A three-dimensional thermal-hydraulic calculation method for pebble bed high temperature gas cooled reactor

Abstract

The present application relates to the technical field of nuclear reactor core thermal-hydraulic calculation, and discloses a three-dimensional thermal-hydraulic calculation method for a pebble bed high-temperature gas-cooled reactor. The present application simulates the natural accumulation process of fuel balls in a reactor core container based on the finite volume method, accurately restores the three-dimensional spatial arrangement of the fuel balls and obtains a stable pebble bed structure. The accumulation structure is then imported into a three-dimensional modeling software to complete the reconstruction of the pebble bed geometry model of the reactor core and the spatial region division, and the local porosity distribution of each region is extracted synchronously. Subsequently, according to the extracted porosity, the key parameters such as the resistance coefficient, the inter-phase convective heat transfer coefficient and the permeability of the porous medium region are calculated through an empirical model, and finally a porous medium model based on control equations is constructed to simulate the whole process of flow and heat transfer inside the reactor core and output the temperature field distribution of the reactor core region, thereby providing accurate data support for the thermal-hydraulic characteristic analysis and safety design of the reactor core.

Description

Technical Field

[0001] This invention relates to the field of thermal-hydraulic calculation technology for nuclear reactor cores, and particularly to a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor. Background Technology

[0002] The pebble bed modular high-temperature gas-cooled reactor uses helium as a coolant and graphite as a moderator and structural material. Its fuel elements are spherical fuel balls containing TRISO-coated particles. This design gives the reactor extremely high inherent safety and high-temperature operating potential.

[0003] However, its core is composed of tens of thousands of randomly stacked fuel spheres, forming a complex, highly non-uniform porous medium structure, resulting in strong spatial anisotropy in coolant flow and heat transfer behavior. Accurate prediction of the temperature, pressure, and velocity fields inside the core is crucial for the safe design and operational assessment of the reactor.

[0004] In practical engineering analysis, to reduce computational complexity, traditional methods often simplify the three-dimensional pebble bed reactor core into a two-dimensional axisymmetric model and homogenize the complex structure into an equivalent medium. This simplification method cannot truly reflect the geometric and physical property differences of the reactor core in the circumferential direction. Therefore, when dealing with actual working conditions such as uneven flow in cold helium channels, circumferential bypass flow, and asymmetric power distribution, it is difficult to accurately predict local hot spots and there is a risk of insufficient safety margin assessment. In addition, traditional methods often calculate the reactor core and internal flow channels separately, which destroys the overall conservation of mass, momentum, and energy equations. Moreover, the numerical solution methods used are sensitive to initial values, have low computational efficiency, and are prone to convergence difficulties. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor.

[0006] This invention provides a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor, comprising the following steps: Set parameters for the core model of the pebble bed type high-temperature gas-cooled reactor, including core size and distribution parameters and material parameters; A three-dimensional structured cylindrical coordinate computational mesh is constructed, and the equivalent material parameters of each mesh element are calculated using a weighted formula based on the mesh and core model parameters. Key model parameters were obtained, and the drag coefficients, Reynolds numbers, and interphase convective heat transfer coefficients of the fuel spherical bed core region and the interphase channel region were obtained through the core model parameters. Based on the finite volume method to discretize the governing equations of three-dimensional porous media, a fully implicit linear equation system describing the heat transfer, coolant flow and heat exchange behavior of solids in the reactor core is constructed. A hybrid solution strategy combining the PARDISO direct solver and the BICGSTAB iterative solver was adopted to solve the fully implicit linear equations and obtain the three-dimensional thermal-hydraulic parameter distribution of the reactor core. Output the three-dimensional and two-dimensional thermal-hydraulic parameter distribution results.

[0007] Furthermore, the core dimensions and distribution parameters include the fuel sphere size, core cavity diameter, reflector thickness, and the distribution of various materials. The material parameters include the thermal conductivity, heat capacity, porosity, and emissivity of the fuel spheres, reflector, and materials outside the neutron diffusion region.

[0008] Furthermore, the construction of the three-dimensional structured computational grid specifically involves: setting a fine grid in the central region of the core and regions with large parameter change gradients, and setting a coarse grid in the inert regions at the top / bottom of the core and regions with gentle parameter gradients, based on the parameter change gradient within the core.

[0009] Furthermore, the formula for obtaining the drag coefficient of the fuel spherical bed core is as follows: The formula for obtaining the resistance coefficient of the gap channel is as follows: In the formula: The flow resistance coefficient is expressed as kg·m⁻³·s⁻¹. The fuel ball diameter is represented by a unit of length (m). The dynamic viscosity of helium is given by kJ·m⁻¹·s⁻¹. The fluid mesh velocity is given in m·s⁻¹. Helium density (kg·m⁻³); Porosity; It is the Reynolds number; Additional resistance / m-1; Hydraulic diameter / m; This represents the gap flow resistance coefficient.

[0010] Furthermore, the Reynolds number calculation formula for the fuel spherical bed core is as follows: The Reynolds number of the gap channel is calculated using the following formula: Furthermore, the interphase convective heat transfer coefficients of the fuel spherical bed reactor core and the gap channels are derived and calculated using the empirical formula for the Nusselt number. The empirical formula for the Nusselt number of the fuel spherical bed reactor core is as follows: The empirical formula for the Nusselt number of the gap channel is as follows: In the formula: For Nusselt number; Helium thermal conductivity / W·m -1 ·K -1 ; The fuel ball diameter is represented by a unit of length (m). The value is the hydraulic diameter in meters (m).

[0011] Furthermore, the fully implicit linear equation set includes the thermal conductivity equation for porous media solids, the mass conservation equation, the momentum conservation equation, and the fluid energy conservation equation, specifically: Thermal conductivity equation for porous media solids: Mass conservation equation and momentum conservation equation: Fluid energy conservation equation: In the formula: Porosity; Density of porous media / kg·m -3 ; Specific heat capacity of porous media / J·kg -1 ·K -1 ; Equivalent thermal conductivity / W·m -1 ·K -1 ; Power density / W·m -3 ; The fluid-solid heat transfer coefficient; The area of ​​the fluid-solid heat exchanger; Fluid density / kg·m -3 ; Mass flow rate source / kg·m -3 ·s -1 ; fluid velocity / m·s -1 ; Acceleration due to gravity / m·s -2 ; Pressure (Pa); Fluid thermal conductivity / W·m -1 ·K -1 ; Friction drag coefficient / kg·m -3 ; Heat transfer coefficient / W·m -2 ·K -1 ; fluid-solid contact area / m 2 ; Solid volume per m 3 .

[0012] A three-dimensional thermal-hydraulic calculation system for a pebble bed type high-temperature gas-cooled reactor includes: The core parameter input module for the pebble bed type high-temperature gas-cooled reactor allows users to input initial parameters such as core geometry, material parameters, operating conditions, and boundary conditions, which are then transferred to the 3D model generation module and the physical property calculation module. The three-dimensional cylindrical coordinate model generation module generates a coarse-fine mesh structure of the core based on user input, and transmits the mesh information to the physical property and drag coefficient calculation module and the finite volume method discretization module; The property and drag coefficient calculation module calculates parameters such as porosity, temperature, drag coefficient, material properties, and dimensionless number for each grid cell, and uses these parameters as inputs to the fully implicit discretization module of the finite volume method. The finite volume method fully implicit discretization module is used to discretize partial differential equations, form a grid-based fully implicit linear system of equations, and pass it to the PARDISO-BICGSTAB hybrid solver module. This module, based on the PARDISO-BICGSTAB hybrid linear equations solver, is used to solve discrete linear equations in 3D modeling, improving solution efficiency. The solution results include pressure, velocity, and other thermo-hydraulic parameters for each mesh element.

[0013] The output module is used to output three-dimensional temperature distribution parameters, three-dimensional pressure distribution parameters, etc., for analysis, visualization or further engineering calculations.

[0014] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method steps described above.

[0015] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0016] Compared with the prior art, the technical solution provided by the embodiments of the present invention has the following advantages: The present invention simulates the natural stacking process of fuel spheres in the reactor core container based on the finite volume method, accurately restores the three-dimensional spatial arrangement of fuel spheres and obtains a stable sphere bed structure, and then imports the stacking structure into three-dimensional modeling software to complete the reconstruction of the geometric model of the reactor core sphere bed and the division of spatial regions. Simultaneously, the local porosity distribution of each region is extracted. Then, based on the extracted porosity, key parameters such as the drag coefficient, interphase convective heat transfer coefficient and permeability of the porous medium region are calculated through an empirical model. Finally, a porous medium model based on the governing equation is constructed to simulate the entire process of flow and heat transfer inside the reactor core and output the temperature field distribution of the reactor core region, thereby providing accurate data support for the analysis of the thermal-hydraulic characteristics of the reactor core and safety design. Attached Figure Description

[0017] Figure 1 A schematic diagram of the overall method steps for a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor; Figure 2 This is a structural block diagram of the overall method steps for a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor.

[0018] Figure 3 This is a schematic diagram of the overall structure of a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor. Detailed Implementation

[0019] The following detailed description of a specific embodiment of the present invention is provided in conjunction with the accompanying drawings. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0020] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0021] The present invention will be described below through several specific embodiments. To keep the following description of the embodiments clear and concise, detailed descriptions of known functions and components may be omitted. When any component of an embodiment of the present invention appears in more than one drawing, the component may be represented by the same reference numerals in each drawing.

[0022] Example 1 like Figure 1The diagram shows the overall method steps and structure of a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor. Figure 2 The diagram shows the overall steps and structure of a three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor.

[0023] A three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor includes the following steps: S1: Set the parameters of the pebble bed type high temperature gas-cooled reactor core model, including core size and distribution parameters and material parameters; Specifically, the relevant parameters of the pebble bed type high-temperature gas-cooled reactor core model are divided into two main categories: core size and distribution, and material parameters. Core size and distribution parameters include the size of the fuel spheres inside the core, the diameter of the core cavity, the thickness of the reflector, the distribution of various materials, and key geometric parameters such as fuel sphere packing density, gap channel width, and core axial height. The fuel sphere size must match the actual core design specifications, typically selecting spherical fuel elements with a diameter of 50-80mm. The core cavity diameter is set according to the reactor power rating; for small and medium-sized cores, it is generally 1.0-2.0m. The reflector thickness must meet neutron shielding and insulation requirements, typically 0.2-0.5m. Material parameters include the material... Parameters such as thermal conductivity, heat capacity, porosity, and emissivity also cover the physical properties of the fuel core, cladding, reflector material, and coolant (helium). Among them, the thermal conductivity of the fuel core needs to be corrected for temperature variations, and the thermal conductivity, dynamic viscosity, and other physical properties of helium need to be precisely selected according to the core operating temperature range (300-1200K). All of the above parameters need to be specifically selected and set according to the specific design requirements, operating conditions, and material characteristics of the core. At the same time, they need to be calibrated with reference to relevant nuclear power industry standards and experimental data to ensure that the results obtained in the simulation process have good physical realism and engineering applicability, laying a reliable foundation for subsequent mesh construction, model calculation, and equation solving.

[0024] S2: Construct a three-dimensional structured cylindrical coordinate computational mesh, and calculate the equivalent material parameters of each mesh element based on the mesh and core model parameters using a weighted formula; Specifically, the three-dimensional thermal-hydraulic calculation method for the pebble bed high-temperature gas-cooled reactor of this invention is executed by a computer program. Considering that the core of the pebble bed high-temperature gas-cooled reactor is a cylindrical symmetrical structure, the core computational domain is spatially discretized in cylindrical coordinates. A structured three-dimensional cylindrical coordinate computational grid is constructed along the radial, circumferential, and axial directions. The structured grid has the advantages of high computational accuracy, fast convergence speed, and easy equation discretization, which can effectively adapt to the computational requirements of the symmetrical core structure. Among them, fine grids are set in the main flow region of the core (such as the densely packed fuel sphere area and the helium main flow channel area) and the region with large parameter change gradients (such as the power-dense area in the core center and the coolant inlet and outlet transition area), with a grid size of 3-8 mm, to accurately capture the abrupt changes in local parameters and improve computational accuracy. Coarse grids are set in the region with small structural changes and gentle parameter gradients (such as the region where the reflector is far from the core center and the inert region at the top / bottom of the core), with a grid size of 15-30 mm, to reduce computational overhead, shorten the computation cycle, and achieve a balance between computational accuracy and efficiency.

[0025] Based on the constructed mesh setting of material distribution, the mapping and matching of material parameters and mesh cells are completed: For regions with a single material composition in the core (such as pure reflector layer regions or pure fuel sphere stacking regions), a single mesh cell corresponds to one material, and its material parameters (thermal conductivity, heat capacity, etc.) are directly assigned to the mesh cell without additional correction; For mesh cells located at the interface of different materials (such as the interface between fuel spheres and reflector layer, or the interface between fuel spheres and helium) or in the equivalent porous medium region of the sphere bed, a multi-material mixing method is used to represent them. In such mesh cells, multiple materials coexist. It is necessary to calculate the material properties based on the volume fraction of each material in the mesh cell. The weighting formula adopts a linear weighting model, that is, equivalent material parameter = Σ (volume fraction of a certain material × corresponding material property parameter), so as to obtain the equivalent material parameter of the mesh cell and avoid the calculation deviation caused by insufficient confidence in the material interface treatment.

[0026] Based on the constructed computational grid and mapped material parameters, the conservation equations for core mass, momentum, and energy are discretized and iteratively solved using the finite volume method. The finite volume method rigorously guarantees the conservation of physical quantities and is suitable for computational requirements related to flow and heat transfer in porous media. During discretization, a second-order upwind scheme is used to handle the convection term, improving computational accuracy, while a central difference scheme is employed to handle the diffusion term, ensuring numerical stability. Through preliminary iterative solutions, relevant parameters such as temperature, pressure, flow rate, velocity, and porosity of each grid cell are obtained, providing fundamental data for subsequent calculations of key model parameters and enabling preliminary calculations of the core's three-dimensional thermal-hydraulic properties.

[0027] S3: Obtain key model parameters, and obtain the differential drag coefficients, Reynolds numbers and interphase convective heat transfer coefficients of the fuel ball bed core region and the interphase channel region through the core model parameters; Specifically, the flow state and heat transfer characteristics of helium gas in the fuel spherical bed and the interstitial channels within the reactor core differ significantly. If a uniform model is used for calculation, it will lead to large parameter deviations. Therefore, it is necessary to construct a differentiated model specifically for this purpose. Based on the porosity distribution in the spherical bed core and the flow velocity, temperature, and other parameters obtained in step S2, the drag coefficient, Reynolds number, and interphase convective heat transfer coefficient are calculated to provide accurate parameter inputs for solving the subsequent equations. The drag coefficient is determined by setting its own drag coefficient model based on the structural differences between the fuel spherical bed and the gap channels. The formula for obtaining the drag coefficient of the fuel spherical bed core is as follows: The formula for obtaining the resistance coefficient of the gap channel is as follows: In the formula: The flow resistance coefficient is expressed as / kg·m -3 ·s -1 It is used to characterize the sum of frictional resistance and local resistance encountered during fluid flow; The fuel ball diameter is expressed in meters (m) and is determined based on the core design parameters. Helium dynamic viscosity / kg·m -1 ·s -1 It is corrected in real time according to temperature changes; Fluid mesh velocity / m·s -1 It is obtained by preliminary iterative solution in step S2; Helium density / kg·m -3 It is determined based on the core pressure and temperature conditions. Porosity is calculated from the fuel pellet packing density and the material distribution of the grid cells; is the Reynolds number, a dimensionless number that characterizes the fluid flow state (laminar flow, turbulent flow); Additional resistance (input by input card) / m -1 The main considerations are the additional resistance caused by the surface roughness and irregularity of the fuel balls, and the determination is based on experimental data. The hydraulic diameter is expressed in meters (m). The hydraulic diameter of the gap channel is calculated based on the channel cross-sectional dimensions. is the gap flow resistance coefficient, which is an empirical coefficient with a value range of 0.01-0.05, and is calibrated according to the gap channel structure and flow conditions.

[0028] The Reynolds number calculation formulas mentioned above also differ and need to be adapted to the flow characteristics of pebble bed cores and gap channels respectively: The formula for calculating the Reynolds number of a fuel spherical bed reactor core is as follows: The formula for calculating the Reynolds number of the gap channel is as follows: The Reynolds number calculation for the reactor core is based on the diameter of the fuel spheres as the characteristic length, while the Reynolds number for the gap channels is based on the hydraulic diameter as the characteristic length. When the Reynolds number is less than 2300, it is laminar flow; when it is greater than 4000, it is turbulent flow; and when it is between 2300 and 4000, it is transitional flow. Under different flow conditions, the calculation of the drag coefficient and heat transfer coefficient needs to be corrected in combination with the flow characteristics to ensure the accuracy of the parameter calculation.

[0029] Based on the porosity distribution, temperature distribution, and flow velocity parameters of the fuel spherical bed and interstitial channels, the interphase convective heat transfer coefficient is obtained. This coefficient is derived using the empirical formula for the Nusselt number. The empirical formula for the Nusselt number of a fuel spherical bed reactor core is as follows: The empirical formula for the Nusselt number of the gap channel is as follows: In the formula: , where is the Nusselt number, a dimensionless number; the larger the value, the stronger the convective heat transfer. Helium thermal conductivity / W·m -1 ·K -1 It is corrected in real time according to temperature changes; The fuel ball diameter is represented by a unit of length (m). Hydraulic diameter / m; The empirical formula for the Nusselt number in the reactor core is applicable to convective heat transfer in porous media formed by fuel sphere stacking. The empirical formula for the Nusselt number in gap channels is applicable to convective heat transfer in parallel channels or annular gaps. The values ​​of the coefficients in the empirical formulas need to be calibrated based on experimental data and reactor core operating conditions to ensure the accuracy of the heat transfer coefficient calculation and provide reliable support for subsequent fluid-solid heat transfer calculations.

[0030] S4: Based on the finite volume method to discretize the governing equations of three-dimensional porous media, a fully implicit linear equation system is constructed to describe the solid heat transfer, coolant flow and heat exchange behavior in the reactor core. Specifically, the core of a pebble-bed high-temperature gas-cooled reactor can be equivalently represented as a porous medium structure, with the fuel sphere stacking area forming the porous medium framework and helium as the flow medium. A porous medium model is constructed for calculating flow and heat transfer within the core region. The model is discretized using the finite volume method, which strictly guarantees the conservation of mass, momentum, and energy, and is suitable for the computational needs of complex flow and heat transfer in porous media. This model comprehensively describes the solid heat transfer, coolant (helium) flow, and coolant heat exchange behavior in the porous medium of the reactor core region, covering complex processes such as fuel sphere heat conduction, helium convection heat transfer, fluid-solid radiative heat transfer, and nuclear power generation. The equations constructed by this model are in a fully implicit scheme, which has the advantages of good numerical stability and allows for large time steps, effectively shortening the calculation cycle and adapting to the needs of rapid engineering calculations. The specific model equations include:

[0031] Porous media solid thermal conductivity: Solving the pressure-velocity equation (mass conservation equation and momentum conservation equation): Fluid convection heat transfer (energy conservation equation): In the formula, Porosity is the volume fraction of the fluid-flowable region in a porous medium. Density of porous media / kg·m -3 , that is, the density of solid materials such as fuel balls and reflective layers; Specific heat capacity of porous media / J·kg -1 ·K -1 The specific heat capacity of solid materials is corrected as temperature changes. Equivalent thermal conductivity / W·m -1 ·K -1 The equivalent material parameters of the mesh elements calculated in step S2 are used to determine the parameters. Power density / W·m -3 The power distribution generated by the nuclear reaction in the reactor core is set based on the core design and nuclear physics calculations. The fluid-solid heat transfer coefficient is calculated in step S3 and characterizes the heat transfer intensity between the solid and the fluid. The contact area between the solid and the fluid per unit volume is the fluid-solid heat transfer area, which is determined by the bulk density of the fuel pellets. Fluid density / kg·m -3 That is, the density of helium; Mass flow rate source / kg·m -3 ·s -1 This value is used to account for possible mass injection or leakage within the reactor core, and is set to 0 under normal operating conditions. fluid velocity / m·s -1 The flow velocity of helium within the grid cell; Acceleration due to gravity / m·s -2 The value is 9.8 m·s -2 The direction is downward along the axial direction; Pressure is expressed in Pa, representing the static pressure of helium within a grid cell. Fluid thermal conductivity / W·m -1 ·K -1 , that is, the thermal conductivity of helium; Friction drag coefficient / kg·m -3 The flow resistance coefficient is determined by the flow resistance coefficient calculated in step S3; Heat transfer coefficient / W·m -2 ·K -1 It is consistent with the fluid-solid heat transfer coefficient, characterizing the heat transfer capacity between the fluid and the solid. fluid-solid contact area / m 2 The actual contact area between the solid and the fluid within the grid cell; Solid volume per m 3 The volume occupied by solids and fluids within a grid cell.

[0032] By solving the equations for this porous medium, the solid temperature distribution, pressure distribution, flow rate distribution, and gas temperature distribution within the core sphere bed can be obtained comprehensively, accurately reflecting the thermal-hydraulic characteristics within the core and providing data support for core safety assessment.

[0033] S5: A hybrid solution strategy combining the PARDISO direct solver and the BICGSTAB iterative solver is adopted to solve the fully implicit linear equations and obtain the three-dimensional thermal-hydraulic parameter distribution of the reactor core. Specifically, the three-dimensional thermal-hydraulic governing equations of the reactor core are coupled nonlinear equations. After discretization, a large-scale fully implicit linear equation system is obtained. Such equation systems have many variables and strong coupling, making it difficult for a single solver to simultaneously achieve solution accuracy, efficiency, and stability. To ensure the numerical stability of the three-dimensional thermal-hydraulic equations of the reactor core and allow for large time steps (time steps can be selected from 0.1 to 1.0 s), a fully implicit scheme is used to discretize the mass, momentum, and energy conservation equations over time. The fully implicit scheme can effectively avoid numerical oscillations and improve solution stability.

[0034] Furthermore, considering the significant impact of initial values ​​on the convergence speed and accuracy of the equation solution, improper initial values ​​can easily lead to divergence or extremely slow convergence in the iterative solution. Therefore, the PARDISO direct solver is first used to directly solve the pressure-velocity linear equation system. The PARDISO direct solver is suitable for solving large-scale sparse linear equation systems, possessing advantages such as high solution accuracy and strong stability. It can quickly obtain stable initial pressure and velocity distributions, providing reliable initial conditions for subsequent iterative solutions. Then, this initial result is used as the initial value for the BICGSTAB iterative solver to accelerate the iterative solution of the coupled equation system. The BICGSTAB iterative solver is an efficient iterative solution method that combines the advantages of BiCG and GMRES solvers, with fast convergence speed and low memory consumption, effectively adapting to the solution requirements of large-scale coupled equation systems.

[0035] Furthermore, the iterative process uses an iteration increment less than a preset tolerance as the convergence criterion. The tolerance is set according to the required computational accuracy, typically 1×10⁻⁶. -6 -1×10 -8 When the iterative increments of parameters such as pressure, velocity, and temperature in each grid cell are all less than the preset tolerance, the equation set is determined to be converged, thereby obtaining the pressure, velocity, and other thermal-hydraulic parameters (such as temperature, flow rate, porosity, etc.) of each grid cell, and completing the accurate solution of the three-dimensional thermal-hydraulic parameters of the reactor core.

[0036] S6: Outputs three-dimensional and two-dimensional thermo-hydraulic parameter distribution results This system outputs three-dimensional thermal-hydraulic parameter distributions, two-dimensional profile parameter distributions, and inlet / outlet parameter information for pebble-bed high-temperature gas-cooled reactors. The three-dimensional thermal-hydraulic parameter distribution includes three-dimensional temperature, pressure, velocity, flow rate, and porosity distributions across the entire core, providing a clear view of the spatial distribution characteristics of parameters within the core. The two-dimensional profile parameter distribution includes parameter distributions in the radial, axial, and circumferential sections of the core, facilitating the analysis of parameter variation patterns in local areas, with a focus on parameter distributions in key areas such as the core center and coolant inlets / outlets. Inlet / outlet parameter information includes coolant inlet / outlet temperatures, pressures, flow rates, and pressure losses, used to assess the core's heat transfer efficiency and flow resistance characteristics. The output results can be exported to common data formats (such as TXT and CSV) for engineers to perform subsequent analysis, visualization (e.g., drawing cloud maps and streamline diagrams using ParaView), or further engineering calculations, providing comprehensive and accurate data support for the design optimization, safety margin assessment, and operational parameter adjustment of pebble-bed high-temperature gas-cooled reactors.

[0037] Example 2 like Figure 3 The diagram shows the overall structural composition of a three-dimensional thermal-hydraulic calculation method for a pebble bed high-temperature gas-cooled reactor. This embodiment provides a three-dimensional thermal-hydraulic calculation system for a pebble bed high-temperature gas-cooled reactor based on the calculation method described in Embodiment 1. It adopts a modular design, possessing advantages such as strong scalability, convenient operation, and high computational efficiency. It can automate the entire process of core parameter input, model construction, equation discretization, equation system solution, and result output, adapting to the calculation needs of pebble bed high-temperature gas-cooled reactors of different specifications. Specifically, it includes a pebble bed high-temperature gas-cooled reactor core parameter input module, a three-dimensional cylindrical coordinate model generation module, a finite volume method fully implicit discretization module, a physical property and drag coefficient calculation module, a PARDISO-BICGSTAB hybrid linear equation system solution module, and an output module. All modules work collaboratively and communicate data, ensuring the smoothness of the calculation process and the reliability of the calculation results. Specifically: The core parameter input module for the pebble bed high-temperature gas-cooled reactor serves as the input point for the entire system, possessing parameter input, verification, storage, and transmission functions. Users can input initial parameters such as core geometry, material parameters, operating conditions, and boundary conditions through a visual interface (e.g., a GUI). Boundary conditions include key parameters such as core coolant inlet and outlet pressures, inlet and outlet flow rates, core wall temperature, and nuclear power distribution boundaries. This module incorporates parameter verification logic to check the rationality and completeness of input parameters (e.g., verifying whether the fuel sphere diameter and mesh size range conform to engineering specifications, and verifying the consistency of parameter units), avoiding calculation errors caused by invalid parameters. Simultaneously, this module synchronously transmits the verified initial parameters to the 3D model generation module and the physical property calculation module, ensuring consistent parameters used by each module and providing a unified parameter basis for subsequent calculations. Input parameters can be stored as parameter configuration files for easy subsequent calling, modification, and reuse.

[0038] The 3D cylindrical coordinate model generation module receives initial parameters from the core parameter input module and constructs a 3D structured mesh of the core based on the cylindrical coordinate system. Its core feature is the adaptive partitioning of coarse and fine meshes, automatically identifying the partitioning regions based on the gradient of core parameter changes, eliminating the need for manual user settings and reducing operational complexity. Simultaneously, this module maps material distribution to mesh elements, generating a mesh information file (containing mesh coordinates, mesh size, material type, volume fraction, etc.) and synchronously transmitting this mesh information to the physical property and drag coefficient calculation modules and the finite volume method discretization module, providing mesh support for subsequent parameter calculations and equation discretization. Furthermore, this module has a mesh quality check function, capable of checking the orthogonality, stretch ratio, and other indicators of the constructed mesh to ensure that the mesh quality meets the requirements of numerical calculations and avoids computational deviations or convergence difficulties caused by poor mesh quality.

[0039] The property and drag coefficient calculation module receives mesh information from the 3D cylindrical coordinate model generation module and, combined with initial parameters from the core parameter input module, calculates key parameters for each mesh cell, including porosity, temperature (initial temperature distribution), drag coefficient, material properties (equivalent thermal conductivity, equivalent heat capacity, etc.), dimensionless numbers (Reynolds number, Nusselt number), and interphase convective heat transfer coefficient. This module has a built-in property parameter database storing the property parameters of helium and various solid materials under different temperature and pressure conditions. It can automatically retrieve and correct property parameters according to core operating conditions. Simultaneously, based on the differentiated model described in Example 1, this module calculates the drag coefficient, Reynolds number, and interphase convective heat transfer coefficient for the fuel spherical bed and interstitial channels, ensuring the accuracy of parameter calculations. After calculation, this module organizes all key parameters into a standardized data format as input data for the finite volume method fully implicit discretization module, ensuring data transfer compatibility.

[0040] The finite volume method fully implicit discretization module's core function is to discretize partial differential equations. It receives key parameters from the property and drag coefficient calculation module and mesh information from the 3D cylindrical coordinate model generation module. Based on the finite volume method, it performs fully implicit discretization on the thermal conductivity equation, mass conservation equation, momentum conservation equation, and fluid energy conservation equation of the porous medium solid described in Example 1. A second-order accuracy scheme is used during discretization to balance computational accuracy and numerical stability. Simultaneously, the module organizes the discretized equations into a large-scale fully implicit linear equation system, performing sparsification to reduce the computational cost of subsequent solutions. This sparse linear equation system is then transferred to the PARDISO-BICGSTAB hybrid solution module. Furthermore, the module has an equation discretization verification function to check the correctness of the discretization process, ensuring consistency between the discretized equation system and the original partial differential equations.

[0041] The PARDISO-BICGSTAB hybrid linear equation solving module is the core solution unit of the entire system. It receives the sparse linear equations from the finite volume method fully implicit discretization module and employs the hybrid solution strategy described in Example 1, integrating the PARDISO direct solver and the BICGSTAB iterative solver to achieve efficient solution of the equations. This module features configurable solution parameters, allowing users to set convergence tolerance, time step, and upper limit of iterations according to computational needs. Simultaneously, the module monitors the solution process in real time, recording solution information such as the number of iterations and convergence speed. If divergence or slow convergence occurs, it automatically adjusts the solution parameters or regenerates initial values ​​to ensure the stability of the solution process. After completion, the module outputs the thermal-hydraulic parameters such as pressure, velocity, temperature, and flow rate of each grid cell and transmits the solution results to the output module.

[0042] The output module receives the calculation results from the hybrid solver module, organizes, formats, and visualizes the results, and has multi-dimensional output capabilities: it can output three-dimensional thermal-hydraulic parameter distribution data, two-dimensional profile parameter distribution data, and inlet and outlet parameter information, and supports exporting results to common data formats (TXT, CSV, VTK, etc.) for easy subsequent analysis and secondary calculations. Simultaneously, this module has built-in visualization functions, which can directly draw three-dimensional parameter cloud maps, two-dimensional profile cloud maps, streamline diagrams, trend curves, etc., intuitively displaying the distribution characteristics and variation patterns of core thermal-hydraulic parameters, facilitating engineers to quickly capture key information (such as core hot spot temperature, maximum pressure loss, etc.). Furthermore, this module has a result comparison function, which can compare the current calculation results with historical calculation results and experimental data to evaluate the accuracy of the calculation results and provide a basis for model optimization.

[0043] The technical solutions involved in this invention, if their functions are implemented in the form of software functional units and can be sold or used as independent products, can be stored in a computer-readable storage medium. This computer software product, stored in a storage medium, contains several instructions to cause a computer device (such as a personal computer, server, or network device) to execute all or part of the steps of the methods in the embodiments of this invention. The aforementioned storage medium includes, but is not limited to, any medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, adaptable to software storage and retrieval needs in different scenarios.

[0044] The logic and steps described in flowcharts or otherwise can be considered as a sequence of executable instructions that implement logical functions. These instructions can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a processor-containing system, or other system capable of fetching and executing instructions). In the context of this specification, "computer-readable medium" can mean any means capable of containing, storing, transmitting, propagating, or delivering a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0045] Specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) with one or more wires enabling wired transmission of program code; portable computer disks (magnetic devices) for storing program code and facilitating portability; random access memory (RAM) for real-time reading and writing of program code to meet the operational needs of computer devices; read-only memory (ROM) for permanent storage of program code, ensuring stable program access; erasable programmable read-only memory (EPROM or flash memory) for multiple erasures and reprogramming, offering flexibility; fiber optic devices for high-speed transmission of program code; and portable optical disc read-only memory (CD-ROM) for storing large amounts of program code, facilitating distribution and reuse. Furthermore, computer-readable media can even be paper or other suitable media capable of printing programs, as such paper or media can be optically scanned, then edited, interpreted, or otherwise processed to obtain the program electronically and store it in computer memory, enabling program storage and retrieval.

[0046] Furthermore, this embodiment also provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements all the steps of the three-dimensional thermal-hydraulic calculation method for the pebble bed type high-temperature gas-cooled reactor described in Embodiment 1 of the present invention. This computer device can be an industrial server, a high-performance workstation, etc., and has sufficient computing power to support high-intensity computing tasks such as large-scale grid discretization and equation solving. The processor can be a multi-core CPU or combined with a GPU to accelerate computing, further improving computing efficiency. The memory can be a large-capacity solid-state drive (SSD) to ensure the smoothness of program operation and data storage, and to meet the needs of large-scale engineering computing.

[0047] The above inventions are merely a few specific embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor, characterized in that, Includes the following steps: Set parameters for the core model of the pebble bed type high-temperature gas-cooled reactor, including core size and distribution parameters and material parameters; A three-dimensional structured cylindrical coordinate computational mesh is constructed, and the equivalent material parameters of each mesh element are calculated using a weighted formula based on the mesh and core model parameters. Key model parameters were obtained, and the drag coefficients, Reynolds numbers, and interphase convective heat transfer coefficients of the fuel spherical bed core region and the interphase channel region were obtained through the core model parameters. Based on the finite volume method to discretize the governing equations of three-dimensional porous media, a fully implicit linear equation system describing the heat transfer, coolant flow and heat exchange behavior of solids in the reactor core is constructed. A hybrid solution strategy combining the PARDISO direct solver and the BICGSTAB iterative solver was adopted to solve the fully implicit linear equations and obtain the three-dimensional thermal-hydraulic parameter distribution of the reactor core. Output the three-dimensional and two-dimensional thermal-hydraulic parameter distribution results.

2. The three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor as described in claim 1, characterized in that, The core dimensions and distribution parameters include the fuel sphere size, core cavity diameter, reflector thickness, and the distribution of various materials. The material parameters include the thermal conductivity, heat capacity, porosity, and emissivity of the fuel sphere, reflector, and materials outside the neutron diffusion region.

3. The three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor as described in claim 1, characterized in that, The construction of the three-dimensional structured computational grid is specifically as follows: based on the parameter variation gradient within the core, a fine grid is set in the central region of the core and regions with large parameter variation gradients, while a coarse grid is set in the inert regions at the top / bottom of the core and regions with gentle parameter gradients.

4. The three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor as described in claim 3, characterized in that, The formula for obtaining the drag coefficient of the fuel spherical bed reactor core is as follows: The formula for obtaining the resistance coefficient of the gap channel is as follows: In the formula: The flow resistance coefficient is expressed as / kg·m -3 ·s -1 ; The fuel ball diameter is represented by a unit of length (m). Helium dynamic viscosity / kg·m -1 ·s -1 ; Fluid mesh velocity / m·s -1 ; Helium density / kg·m -3 ; Porosity; It is the Reynolds number; Additional resistance / m -1 ; Hydraulic diameter / m; This represents the gap flow resistance coefficient.

5. The three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor as described in claim 4, characterized in that, The Reynolds number of the fuel spherical bed reactor core is calculated using the following formula: The Reynolds number of the gap channel is calculated using the following formula: The three-dimensional thermal-hydraulic calculation method for a pebble-bed high-temperature gas-cooled reactor as described in claim 5 is characterized in that the interphase convective heat transfer coefficients of the fuel pebble-bed reactor core and the interstitial channels are derived and calculated using the empirical formula for the Nusselt number. The empirical formula for the Nusselt number of the fuel pebble-bed reactor core is as follows: The empirical formula for the Nusselt number of the gap channel is as follows: In the formula: For Nusselt number; Helium thermal conductivity / W·m -1 ·K -1 ; The fuel ball diameter is represented by a unit of length (m). The value is the hydraulic diameter in meters (m).

6. The three-dimensional thermal-hydraulic calculation method for a pebble bed type high-temperature gas-cooled reactor as described in claim 1, characterized in that, The fully implicit linear equations include the thermal conductivity equation for porous media, the mass conservation equation, the momentum conservation equation, and the fluid energy conservation equation, specifically: Thermal conductivity equation for porous media solids: Mass conservation equation and momentum conservation equation: Fluid energy conservation equation: In the formula: Porosity; Density of porous media / kg·m -3 ; Specific heat capacity of porous media / J·kg -1 ·K -1 ; Equivalent thermal conductivity / W·m -1 ·K -1 ; Power density / W·m -3 ; The fluid-solid heat transfer coefficient; The area of ​​the fluid-solid heat exchanger; Fluid density / kg·m -3 ; Mass flow rate source / kg·m -3 ·s -1 ; fluid velocity / m·s -1 ; Acceleration due to gravity / m·s -2 ; Pressure (Pa); Fluid thermal conductivity / W·m -1 ·K -1 ; Friction drag coefficient / kg·m -3 ; Heat transfer coefficient / W·m -2 ·K -1 ; fluid-solid contact area / m 2 ; Solid volume per m 3 .

7. A three-dimensional thermal-hydraulic calculation system for a pebble bed type high-temperature gas-cooled reactor based on the method of any one of claims 1-7, characterized in that, include: The core parameter input module for the pebble bed type high-temperature gas-cooled reactor allows users to input initial parameters such as core geometry, material parameters, operating conditions, and boundary conditions, which are then transferred to the 3D model generation module and the physical property calculation module. The three-dimensional cylindrical coordinate model generation module generates a coarse-fine mesh structure of the core based on user input, and transmits the mesh information to the physical property and drag coefficient calculation module and the finite volume method discretization module; The property and drag coefficient calculation module calculates parameters such as porosity, temperature, drag coefficient, material properties, and dimensionless number for each grid cell, and uses these parameters as inputs to the fully implicit discretization module of the finite volume method. The finite volume method fully implicit discretization module is used to discretize partial differential equations, form a grid-based fully implicit linear system of equations, and pass it to the PARDISO-BICGSTAB hybrid solver module. Based on the PARDISO-BICGSTAB hybrid linear equation solving module, it is used to solve discrete linear equations under 3D modeling, improves the solution efficiency, and the solution results include pressure, velocity and other thermo-hydraulic parameters of each mesh element; The output module is used to output three-dimensional temperature distribution parameters, three-dimensional pressure distribution parameters, etc., for analysis, visualization or further engineering calculations.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method steps of any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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