aforementioned parameters, the loss, migration, scattering, fission multiplication, and slow-emission neutron dynamics of neutrons during transient processes can be characterized more completely. This overcomes the problem that it is difficult to fully describe the changes in neutron flux in the spatial, energy, and temporal dimensions when only a few cross-sectional parameters are used. It provides a complete parameter basis for the transient solution of the neutron transport equation and the dynamic updating of power distribution under nuclear thermal feedback conditions, thereby improving the physical integrity and reliability of transient neutron physics calculations.

[0020] Step 3: Based on the spatial boundaries of the coolant subchannel control bodies, establish virtual coolant mapping sub-regions corresponding to each coolant subchannel control body in the neutron physics model, and establish the correspondence between the fuel rod region and the neutron physics fuel calculation region. By setting virtual coolant mapping sub-regions that correspond one-to-one with the coolant subchannel control bodies, the problem of difficulty in corresponding and transferring local parameters caused by the difference in mesh topology and spatial scale between the thermal-hydraulic model and the neutron physics model is solved, reducing the spatial information loss caused by regional average transfer. The thermal-hydraulic model transfers the coolant temperature of each coolant subchannel control body and the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model, and the neutron physics model transfers the normalized fuel rod power distribution to the thermal-hydraulic model. Preferably, based on the radial and axial boundaries of the coolant subchannel control body, virtual coolant mapping sub-regions are established in the neutron physics model, with the number and spatial range corresponding to each coolant subchannel control body; the virtual coolant mapping sub-region to which it belongs is determined based on the center coordinates of the neutron physics model grid, so that the coolant calculation grid within the same virtual coolant mapping sub-region receives the coolant temperature of the corresponding thermal-hydraulic model coolant subchannel control body.

[0021] Step 4: Complete the initial steady-state calculations for the thermal-hydraulic model and the neutron physics model respectively, and use the initial steady-state calculation results as the initial conditions for the transient calculation; conduct semi-implicit transient coupling calculations of the thermal-hydraulic model and the neutron physics model: within each transient time step, perform Picard fixed-point iterations according to the data transfer direction of the thermal-hydraulic model and the neutron physics model in Step 3, until the changes in coolant temperature, fuel cladding temperature, and fuel pellet temperature between two adjacent iterations are not greater than the preset convergence criterion, and then proceed to the next time step. By repeatedly updating the thermal-hydraulic parameters and neutron physics parameters within the same transient time step, and advancing the time step only after all three satisfy the convergence condition, the time lag caused by a single explicit parameter exchange can be reduced, and the consistency and computational stability of the two physical field solutions under strong feedback transient conditions can be improved; after reaching the set transient end time, output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature, and fuel rod power distribution within the fuel assembly.

[0022] Preferably, the Picard fixed-point iteration includes the following steps: Step 4-1: Complete the initial steady-state calculations of the thermal-hydraulic model and the neutron physics model, establish the coupling parameter mapping relationship between the coolant subchannel control volume, the fuel rod control volume and the fuel region of the neutron physics model, and use the converged initial steady-state calculation results as the initial conditions for transient calculations; Step 4-2: In the first coupled iteration of the current time step, the convergence result of the previous time step is used as the initial iteration value; the thermal-hydraulic model transmits the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model; the neutron physics model performs three-dimensional interpolation based on the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod in the neutronics parameter database of different energy groups, updates the neutronics parameters of different energy groups in each neutron physics model region, and solves the neutron transport equation to obtain the power distribution; Step 4-3: The neutron physics model integrates and normalizes the power distribution within the neutron physics model region corresponding to each fuel rod, and transfers the obtained normalized fuel rod power distribution to the thermal-hydraulic model; the thermal-hydraulic model calculates the coolant temperature, coolant velocity, fuel cladding temperature, and fuel pellet temperature based on the total power at the current time step and the normalized fuel rod power distribution; the results of this iteration are used as the input for the next iteration; Repeat steps 4-2 and 4-3 within the current time step; calculate the maximum absolute change in coolant temperature, fuel cladding temperature and fuel pellet temperature between two adjacent iterations, and determine that the current time step is coupled and converged only if all three are not greater than the preset convergence criterion. Step 4-4: Use the convergence result of the current time step as the initial condition for the next time step and continue iterative calculation until the set transient end time is reached; output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature and fuel rod power distribution in the fuel assembly.

[0023] Preferably, the convergence criterion preset in the Picard fixed-point iteration step is as follows: the difference between the coolant temperature, fuel cladding temperature, and fuel pellet temperature calculated by the thermal-hydraulic model between two iterations is less than 1.2 K. Using 1.2 K as the convergence threshold can limit the temperature field change between adjacent iterations to a preset range, reduce the influence of insufficiently converged thermal-hydraulic parameters on the neutronics parameters and power distribution in the next time step, and control the number of coupled iterations within the time step under the calculation conditions of this embodiment.

[0024] Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. The method of this invention establishes a two-way coupling mechanism between the thermal-hydraulic model and the neutron physics model. It simultaneously considers the influence of fuel rod power on fuel cladding temperature, fuel pellet temperature and coolant thermal-hydraulic parameters, as well as the feedback of coolant temperature, fuel cladding temperature and fuel pellet temperature changes on the neutron transport process through the neutron parameters of different energy groups. Compared with the thermal-hydraulic model alone, it can more accurately describe the multi-physics coupling characteristics in the reactor core. 2. The method of the present invention establishes a coupling mapping relationship between the coolant subchannel control volume, the fuel rod control volume and the fuel region of the neutron physics model, and uses the local coolant temperature, fuel cladding temperature and fuel pellet temperature to perform three-dimensional interpolation of neutron parameters of different energy groups, which can reduce the spatial information loss caused by parameter transfer between heterogeneous computing grids; 3. The method of this invention adopts a semi-implicit transient coupling strategy based on Picard fixed-point iteration. It iteratively updates the thermal hydraulic parameters and neutron physics parameters in each time step, and requires that each convergence judgment quantity simultaneously meet the threshold before advancing the time step, which is beneficial to improving the computational stability under strong feedback transient conditions. Attached Figure Description

[0025] Figure 1 This is a flowchart of the overall process for the nuclear thermal coupling transient analysis method at the fuel assembly level of the present invention.

[0026] Figure 2 This is the mesh generation diagram for the thermal-hydraulic model.

[0027] Figure 3 This is a mesh partitioning diagram for a neutron physics model.

[0028] Figure 4 This is a schematic diagram showing the equivalent treatment of neutronics parameters for different energy groups in the fuel region.

[0029] Figure 5 This is a schematic diagram showing the equivalent treatment of neutronics parameters for different energy groups in the fuel region of the entire assembly.

[0030] Figure 6 This is a flowchart of transient coupled computation based on Picard fixed-point iteration.

[0031] Figure 7 When an external neutron source is introduced into the operating condition, the spatial distribution cloud map of the coolant temperature difference obtained by coupled calculation and uncoupled calculation in this invention is shown.

[0032] Figure 8 When an external neutron source is introduced into the operating condition, the spatial distribution cloud map of the temperature difference at the center of the fuel pellet obtained by coupled calculation and uncoupled calculation in this invention is shown.

[0033] Figure 9 The graph shows the trend of the highest coolant temperature over time obtained by coupled and uncoupled calculations of this invention when an external neutron source is introduced into the operating condition.

[0034] Figure 10 for Figure 9 A graph showing the trend of the difference in maximum coolant temperature between coupled and uncoupled calculations over time.

[0035] Figure 11 The graph shows the trend of the highest temperature at the center of the fuel pellet over time, obtained by coupled and uncoupled calculations of the present invention, when an external neutron source is introduced into the operating condition.

[0036] Figure 12 for Figure 11 A graph showing the trend of the difference in the highest temperature at the center of the fuel pellet obtained from coupled and uncoupled calculations over time. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0038] This invention provides a method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies, the specific method of which is as follows: First, based on the geometric parameters of the reactor core fuel assemblies, a thermo-hydraulic model discretized using subchannels and a neutron physics model discretized using unstructured meshes are established. Second, the Monte Carlo method is used to calculate the neutron parameters of different energy groups at multiple coolant temperature, fuel cladding temperature, and fuel pellet temperature state points. After equivalent processing of the fuel region in the neutron physics model, an equivalent neutron parameter database of three parameters for different energy groups is formed. Third, the coupling parameter mapping relationship between the coolant subchannel control volume, the fuel rod control volume, and the fuel calculation region of the neutron physics model is established. Finally, Picard fixed-point iteration is performed in each transient time step, with the thermo-hydraulic model transmitting coolant temperature, fuel cladding temperature, and fuel pellet temperature to the neutron physics model, and the neutron physics model transmitting the normalized fuel rod power distribution back to the thermo-hydraulic model. The time step is advanced after all convergence criteria are met simultaneously.

[0039] like Figure 1 As shown, taking a fuel assembly with a cross-section of 6×6 fuel rod array as an example, a method for nuclear thermal coupling transient analysis of a nuclear reactor core fuel assembly includes the following four steps: Step 1: Based on the geometric parameters such as the number of fuel rods, fuel rod arrangement, fuel rod pitch, fuel pellet radius, air gap thickness, fuel cladding thickness, assembly width, and assembly height, establish a thermal-hydraulic model and a neutron physics model. The thermal-hydraulic model consists of the following equations: Coolant mass conservation equation:

[0040] Coolant momentum conservation equation:

[0041] Coolant energy conservation equation:

[0042] The thermal conduction equation for fuel rods is as follows:

[0043] In the formula: — Coolant sub-channel number; ——No. i Coolant subchannel density, kg / m³3 ; ——No. i The flow area of ​​each coolant sub-channel is [m²]. 2 ; ——No. i Axial flow velocity of each coolant sub-channel, m / s; —Axial coordinates of the coolant subchannel, in meters; —Time, s; —Net mass exchange source term generated by lateral flow per unit length, kg / (m·s); ——No. i Pressure of each coolant sub-channel, Pa; — Friction coefficient; ——No. i Hydraulic diameter of each coolant sub-channel, m; —Axial component of gravitational acceleration, m / s 2 ; —Net momentum exchange source term generated by lateral flow per unit length, kg / s 2 ; ——No. i Specific enthalpy of each coolant sub-channel, J / kg; —Fuel rods towards the first i Heat transferred per unit axial length by each coolant sub-channel, W / m; —Net energy exchange source term from lateral flow and turbulent mixing per unit length, W / m; —Radial region numbering of fuel rods; —Radial coordinates of the fuel rod, in meters; ——No. j Layer material temperature, K; ——No. j Layer material density, kg / m 3 ; ——No. j Specific heat capacity of the layered material, J / (kg·K); ——No. j Thermal conductivity of the layer material, W / (m·K); ——No. j Volumetric heat source density of layered material, W / m 3 .

[0044] The neutron physics model consists of the following neutron transport equations:

[0045] In the formula: —Group number; ——No. g The average velocity of neutrons in an energy group, cm / s; ——No. g Neutron angular flux of the energy group, n / (cm) 2 ·s·sr); —The unit vector of the direction of neutron motion; ——No. g The total macroscopic cross section of the energy group, cm -1 ; ——No. g Neutron source term of the energy group, n / (cm) 3 ·s·sr).

[0046] The coolant flow area, axial coordinates of the coolant sub-channels, and radial coordinates of the fuel rods in the thermal-hydraulic model are calculated based on the geometric parameters.

[0047] like Figure 2 As shown, the thermal-hydraulic model divides the coolant region into coolant sub-channel control volumes according to the sub-channel boundaries, and divides the fuel rod region into radial fuel rod control volumes according to the fuel cladding, air gap, and fuel pellets; as shown... Figure 3 As shown, the neutron physics model uses the fuel region boundary as a constraint to divide the unstructured triangular computational mesh; Step 2: Select multiple state points for coolant temperature, fuel cladding temperature, and fuel pellet temperature, and use the Monte Carlo method to calculate the neutron parameters of different energy groups of the actual geometry of the fuel assembly at each state point; perform equivalent processing on the neutron parameters of the different energy groups according to the fuel region in the neutron physics calculation model, and establish a database of neutron parameters of different energy groups with coolant temperature, fuel cladding temperature, and fuel pellet temperature as three independent variables; Specifically, based on the common steady-state thermal parameters of pressurized water reactors (operating pressure 15.5 MPa, inlet temperature 573.17 K, outlet temperature 603.15 K), the following energy groups were selected: coolant temperature points (540, 555, 570, 585, 600, and 615 K), fuel cladding temperature points (560, 575, 590, 605, 620, and 635 K), and fuel pellet temperature points (600, 750, 900, 1050, 1200, and 1350 K). The OpenMC Monte Carlo program was used to perform 16-energy group calculations on the operating points composed of these three independent variables, with an energy group boundary of 1.0 × 10⁻⁶. -5 eV, 1.0×10 -2 eV, 3.0×10 -2 eV, 5.8×10 -2 eV, 0.1eV, 0.14eV, 0.28eV,0.625eV, 1.0eV, 4.0eV, 10.0eV, 100.0eV, 1.0×10 3 eV, 5.53×10 3 eV, 1.0×10 5 eV, 8.21×10 5 eV, 2.0×10 7 After the calculation is completed, the neutron parameters are equivalently processed by area weighting to obtain the 16-energy-group neutron parameter database for the three independent variable temperature points mentioned above.

[0048] Step 3: Based on the spatial boundaries of the coolant subchannel control volumes, establish virtual coolant mapping sub-regions corresponding to each coolant subchannel control volume in the neutron physics model, and establish the correspondence between the fuel rod region and the neutron physics fuel calculation region; the thermal-hydraulic model transmits the coolant temperature of each coolant subchannel control volume, as well as the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model, and the neutron physics model transmits the normalized fuel rod power distribution to the thermal-hydraulic model; Step 4: Complete the initial steady-state calculations for the thermal-hydraulic model and the neutron physics model respectively, and use the initial steady-state calculation results as the initial conditions for the transient calculation. Conduct semi-implicit transient coupled calculations of the thermal-hydraulic model and the neutron physics model: In each transient time step, perform Picard fixed-point iterations according to the data transfer direction described in Step 3 until the absolute changes of the coolant temperature, fuel cladding temperature, and fuel pellet temperature in two adjacent iterations are not greater than the preset convergence criterion, and then proceed to the next time step; after reaching the set transient end time, output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature, and fuel rod power distribution in the fuel assembly.

[0049] like Figure 4 and Figure 5 As shown, in a 6×6 fuel assembly, the equivalent neutronics parameters of different energy groups in the overall fuel region of the neutron physics model are obtained by using an area-weighted method for the fuel rods consisting of fuel cladding, air gaps, and fuel pellets:

[0050] In the formula: —Group number; — Neutronics parameter types; —Nengqun g Neutronics parameter types in the whole fuel region x The corresponding equivalent neutronics parameters; —Area of ​​fuel cladding region, m 2 ; —Area of ​​the air gap region, m 2 ; —Area of ​​fuel pellet region, m 2 ; —Nengqun g Neutron parameter types in the fuel cladding region x Corresponding neutron parameters; —Nengqun g Neutron parameters in the middle gas gap region x Corresponding neutron parameters; —Nengqun g Neutron parameters in the fuel pellet region x The corresponding neutron parameters.

[0051] The types of neutronics parameters for different energy groups include total cross section, absorption cross section, transport cross section or diffusion coefficient, inter-group scattering matrix, fission neutron production cross section and fission spectrum, and, depending on the needs of the transient neutronics model, delayed neutron fraction and precursor nuclear decay constant.

[0052] For a fuel assembly with a 6×6 cross-section fuel rod array, each lateral computational layer contains 7×7 coolant sub-channels. Based on the boundaries of the 49 coolant sub-channels, 49 corresponding virtual coolant mapping sub-regions are established in the neutron physics model. The virtual coolant mapping sub-region to which each neutron physics coolant computational grid cell belongs is determined according to the center coordinates of the grid cells, thus enabling each coolant computational grid cell to receive the coolant temperature of the corresponding coolant sub-channel control volume. The fuel cladding temperature and fuel pellet temperature of each fuel rod are transferred to the corresponding neutron physics fuel computational region according to the fuel rod number and axial computational layer.

[0053] like Figure 6 As shown, the semi-implicit transient coupling computation based on Picard fixed-point iteration includes the following steps: Step 4-1: Complete the initial steady-state calculations of the thermal-hydraulic model and the neutron physics model, establish the coupling parameter mapping relationship between the coolant subchannel control volume, the fuel rod control volume and the fuel region of the neutron physics model, and use the converged initial steady-state calculation results as the initial conditions for transient calculations; Step 4-2: In the first coupled iteration of the current time step, the convergence result of the previous time step is used as the initial iteration value; the thermal-hydraulic model transmits the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model; the neutron physics model performs three-dimensional interpolation based on the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod in the neutronics parameter database of different energy groups, updates the neutronics parameters of different energy groups in each neutron physics model region, and solves the neutron transport equation to obtain the power distribution; Step 4-3: The neutron physics model integrates and normalizes the power distribution within the neutron physics model region corresponding to each fuel rod, and transfers the obtained normalized fuel rod power distribution to the thermal-hydraulic model. The thermal-hydraulic model converts the normalized fuel rod power distribution into heat sources for each fuel rod based on the total power of the current time step, and calculates the coolant temperature, coolant velocity, fuel cladding temperature, and fuel pellet temperature. The result of this iteration is used as the input for the next iteration, and steps 4-2 and 4-3 are repeated within the current time step. The maximum absolute change in coolant temperature, fuel cladding temperature, and fuel pellet temperature between two adjacent iterations is calculated respectively. The current time step is considered to have converged only when all three are not greater than their respective preset convergence criteria. The preset convergence criteria are as follows: the difference between the coolant temperature, fuel cladding temperature, and fuel pellet temperature calculated by the thermal-hydraulic model between two adjacent iterations is less than 1.2K. Step 4-4: Use the convergence result of the current time step as the initial condition for the next time step and continue iterative calculation until the set transient end time is reached; output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature and fuel rod power distribution in the fuel assembly.

[0054] Figure 7 This is a spatial distribution cloud map of the coolant temperature difference obtained from coupled and uncoupled calculations at 0.20 s when the present invention is applied to the condition of introducing an external neutron source. As shown in the figure, the coolant temperature difference is negative in most regions, with the lowest being approximately... The temperature difference is 0.33℃, with the more significant negative temperature difference mainly distributed near the external neutron source. A few regions exhibit smaller positive temperature differences, reflecting power redistribution and coolant flow heat transfer processes caused by coupling feedback. Overall, the coupled calculations consider the feedback effects of coolant, fuel cladding temperature, and fuel pellet temperature changes on the neutron transport process, enabling dynamic correction of local power distribution. Therefore, the predicted coolant temperature in the external source influence region is lower than that obtained from the uncoupled calculations.

[0055] Figure 8 This is a spatial distribution cloud map of the fuel pellet center temperature difference at 0.20 s, obtained from coupled and uncoupled calculations of this invention when applied to the external neutron source introduction condition. As shown in the figure, the fuel pellet center temperature difference exhibits a significantly negative value near the external neutron source, with the lowest value being approximately [missing value]. The temperature difference was 66℃, while the difference was relatively small in regions far from the external neutron source. This indicates that the fuel pellet temperature has a fast and significant response to local power disturbances and neutron feedback. Coupled calculations, by considering the Doppler negative feedback caused by the increase in fuel pellet temperature, suppress further increases in local power and fuel pellet temperature, avoiding the temperature overestimation caused by neglecting the feedback effect in uncoupled calculations.

[0056] Figure 9 This paper presents the trend of the maximum coolant temperature over time obtained from coupled and uncoupled calculations when the present invention is applied to the condition of an external neutron source. After the introduction of an external neutron source, the local power increases and heat is transferred to the coolant through the fuel rods, causing the maximum coolant temperature to change over time. The maximum coolant temperature obtained from the coupled calculation is generally lower than that obtained from the uncoupled calculation. This is because the coupled process can correct the neutronics parameters and power distribution in real time based on the continuously updated coolant, fuel cladding temperature, and fuel pellet temperature, thus demonstrating the suppressive effect of temperature negative feedback on coolant temperature rise. This result shows that the present invention can describe the dynamic coupling relationship between neutron power and the thermal-hydraulic state of the coolant under external disturbances.

[0057] Figure 10 for Figure 9The variation trend of the coolant maximum temperature difference obtained from coupled and uncoupled calculations over time is shown in the figure. As can be seen from the figure, after the introduction of an external neutron source, the coolant maximum temperature difference is generally negative, and gradually exhibits a coupled feedback effect during the external source's operation. Since the heat generated by the fuel needs to be transferred to the coolant after passing through the fuel pellets, air gap, and cladding, the coolant temperature exhibits a certain thermal inertia and response delay to power disturbances; therefore, its difference changes relatively smoothly. This result indicates that the present invention can reflect the transient response under the combined action of neutronics negative feedback and the coolant heat transfer process.

[0058] Figure 11 This paper presents the trend of the maximum temperature at the center of the fuel pellet over time, obtained from coupled and uncoupled calculations, when the present invention is applied to the condition of external neutron source introduction. Compared with the coolant temperature, the fuel pellet center temperature responds more quickly to the local power changes caused by the external neutron source. The maximum temperature at the center of the fuel pellet obtained from the coupled calculation is generally lower than that obtained from the uncoupled calculation, and the difference is more significant during periods of strong external source disturbance. This is because the coupled calculation considers the influence of fuel cladding temperature and fuel pellet temperature changes on neutronics parameters, and adjusts the local power in a timely manner through Doppler negative feedback, thereby more reasonably predicting the transient temperature response of the fuel pellet.

[0059] Figure 12 for Figure 11 The graph shows the trend of the maximum temperature difference at the center of the fuel pellet obtained from coupled and uncoupled calculations over time. As can be seen from the figure, after the introduction of an external neutron source, the maximum temperature difference at the center of the fuel pellet rapidly changes towards a negative value, indicating that the negative temperature feedback has a significant impact on fuel pellet temperature prediction. After the removal of the external neutron source, the coupling effect continues for a period of time due to fuel thermal inertia and residual heat transfer. Compared with the maximum temperature difference of the coolant, the maximum temperature difference at the center of the fuel pellet is more pronounced, indicating that ignoring the bidirectional feedback between neutronics and thermal-hydraulic processes may significantly overestimate the fuel pellet temperature. This invention can improve the physical rationality of fuel pellet temperature prediction during transients with the introduction of an external neutron source, providing a more reliable calculation basis for fuel thermal safety margin and reactor transient safety analysis.

[0060] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A method for transient analysis of nuclear thermal coupling in fuel assemblies of a nuclear reactor core, characterized in that, Includes the following steps: Step 1: Establish a thermal-hydraulic model and a neutron physics model based on the geometric parameters of the nuclear reactor core fuel assemblies. The thermal-hydraulic model divides the coolant region into coolant sub-channel control volumes according to the sub-channel boundaries, and divides the fuel rod region into radial fuel rod control volumes according to the fuel cladding, air gaps, and fuel pellets. The neutron physics model divides the unstructured computational mesh with the fuel region boundaries as constraints. Step 2: Select multiple state points for coolant temperature, fuel cladding temperature, and fuel pellet temperature, and use the Monte Carlo method to calculate the neutron parameters of different energy groups for the actual geometry of the fuel assembly at each state point; perform equivalent processing on the neutron parameters of the different energy groups according to the fuel region in the neutron physics model, and establish a database of equivalent neutron parameters for different energy groups with coolant temperature, fuel cladding temperature, and fuel pellet temperature as three independent variables; Step 3: Based on the spatial boundaries of the coolant subchannel control volumes, establish virtual coolant mapping sub-regions corresponding to each coolant subchannel control volume in the neutron physics model, and establish the correspondence between the fuel rod region and the neutron physics fuel calculation region; the thermal-hydraulic model transmits the coolant temperature of each coolant subchannel control volume and the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model, and the neutron physics model transmits the normalized fuel rod power distribution to the thermal-hydraulic model; Step 4: Complete the initial steady-state calculations for the thermal-hydraulic model and the neutron physics model respectively, and use the initial steady-state calculation results as the initial conditions for the transient calculation. Conduct semi-implicit transient coupling calculations of the thermal-hydraulic model and the neutron physics model: In each transient time step, perform Picard fixed-point iterations according to the data transfer direction of the thermal-hydraulic model and the neutron physics model in Step 3 until the changes in coolant temperature, fuel cladding temperature and fuel pellet temperature in two adjacent iterations are not greater than the preset convergence criterion, and then proceed to the next time step; after reaching the set transient end time, output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature and fuel rod power distribution in the fuel assembly.

2. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 1, the geometric parameters of the nuclear reactor core fuel assembly include the number of fuel rods, the arrangement of fuel rods, the fuel rod grid pitch, the fuel pellet radius, the air gap thickness, the fuel cladding thickness, the assembly width, and the assembly height.

3. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 1, the established thermal-hydraulic model consists of the following equations: Coolant mass conservation equation: Coolant momentum conservation equation: Coolant energy conservation equation: The thermal conduction equation for fuel rods is as follows: In the formula: — Coolant sub-channel number; ——No. i Coolant subchannel density, kg / m³ 3 ; ——No. i The flow area of ​​each coolant sub-channel is [m²]. 2 ; ——No. i Axial flow velocity of each coolant sub-channel, m / s; —Axial coordinates of the coolant subchannel, in meters; —Time, s; —Net mass exchange source term generated by lateral flow per unit length, kg / (m·s); ——No. i Pressure of each coolant sub-channel, Pa; — Friction coefficient; ——No. i Hydraulic diameter of each coolant sub-channel, m; —Axial component of gravitational acceleration, m / s 2 ; —Net momentum exchange source term generated by lateral flow per unit length, kg / s 2 ; ——No. i Specific enthalpy of each coolant sub-channel, J / kg; —Fuel rods towards the first i Heat transferred per unit axial length by each coolant sub-channel, W / m; —Net energy exchange source term from lateral flow and turbulent mixing per unit length, W / m; —Radial region numbering of fuel rods; —Radial coordinates of the fuel rod, in meters; ——No. j Layer material temperature, K; ——No. j Layer material density, kg / m 3 ; ——No. j Specific heat capacity of the layered material, J / (kg·K); ——No. j Thermal conductivity of the layer material, W / (m·K); ——No. j Volumetric heat source density of layered material, W / m 3 .

4. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 1, the established neutron physics model consists of the following neutron transport equations: In the formula: —Group number; ——No. g The average velocity of neutrons in an energy group, cm / s; ——No. g Neutron angular flux of the energy group, n / (cm) 2 ·s·sr); —The unit vector of the direction of neutron motion; ——No. g The total macroscopic cross section of the energy group, cm -1 ; ——No. g Neutron source term of the energy group, n / (cm) 3 ·s·sr).

5. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 2, the equivalent processing method for neutronics parameters of different energy groups is as follows: The equivalent neutronics parameters of different energy groups in the overall fuel region of the neutron physics model are obtained by using an area-weighted method for the fuel rod composed of fuel cladding, gas gap, and fuel pellets. In the formula: —Group number; — Neutronics parameter types; —Nengqun g Neutronics parameter types in the whole fuel region x The corresponding equivalent neutronics parameters; —Area of ​​fuel cladding region, m 2 ; —Area of ​​the air gap region, m 2 ; —Area of ​​fuel pellet region, m 2 ; —Nengqun g Neutron parameter types in the fuel cladding region x The corresponding neutron parameters; —Nengqun g Neutron parameters in the middle gas gap region x The corresponding neutron parameters; —Nengqun g Neutron parameters in the fuel pellet region x The corresponding neutron parameters.

6. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 5, characterized in that, The neutronics parameters of the different energy groups include the total cross section, absorption cross section, transport cross section or diffusion coefficient, inter-energy group scattering matrix, fission neutron production cross section and fission spectrum, and, according to the needs of the transient neutronics model, the delayed neutron fraction and the precursor nuclear decay constant.

7. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 3, based on the radial and axial boundaries of the coolant subchannel control body, virtual coolant mapping sub-regions are established in the neutron physics model, with the number and spatial range corresponding to each coolant subchannel control body. The virtual coolant mapping sub-region to which it belongs is determined based on the center coordinates of the neutron physics model grid, so that the coolant calculation grid within the same virtual coolant mapping sub-region receives the coolant temperature of the corresponding thermal-hydraulic model coolant subchannel control body.

8. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 1, characterized in that, In step 4, the Picard fixed-point iteration includes the following steps: Step 4-1: Complete the initial steady-state calculations of the thermal-hydraulic model and the neutron physics model, establish the coupling parameter mapping relationship between the coolant subchannel control volume, the fuel rod control volume and the fuel region of the neutron physics model, and use the converged initial steady-state calculation results as the initial conditions for transient calculations; Step 4-2: In the first coupled iteration of the current time step, the convergence result of the previous time step is used as the initial iteration value; the thermal-hydraulic model transmits the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod to the neutron physics model; the neutron physics model performs three-dimensional interpolation based on the coolant temperature and the fuel cladding temperature and fuel pellet temperature of each fuel rod in the neutronics parameter database of different energy groups, updates the neutronics parameters of different energy groups in each neutron physics model region, and solves the neutron transport equation to obtain the power distribution; Step 4-3: The neutron physics model integrates and normalizes the power distribution within the neutron physics model region corresponding to each fuel rod, and transfers the obtained normalized fuel rod power distribution to the thermal-hydraulic model; the thermal-hydraulic model calculates the coolant temperature, coolant velocity, fuel cladding temperature, and fuel pellet temperature based on the total power at the current time step and the normalized fuel rod power distribution; the results of this iteration are used as the input for the next iteration; Repeat steps 4-2 and 4-3 within the current time step; calculate the maximum absolute change in coolant temperature, fuel cladding temperature and fuel pellet temperature between two adjacent iterations, and determine that the current time step is coupled and converged only if all three are not greater than the preset convergence criterion. Step 4-4: Use the convergence result of the current time step as the initial condition for the next time step and continue iterative calculation until the set transient end time is reached; output the coolant temperature, coolant flow rate, fuel cladding temperature, fuel pellet temperature and fuel rod power distribution in the fuel assembly.

9. The method for transient analysis of nuclear thermal coupling in nuclear reactor core fuel assemblies according to claim 8, characterized in that, The convergence criterion preset in the Picard fixed-point iteration step is that the difference between the coolant temperature, fuel cladding temperature and fuel pellet temperature calculated by the thermal-hydraulic model between two adjacent iterations is less than 1.2K.

Images