Method and device for calculating radiation heat transfer of stack top cavity, electronic equipment and storage medium

Abstract

The present disclosure provides a reactor core cavity radiation heat transfer calculation method and device, electronic equipment and storage medium, which relates to the technical field of nuclear reactors, and through obtaining the temperature distribution and interfacial heat transfer coefficient of the fluid in the reactor core, the temperature of the upper surface and the lower surface of the cavity region is obtained based on the grid division of the reactor core heat conduction calculation model to solve the heat conduction equation, and then the radiation heat transfer is calculated according to the temperature, and the equivalent heat conduction coefficient is determined based on the equivalent relationship of radiation heat transfer and heat conduction, and finally the equivalent heat conduction coefficient is substituted into the heat conduction equation for iterative calculation, and the convergence is judged by comparing the relative changes of the cavity surface temperature and the equivalent heat conduction coefficient before and after iteration, so that the problems of exponential increase of calculation complexity with the number of grids, poor iterative convergence and time-consuming calculation in the prior art can be solved.

Description

Technical Field

[0001] This disclosure relates to the field of nuclear reactor technology, and in particular to a method and apparatus for calculating radiation heat transfer in the reactor top cavity, electronic equipment, and storage medium. Background Technology

[0002] The pebble bed high-temperature gas-cooled reactor is a core technology of fourth-generation nuclear energy systems. Its core thermal analysis system needs to combine gas flow calculations, thermal conductivity models, and radiative heat transfer theory, covering key aspects such as fluid temperature field calculations, solving solid thermal conductivity equations, cylindrical coordinate mesh generation, and setting boundary conditions such as isothermal, adiabatic, and axisymmetric conditions. Among these, radiative heat transfer modeling of the cavity region at the top of the core is the focus of thermal calculations, a process involving the nonlinear coupling of parameters such as the viewing angle factor, surface emissivity, and fourth-order temperature term.

[0003] However, traditional radiative heat transfer calculations do not fully consider the cavity geometry and multi-physics synergy, employing a direct coupling of the viewpoint factor matrix and the fourth-order temperature term, leading to an exponential increase in computational complexity with the number of grid cells. Furthermore, the nonlinearity of radiative heat transfer inherently conflicts with the linear solver of the heat conduction equation, resulting in poor iterative convergence and increased computation time. In practical engineering, the computational efficiency of the temperature field in the cavity region at the top of the reactor core is low, making it difficult to meet the real-time requirements of design optimization and safety analysis. Summary of the Invention

[0004] This disclosure provides a method and apparatus for calculating radiative heat transfer in a reactor top cavity, as well as electronic equipment and a storage medium. Its main objective is to at least partially address one of the technical problems in the related art.

[0005] According to a first aspect of this disclosure, a method for calculating radiative heat transfer in a reactor top cavity is provided, comprising: To obtain the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core; The heat conduction equation is solved by mesh generation based on the core heat conduction calculation model to obtain the temperature of the upper and lower surfaces of the cavity region; The radiative heat transfer is calculated based on the temperatures of the upper and lower surfaces, and the equivalent thermal conductivity is determined based on the equivalence between radiative heat transfer and thermal conductivity. The equivalent thermal conductivity is substituted into the thermal conductivity equation for iterative calculation. The relative changes in cavity surface temperature and equivalent thermal conductivity before and after the iteration are compared to determine whether the convergence condition is met. If the condition is met, the iteration is terminated; otherwise, the equivalent thermal conductivity is updated and the calculation is repeated.

[0006] Optionally, calculating the radiative heat transfer based on the temperatures of the upper and lower surfaces includes: Assume that the upper and lower surfaces of the cavity satisfy the radiation angle coefficient condition that they are fully visible to each other; Based on the equal surface areas of the upper and lower surfaces and the surface emissivity parameters, the radiative heat transfer is calculated using the fourth-power temperature difference formula.

[0007] Optionally, the step of determining whether the convergence condition is met by comparing the relative changes in the cavity surface temperature and equivalent thermal conductivity before and after the iteration includes: Calculate the relative errors of the upper and lower surface temperatures and equivalent thermal conductivity of the cavity before and after the iteration; When all relative errors are less than the preset threshold, the process is considered convergent.

[0008] Optionally, the mesh generation and solution of the heat conduction equation based on the core heat conduction calculation model includes: Discretize the core energy conservation equation in cylindrical coordinates; The temperature gradient at the grid interface is calculated by integrating the computational grid by volume and taking into account the assumption that the temperature is linearly distributed between adjacent grids.

[0009] Optionally, obtaining the temperature distribution and interphase heat transfer coefficient of the fluid within the reactor core includes: Gas flow parameters are dynamically corrected using a multiphysics coupling model; An empirical correction factor is introduced based on the ratio of the contact area between particles and gas in the reactor core to adjust the calculation results of the interphase heat transfer coefficient.

[0010] Optional, also includes: Set boundary conditions for the cavity region, including top isothermal boundary, bottom isothermal boundary, axisymmetric boundary condition and adiabatic boundary condition, to simulate actual operating conditions.

[0011] According to a second aspect of this disclosure, a calculation device for radiative heat transfer in a top cavity is provided, comprising: The acquisition unit is used to acquire the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core. The solver element is used to solve the heat conduction equation based on the core heat conduction calculation model, and obtain the temperature of the upper and lower surfaces of the cavity region. The determining unit is used to calculate the radiative heat transfer based on the temperatures of the upper and lower surfaces, and to determine the equivalent thermal conductivity based on the equivalence relationship between radiative heat transfer and thermal conductivity. The judgment unit is used to substitute the equivalent thermal conductivity into the thermal conductivity equation for iterative calculation. It judges whether the convergence condition is met by comparing the relative changes in cavity surface temperature and equivalent thermal conductivity before and after the iteration. If the condition is met, the iteration is terminated; otherwise, the equivalent thermal conductivity is updated and the calculation is repeated.

[0012] Optionally, the determining unit is also used for: Assume that the upper and lower surfaces of the cavity satisfy the radiation angle coefficient condition that they are fully visible to each other; Based on the equal surface areas of the upper and lower surfaces and the surface emissivity parameters, the radiative heat transfer is calculated using the fourth-power temperature difference formula.

[0013] Optionally, the decision unit is also used for: Calculate the relative errors of the upper and lower surface temperatures and equivalent thermal conductivity of the cavity before and after the iteration; When all relative errors are less than the preset threshold, the process is considered convergent.

[0014] Optionally, the solver element is also used for: Discretize the core energy conservation equation in cylindrical coordinates; The temperature gradient at the grid interface is calculated by integrating the computational grid by volume and taking into account the assumption that the temperature is linearly distributed between adjacent grids.

[0015] Optionally, the acquisition unit is also used for: Gas flow parameters are dynamically corrected using a multiphysics coupling model; An empirical correction factor is introduced based on the ratio of the contact area between particles and gas in the reactor core to adjust the calculation results of the interphase heat transfer coefficient.

[0016] Optional, also includes: The setting unit is used to set the boundary conditions of the cavity region, including the top isothermal boundary, the bottom isothermal boundary, the axisymmetric boundary condition, and the adiabatic boundary condition, in order to simulate the actual operating conditions.

[0017] According to a third aspect of this disclosure, an electronic device is provided, comprising: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described in the first aspect above.

[0018] According to a fourth aspect of this disclosure, a non-transitory computer-readable storage medium is provided storing computer instructions, wherein the computer instructions are configured to cause the computer to perform the method described in the first aspect above.

[0019] According to a fifth aspect of this disclosure, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method described in the first aspect above.

[0020] The method, apparatus, electronic equipment, and storage medium for calculating radiative heat transfer in the reactor core cavity disclosed herein acquire the temperature distribution and interphase heat transfer coefficient of the fluid within the reactor core. Then, based on the mesh generation of the reactor core thermal conductivity calculation model, the thermal conductivity equation is solved to obtain the temperatures of the upper and lower surfaces of the cavity region. The radiative heat transfer is then calculated based on these temperatures, and the equivalent thermal conductivity is determined based on the equivalence between radiative heat transfer and thermal conductivity. Finally, the equivalent thermal conductivity is substituted into the thermal conductivity equation for iterative calculation, and convergence is determined by comparing the relative changes in cavity surface temperature and equivalent thermal conductivity before and after iteration. Therefore, this method solves the problems in existing technologies where the computational complexity increases exponentially with the number of meshes, resulting in poor iterative convergence and time-consuming calculations due to the direct coupling of nonlinear radiative heat transfer terms (such as fourth-order temperature terms and perspective factor coupling terms) with thermal conductivity terms, and the lack of a reasonable convergence judgment mechanism based on both temperature and equivalent thermal conductivity. This method transforms the nonlinear radiative heat transfer problem into a linear thermal conductivity problem, simplifying the calculation process and reducing computational resource consumption. Simultaneously, it improves computational efficiency and accuracy through precise convergence judgment, thus meeting the technical requirements of reactor core thermal analysis engineering applications. It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0021] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein: Figure 1 A schematic flowchart illustrating a method for calculating radiative heat transfer in a top cavity provided in this embodiment of the present disclosure; Figure 2 A schematic diagram of the structure of a radiative heat transfer calculation device for a top cavity provided in an embodiment of this disclosure; Figure 3 A schematic block diagram of an example electronic device provided for embodiments of this disclosure. Detailed Implementation

[0022] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0023] The following description, with reference to the accompanying drawings, outlines an embodiment of the method and apparatus for calculating radiative heat transfer in the top cavity of the reactor, as well as electronic equipment and storage medium.

[0024] Figure 1This is a flowchart illustrating a method for calculating radiative heat transfer in a top cavity provided in an embodiment of this disclosure.

[0025] like Figure 1 As shown, the method includes the following steps: Step 101: Obtain the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core.

[0026] In the embodiments of this disclosure, the core objective of this step is to provide key fundamental thermal parameters for subsequent thermal calculations of the reactor core (such as solving the thermal conductivity equation and determining parameters related to radiative heat transfer), namely, the temperature distribution of the fluid within the reactor core and the interphase heat transfer coefficient. Specifically, this can be achieved by employing calculation programs or analysis models that conform to the physical laws of fluid flow and heat exchange within the reactor core. These programs or models can calculate the temperature variation of the fluid within the reactor core and the heat transfer efficiency between the fluid and solid phases based on the structural characteristics, fluid properties, and operating conditions of the reactor core, thereby outputting temperature distribution data and interphase heat transfer coefficients that meet the accuracy requirements of subsequent calculations. As one implementation method, a gas flow calculation program can be used, combined with the geometry and fluid flow characteristics of a pebble bed high-temperature gas-cooled reactor core, to calculate the temperature distribution of the fluid within the reactor core and the interphase heat transfer coefficient, providing data support for subsequent analysis based on the reactor core thermal conductivity calculation model.

[0027] By obtaining accurate fluid temperature distribution and interphase heat transfer coefficients within the reactor core, a reliable data foundation can be laid for subsequent solutions to the core thermal conductivity equations and equivalent calculations of radiative heat transfer in the cavity region. This effectively avoids deviations in subsequent thermal analysis results due to inaccurate basic thermal parameters, ensuring the accuracy and reliability of the overall thermal calculations of the reactor core.

[0028] Step 102: Solve the heat conduction equation based on the mesh generation of the core heat conduction calculation model to obtain the temperature of the upper and lower surfaces of the cavity region.

[0029] In the embodiments disclosed herein, this step aims to analyze the core temperature field based on previously acquired fundamental thermal parameters using a core thermal conductivity calculation model. The core process involves solving the thermal conductivity equations using a pre-defined mesh partitioning of the core thermal conductivity calculation model to locate and obtain the temperatures of the upper and lower surfaces of the cavity region. Specifically, the mesh partitioning of the core thermal conductivity calculation model must consider the core's geometry, thermal conductivity characteristics, and computational accuracy requirements to construct a mesh system that accurately reflects the thermal conductivity differences between different regions of the core. Solving the thermal conductivity equations must adhere to the core energy conservation law, incorporating key parameters such as the core's internal heat sources and the thermal conductivity of solid regions. The discretized thermal conductivity equations are solved using numerical calculation methods to obtain the temperature distribution of each mesh region within the core, and the temperature data of the upper and lower surfaces of the cavity region are then extracted from this distribution. As one implementation method, based on the cylindrical geometry of the pebble bed high-temperature gas-cooled reactor (corresponding to the common geometry of the reactor core), the core heat conduction calculation model can be meshed using a cylindrical coordinate system (r,π,z). The core energy conservation equation (including internal heat sources and equivalent thermal conductivity parameters) can be substituted into the model for solution. Finally, the temperatures of the upper and lower surfaces of the cavity region can be selected from the calculated core temperature distribution.

[0030] By combining mesh generation with solving the thermal conductivity equation, the temperatures of the upper and lower surfaces of the cavity region can be accurately located and obtained. This provides a direct and crucial temperature basis for subsequent calculations of radiative heat transfer and determination of the equivalent thermal conductivity. At the same time, the rationality of the mesh generation also ensures the accuracy of the thermal conductivity equation solution, effectively avoiding deviations in subsequent radiative heat transfer calculations due to inaccurate temperature data, and ensuring the continuity and reliability of the core thermal analysis process.

[0031] Step 103: Calculate the radiative heat transfer based on the temperatures of the upper and lower surfaces, and determine the equivalent thermal conductivity based on the equivalence between radiative heat transfer and thermal conductivity.

[0032] In the embodiments of this disclosure, the core objective of this step is to transform the nonlinear radiative heat transfer effect of the cavity region into linear parameters that facilitate subsequent iterative calculations of the heat conduction equation. This is achieved through two key operations: First, based on the obtained temperatures of the upper and lower surfaces of the cavity region, and according to the basic physical laws of radiative heat transfer (such as the correlation characteristics between temperature difference and radiative energy transfer), combined with the relevant physical parameters required for radiative heat transfer calculation (such as surface radiation characteristic parameters), the radiative heat transfer between the upper and lower surfaces of the cavity region is calculated. Second, using the equivalence relationship between radiative heat transfer and heat conduction in terms of heat transfer effect, the calculated radiative heat transfer is converted into an equivalent thermal conductivity that can characterize the radiative heat transfer effect. This equivalence relationship needs to match the heat transfer scenario of the cavity region to ensure that the equivalent thermal conductivity can accurately reflect the contribution of radiative heat transfer to the overall heat transfer of the cavity region. As one implementation method, in the scenario of the top cavity of the pebble bed type high temperature gas-cooled reactor core, it can be assumed that the upper and lower surfaces are completely visible to each other and have equal areas. The radiative heat transfer is calculated by combining the Boltzmann constant and the surface emissivity. Then, based on the equivalent expression of radiative heat transfer and conductive heat transfer, the equivalent thermal conductivity is determined by substituting the cavity height parameter.

[0033] By converting nonlinear radiative heat transfer into linear equivalent thermal conductivity, the complex calculation of directly handling nonlinear terms of radiative heat transfer (such as fourth-order temperature terms) is effectively avoided. This provides adaptability parameters for subsequent iterative calculations using the equivalent thermal conductivity as an input to the heat conduction equation, while ensuring the accurate representation of the radiative heat transfer effect. This lays a key foundation for improving the efficiency and accuracy of core thermal calculations.

[0034] Step 104: Substitute the equivalent thermal conductivity into the thermal conductivity equation for iterative calculation. Determine whether the convergence condition is met by comparing the relative changes in cavity surface temperature and equivalent thermal conductivity before and after the iteration. If the condition is met, terminate the iteration; otherwise, continue to update the equivalent thermal conductivity and repeat the calculation.

[0035] In the embodiments disclosed herein, this step aims to ensure the stability and accuracy of the core thermal calculation results through iterative optimization and convergence judgment mechanisms. The core process is as follows: First, the previously determined equivalent thermal conductivity is substituted into the thermal conductivity equation corresponding to the core thermal conductivity calculation model, and the thermal conductivity equation is solved again to update the temperature distribution of the core and cavity regions. Next, a convergence judgment rule based on the change of key parameters is constructed, that is, the relative change of cavity surface temperature and the relative change of equivalent thermal conductivity before and after iteration are calculated, and the two are compared with the preset convergence judgment criteria to measure the reliability of the current calculation results. If the above relative changes meet the convergence criteria, it means that the calculation results have reached the expected accuracy and the iteration can be terminated. If they do not meet the criteria, the equivalent thermal conductivity is re-determined according to the latest updated cavity region temperature, and the process of "equivalent thermal conductivity substitution - thermal conductivity equation solution - convergence judgment" is executed again. As one implementation method, in the calculation scenario of a pebble bed type high-temperature gas-cooled reactor core, a convergence limit value for the relative error between temperature and equivalent thermal conductivity can be preset. When the relative error between the upper and lower surface temperatures of the cavity and the relative error between the equivalent thermal conductivity before and after iteration are both less than the limit value, the iteration is determined to be converged and the calculation is stopped.

[0036] By combining iterative optimization with two-parameter convergence judgment, the calculation deviation can be gradually corrected to ensure the accuracy of the core thermal parameters calculation. At the same time, it can avoid the problem of excessive iteration or unreliable results caused by the lack of clear convergence criteria. It effectively balances the accuracy and efficiency of core thermal calculation and meets the reliability requirements of engineering design and safety analysis for calculation results.

[0037] The method for calculating radiative heat transfer in the reactor core cavity disclosed herein obtains the temperature distribution and interphase heat transfer coefficient of the fluid within the reactor core. Then, based on the mesh generation of the reactor core thermal conductivity calculation model, it solves the thermal conductivity equation to obtain the temperatures of the upper and lower surfaces of the cavity region. Subsequently, it calculates the radiative heat transfer based on these temperatures and determines the equivalent thermal conductivity based on the equivalence relationship between radiative heat transfer and thermal conductivity. Finally, it substitutes the equivalent thermal conductivity into the thermal conductivity equation for iterative calculation and determines convergence by comparing the relative changes in cavity surface temperature and equivalent thermal conductivity before and after iteration. Therefore, it solves the problems in existing technologies where the computational complexity increases exponentially with the number of meshes, resulting in poor iterative convergence and time-consuming calculations due to the direct coupling of nonlinear radiative heat transfer terms (such as fourth-order temperature terms and perspective factor coupling terms) with thermal conductivity terms, and the lack of a reasonable convergence judgment mechanism based on both temperature and equivalent thermal conductivity parameters. This method transforms the nonlinear radiative heat transfer problem into a linear thermal conductivity problem, simplifying the calculation process and reducing computational resource consumption. Simultaneously, it improves computational efficiency and accuracy through precise convergence judgment, thus meeting the technical requirements of reactor core thermal analysis engineering applications.

[0038] As a specific embodiment of this disclosure, based on the basic scheme, the calculation of radiative heat transfer based on the temperature of the upper and lower surfaces is further defined as follows: assuming that the upper and lower surfaces of the cavity satisfy the radiation angle coefficient condition that they are completely visible to each other; and calculating the radiative heat transfer using the fourth-power temperature difference formula based on the equal area of ​​the upper and lower surfaces and the surface emissivity parameters.

[0039] Specifically, when calculating the radiative heat transfer between the upper and lower surfaces of the cavity region, the following assumptions regarding the radiative heat transfer boundary conditions of the upper and lower surfaces of the cavity are first defined: It is assumed that there are no obstructions between the upper and lower surfaces of the cavity, satisfying the radiation angle coefficient condition of complete mutual visibility, that is, the fraction of the radiant energy emitted from surface 1 (upper surface of the cavity) directly projected onto surface 2 (lower surface of the cavity) (radiation angle coefficient F) 12 The fraction of the radiant energy emitted from surface 2 that is directly projected onto surface 1 (radiation angle coefficient F) 21 All are equal to 1, thus simplifying the complex calculation of the angle coefficient in radiative heat transfer. At the same time, considering the geometric symmetry of the cavity at the top of the core, the areas of the upper and lower surfaces of the cavity are set to be equal, that is, the area of ​​the upper surface A1 and the area of ​​the lower surface A2 are the same size (which can be uniformly represented by A), and the surface emissivity parameters of the upper and lower surfaces are determined.

[0040] Assume that the radiative heat transfer between the upper and lower surfaces of the cavity region at the top of the reactor core satisfies the condition that the upper and lower surfaces are completely visible to each other, and that both sides assume that all the radiation emitted by the other falls on each other's surfaces, i.e., the angle factor satisfies:

[0041] The subscripts 1 and 2 refer to the upper and lower surfaces of the cavity. The fraction of the radiant energy emitted from surface 1 that is directly projected onto surface 2. The fraction of the radiant energy emitted from surface 2 that is directly projected onto Table 1.

[0042] And the areas of the upper and lower surfaces are equal, that is, the areas of the upper and lower surfaces satisfy:

[0043] Let be the area of ​​surface 1. Let be the area of ​​surface 2; Therefore, the radiative heat transfer on the upper and lower surfaces of the cavity region at the top of the reactor core is:

[0044] in This refers to the heat exchanged through radiation between the upper and lower surfaces of the cavity. For emission rate, Boltzmann's constant, The surface area above and below the cavity surface. and These are the temperatures of surface 1 and surface 2, respectively. This is based on the equivalent relationship between radiative heat transfer and thermal conduction.

[0045] in The heat exchange occurs between the upper and lower surfaces of the cavity via thermal conduction. The equivalent thermal conductivity is The height of the cavity is the distance between the upper and lower surfaces. The equivalent thermal conductivity, considering radiative heat transfer, is obtained as follows:

[0046] in The equivalent thermal conductivity is For emission rate, Boltzmann's constant, and These are the temperatures of surface 1 and surface 2, respectively.

[0047] By explicitly assuming mutually fully visible angle factors and setting equal upper and lower surface areas, the complex solution process for angle factors and area parameters in radiative heat transfer calculations is greatly simplified. At the same time, by combining the fourth-power temperature difference formula and specific surface emissivity parameters, the accuracy of radiative heat transfer calculations is ensured, and the calculation process is made easier to operate. It can quickly provide accurate heat transfer data for the subsequent determination of equivalent thermal conductivity, and is suitable for the actual engineering needs of core thermal calculations.

[0048] As a specific implementation of this disclosure, based on the basic scheme, the method of judging whether the convergence condition is met by comparing the relative changes of the cavity surface temperature and equivalent thermal conductivity before and after the iteration includes: calculating the relative errors of the cavity upper surface temperature, lower surface temperature and equivalent thermal conductivity before and after the iteration; when all relative errors are less than a preset threshold, it is determined to be converged.

[0049] Specifically, when determining whether the iteration meets the convergence condition, the relative errors before and after the iteration are calculated for two key parameters: cavity surface temperature and equivalent thermal conductivity. For the cavity upper surface temperature, the upper surface temperature before iteration (denoted as T) is used as the relative error. 1ol Using the upper surface temperature (denoted as T) as a reference, the iteratively obtained upper surface temperature is used as the reference. 1ne w) Calculate the relative error.

[0050]

[0051]

[0052] Where subscripts 1 and 2 represent the upper and lower surfaces of the cavity, and superscripts new and old represent the variables before and after the update. The surface temperature of the cavity region. The relative error in temperature calculation and the relative error in the equivalent thermal conductivity of the cavity before and after the update are expressed as:

[0053] in This represents the relative error in the calculation of the equivalent thermal conductivity. The equivalent thermal conductivity is used. The convergence of the helium temperature calculation is determined by checking if the relative error in the calculation of the upper and lower surface temperatures and the calculation error in the equivalent thermal conductivity are less than the convergence limit set before the calculation. If convergence is achieved, the next step is performed; otherwise, iterative calculations are continued based on the updated equivalent thermal conductivity, as shown below:

[0054]

[0055]

[0056] , and Convergence limits set before calculation.

[0057] Then, a preset threshold is set (for example, in the thermal calculation of the core of a pebble bed type high temperature gas-cooled reactor, the preset threshold can be set to 0.1%). The calculated Error1, Error2 and Error3 are compared with the preset threshold respectively. When the three relative errors are all less than the preset threshold, it can be determined that the current iteration meets the convergence condition.

[0058] By clarifying the relative error calculation methods for three key parameters and establishing a unified preset threshold judgment standard, the convergence judgment process has a clear quantitative basis, avoiding deviations caused by subjective judgment. At the same time, it ensures that the iteration is terminated only when both the temperature and the equivalent thermal conductivity reach a stable state, which not only guarantees the accuracy of the core thermal calculation results, but also effectively avoids inaccurate results or waste of computing resources caused by excessive iteration due to premature termination of iteration.

[0059] As a specific embodiment of this disclosure, based on the basic scheme, the mesh generation and solution of the heat conduction equation based on the core heat conduction calculation model are further defined, including: discretizing the core energy conservation equation in cylindrical coordinates; calculating the temperature gradient at the mesh interface by performing volume integration on the computational mesh and combining the assumption that the temperature between adjacent meshes is linearly distributed.

[0060] Specifically, when solving the heat conduction equation based on the core heat conduction calculation model, the grid system of the core heat conduction calculation model is first constructed using a cylindrical coordinate system (where r represents radial coordinates, π represents circumferential coordinates, and z represents axial coordinates), taking into account the cylindrical geometric characteristics of the pebble bed high-temperature gas-cooled reactor core. The core energy conservation equation (which includes the equivalent thermal conductivity κ of the solid region of the core) is then addressed. e The core temperature T and internal heat sources (Q_n) are analyzed, with a focus on discretizing the thermal conductivity term. First, the geometric parameters of the computational grid are determined: the radial length χr, circumferential length χπ, and axial length χz, as well as the corresponding circumferential number i, radial number j, and axial number k. Based on these parameters, the volume of a single computational grid is calculated (obtained by multiplying the radial, circumferential, and axial lengths). Then, the thermal conductivity term on the left-hand side of the core energy conservation equation is integrated over the aforementioned computational grid, transforming the continuous equation into a discrete form. Simultaneously, to simplify temperature gradient calculations, it is assumed that the core temperature is linearly distributed between adjacent computational grids. Based on this assumption, the temperature gradient at the grid interface is obtained through differential calculation using the temperature values ​​of adjacent grids (such as radially adjacent grids numbered j and j+1, and axially adjacent grids numbered k and k+1). For example, the temperature gradient at the radial grid interface can be determined by the ratio of the radial temperature difference between adjacent grids to the radial grid length; the temperature gradients at the circumferential and axial grid interfaces are derived similarly.

[0061] By adopting a cylindrical coordinate system based on the cylindrical geometry of the reactor core, the mesh generation is made to better fit the actual structure of the reactor core, thus improving the applicability of the energy conservation equation. The equation is discretized by integrating the mesh volume, and coupled with the reasonable assumption of linear temperature distribution between adjacent meshes, the calculation process of the temperature gradient is simplified while ensuring the accuracy of the temperature gradient calculation. This lays a reliable discretization foundation for the subsequent accurate solution of the heat conduction equation and the acquisition of the temperature of the reactor core and cavity regions.

[0062] As a specific embodiment of this disclosure, based on the basic scheme, the acquisition of the temperature distribution and interphase heat transfer coefficient of the fluid in the reactor core is further defined as follows: dynamically correcting the gas flow parameters through a multiphysics coupling model; and adjusting the calculation results of the interphase heat transfer coefficient by introducing an empirical correction factor based on the contact area ratio between particles and gas in the reactor core.

[0063] Specifically, when obtaining the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core, a multiphysics coupling model that integrates the fluid flow field and the core heat conduction field is first adopted. This model can correlate the fluid flow state and temperature field changes inside the reactor core in real time. For example, when the temperature rises in a local area of ​​the reactor core due to the release of heat from the internal heat source, the model can adjust the gas flow parameters such as the flow velocity and density of the fluid based on the temperature gradient feedback, avoiding calculation deviations caused by using fixed flow parameters, and ensuring that the output fluid temperature distribution is consistent with the actual operating conditions of the reactor core. Meanwhile, for the calculation of the interphase heat transfer coefficient (i.e., the heat transfer coefficient between solid particles and fluid in the reactor core), the actual contact area ratio between solid particles and fluid is first calculated by combining parameters such as the core particle packing density and fuel ball diameter. Then, an empirical correction factor obtained by fitting a large amount of core heat transfer experimental data is introduced (this factor corresponds to the contact area ratio; the larger the contact area ratio, the closer the correction factor is to 1 to reduce the adjustment range). This factor is multiplied by the initial interphase heat transfer coefficient calculated by basic heat transfer formulas such as the Nusselt number correlation to complete the adjustment of the interphase heat transfer coefficient calculation result, so that the final interphase heat transfer coefficient can match the real heat transfer scenario between particles and fluid in the reactor core.

[0064] The dynamic correction function of the multiphysics coupling model can avoid the deviation of fluid temperature distribution caused by fixed gas flow parameters and improve the accuracy of temperature data. The introduction of an empirical correction factor based on the contact area ratio can make up for the defect that the basic heat transfer formula does not consider the core particle packing characteristics, further improve the calculation accuracy of the interphase heat transfer coefficient, and provide more reliable basic thermal parameters for the subsequent solution of the core heat conduction equation.

[0065] As a specific embodiment of this disclosure, based on the basic scheme, the embodiments of this disclosure further include: setting boundary conditions for the cavity region, including a top constant temperature boundary, a bottom constant temperature boundary, an axisymmetric boundary condition, and an adiabatic boundary condition, in order to simulate actual operating conditions.

[0066] Specifically, before performing thermal calculations on the top cavity region of the reactor core, four types of boundary conditions need to be set for the cavity region based on the actual thermal environment and geometric constraints of the reactor core during operation to construct a calculation environment that closely approximates real-world operating conditions. The top isothermal boundary is used to simulate the thermal contact state between the top of the cavity and the upper structure of the reactor core. Referring to a modified model of a pebble bed high-temperature gas-cooled reactor (such as HTR-PM) (cavity height 67cm, radius 150.275cm), the top boundary temperature is set to 800K to ensure that this temperature matches the heat dissipation characteristics of the upper structure during actual operation, avoiding the influence of calculation results due to deviations in the assumptions about heat transfer at the top. The bottom isothermal boundary corresponds to the thermal connection between the bottom of the cavity and the active region of the reactor core, and is set to 1000K to accurately reflect the heat transfer through conduction in the active region. The stable heat input to the bottom of the cavity closely matches the actual situation of continuous heat release in the active area during core operation. The axisymmetric boundary condition, based on the cylindrical geometry of the core, is applied to the radial inner boundary of the cavity (i.e., the central axis of the cylindrical coordinate system). It stipulates that the temperature gradient in the circumferential direction on this boundary is zero, which not only conforms to the characteristic of uniform circumferential temperature distribution in the actual core, but also reduces redundant calculations caused by geometric symmetry. The adiabatic boundary condition is set on the radial outer boundary of the cavity to simulate the thermal isolation state between the outer side of the cavity and the insulation structure. It is clear that there is no heat transfer at this boundary (heat flux density is zero), which is consistent with the design requirement of the insulation structure to prevent the cavity from dissipating heat outward during actual operation. Through the coordinated setting of the four types of boundary conditions, the thermal boundary constraints of the cavity region during actual core operation are fully reproduced.

[0067] This boundary condition setting scheme can accurately reproduce the actual thermal constraints and geometric characteristics of the cavity region, effectively avoiding calculation deviations caused by boundary condition simplification (such as ignoring adiabatic or axisymmetric characteristics), making the subsequent solution of heat conduction equations and the calculation results of radiation heat transfer more in line with engineering reality, and providing a calculation basis that conforms to real operating conditions for core thermal safety analysis and design optimization.

[0068] It should be noted that the embodiments of this disclosure may include multiple steps. For ease of description, these steps are numbered, but these numbers are not a limitation on the execution time slots or execution order between the steps; these steps can be implemented in any order, and the embodiments of this disclosure do not limit this.

[0069] Corresponding to the above-described method for calculating radiation heat transfer in the reactor top cavity, this disclosure also proposes a device for calculating radiation heat transfer in the reactor top cavity. Since the device embodiments of this disclosure correspond to the method embodiments described above, details not disclosed in the device embodiments can be referred to the method embodiments described above, and will not be repeated here.

[0070] Figure 2 This is a schematic diagram of the structure of a radiative heat transfer calculation device for a top cavity provided in an embodiment of this disclosure, as shown below. Figure 2As shown, it includes: Acquisition unit 21 is used to acquire the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core; Solver 22 is used to solve the heat conduction equation based on the mesh generation of the core heat conduction calculation model to obtain the temperature of the upper and lower surfaces of the cavity region. The determining unit 23 is used to calculate the radiative heat transfer based on the temperatures of the upper and lower surfaces, and to determine the equivalent thermal conductivity based on the equivalence relationship between radiative heat transfer and thermal conductivity. The judgment unit 24 is used to substitute the equivalent thermal conductivity into the thermal conductivity equation for iterative calculation. It judges whether the convergence condition is met by comparing the relative changes of the cavity surface temperature and the equivalent thermal conductivity before and after the iteration. If the condition is met, the iteration is terminated; otherwise, the equivalent thermal conductivity is updated and the calculation is repeated.

[0071] The radiative heat transfer calculation device for the reactor core cavity provided in this disclosure obtains the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core, and then solves the heat conduction equation based on the mesh division of the reactor core heat conduction calculation model to obtain the temperature of the upper and lower surfaces of the cavity region. Based on this temperature, the radiative heat transfer is calculated, and the equivalent heat conduction coefficient is determined based on the equivalence relationship between radiative heat transfer and heat conduction. Finally, the equivalent heat conduction coefficient is substituted into the heat conduction equation for iterative calculation, and convergence is judged by comparing the relative changes in cavity surface temperature and equivalent heat conduction coefficient before and after iteration. Therefore, it can solve the problems in existing technologies where the computational complexity increases exponentially with the number of meshes, the iterative convergence is poor, and the computation is time-consuming due to the direct coupling of nonlinear radiative heat transfer terms (such as fourth-order temperature terms and perspective factor coupling terms) with heat conduction terms, and the lack of a reasonable convergence judgment mechanism based on the two parameters of temperature and equivalent heat conduction coefficient. This achieves the technical effect of transforming the nonlinear radiative heat transfer problem into a linear heat conduction problem to simplify the calculation process and reduce computational resource consumption. At the same time, it improves computational efficiency and accuracy through accurate convergence judgment, meeting the technical requirements of reactor core thermal analysis engineering applications.

[0072] Furthermore, in one possible implementation of this embodiment, the determining unit 23 is further configured to: Assume that the upper and lower surfaces of the cavity satisfy the radiation angle coefficient condition that they are fully visible to each other; Based on the equal surface areas of the upper and lower surfaces and the surface emissivity parameters, the radiative heat transfer is calculated using the fourth-power temperature difference formula.

[0073] Furthermore, in one possible implementation of this embodiment, the determining unit 24 is also used for: Calculate the relative errors of the upper and lower surface temperatures and equivalent thermal conductivity of the cavity before and after the iteration; When all relative errors are less than the preset threshold, the process is considered convergent.

[0074] Furthermore, in one possible implementation of this embodiment, the solving unit 22 is also used for: Discretize the core energy conservation equation in cylindrical coordinates; The temperature gradient at the grid interface is calculated by integrating the computational grid by volume and taking into account the assumption that the temperature is linearly distributed between adjacent grids.

[0075] Furthermore, in one possible implementation of this embodiment, the acquisition unit 21 is also used for: Gas flow parameters are dynamically corrected using a multiphysics coupling model; An empirical correction factor is introduced based on the ratio of the contact area between particles and gas in the reactor core to adjust the calculation results of the interphase heat transfer coefficient.

[0076] Furthermore, in one possible implementation of this embodiment, such as Figure 2 As shown, it also includes: Setting unit 25 is used to set the boundary conditions of the cavity region, including top isothermal boundary, bottom isothermal boundary, axisymmetric boundary conditions and adiabatic boundary conditions, in order to simulate actual operating conditions.

[0077] It should be noted that the foregoing explanation of the method embodiments also applies to the apparatus of this embodiment, and the principle is the same, so it is not limited in this embodiment.

[0078] According to embodiments of this disclosure, this disclosure also provides an electronic device, a readable storage medium, and a computer program product.

[0079] Figure 3 A schematic block diagram of an example electronic device 300 that can be used to implement embodiments of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0080] like Figure 3As shown, the electronic device 300 includes a computing unit 301, which can perform various appropriate actions and processes based on a computer program stored in ROM (Read-Only Memory) 302 or a computer program loaded from storage unit 308 into RAM (Random Access Memory) 303. The RAM 303 may also store various programs and data required for the operation of the electronic device 300. The computing unit 301, ROM 302, and RAM 303 are interconnected via a bus 304. An I / O (Input / Output) interface 305 is also connected to the bus 304.

[0081] Multiple components in electronic device 300 are connected to I / O interface 305, including: input unit 306, such as keyboard, mouse, etc.; output unit 307, such as various types of displays, speakers, etc.; storage unit 308, such as disk, optical disk, etc.; and communication unit 309, such as network card, modem, wireless transceiver, etc. Communication unit 309 allows electronic device 300 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0082] The computing unit 301 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 301 include, but are not limited to, CPUs (Central Processing Units), GPUs (Graphics Processing Units), various special-purpose AI (Artificial Intelligence) computing chips, various computing units running machine learning model algorithms, DSPs (Digital Signal Processors), and any suitable processor, controller, microcontroller, etc. The computing unit 301 performs the various methods and processes described above, such as the method for calculating the radiation heat transfer of a top-mounted cavity. For example, in some embodiments, the method for calculating the radiation heat transfer of a top-mounted cavity can be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as storage unit 308. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 300 via ROM 302 and / or communication unit 309. When the computer program is loaded into RAM 303 and executed by the computing unit 301, one or more steps of the methods described above can be performed. Alternatively, in other embodiments, the computing unit 301 may be configured to perform the aforementioned calculation method for radiative heat transfer in the top cavity by any other suitable means (e.g., by means of firmware).

[0083] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, FPGAs (Field Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), ASSPs (Application-Specific Standard Products), SOCs (System-on-Chips), CPLDs (Complex Programmable Logic Devices), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0084] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0085] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, RAM, ROM, EPROM (Electrically Programmable Read-Only Memory) or flash memory, optical fiber, CD-ROM (Compact Disc Read-Only Memory), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0086] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (Cathode-Ray Tube) or LCD (Liquid Crystal Display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0087] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include LANs (Local Area Networks), WANs (Wide Area Networks), the Internet, and blockchain networks.

[0088] Computer systems can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. A server can be a cloud server, also known as a cloud computing server or cloud host, a hosting product within the cloud computing service system that addresses the shortcomings of traditional physical hosts and VPS (Virtual Private Server) services, such as high management difficulty and weak business scalability. Servers can also be servers for distributed systems or servers incorporating blockchain technology.

[0089] It's important to note that artificial intelligence (AI) is the study of enabling computers to simulate certain human thought processes and intelligent behaviors (such as learning, reasoning, thinking, and planning). It encompasses both hardware and software technologies. AI hardware technologies generally include sensors, dedicated AI chips, cloud computing, distributed storage, and big data processing. AI software technologies primarily include computer vision, speech recognition, natural language processing, machine learning / deep learning, big data processing, and knowledge graph technologies.

[0090] The various numerical designations such as "first," "second," etc., used in this disclosure are merely for ease of description and are not intended to limit the scope of the embodiments of this disclosure, nor do they indicate a sequential order.

[0091] At least one of the features described in this disclosure can also be described as one or more, and multiple features can be two, three, four or more, and this disclosure does not impose any limitations. In the embodiments of this disclosure, for a technical feature, the technical features in that technical feature are distinguished by "first", "second", "third", "A", "B", "C" and "D", etc., and there is no sequential order or size order among the technical features described by "first", "second", "third", "A", "B", "C" and "D".

[0092] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0093] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for calculating radiative heat transfer in a reactor top cavity, characterized in that, include: To obtain the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core; The heat conduction equation is solved by mesh generation based on the core heat conduction calculation model to obtain the temperature of the upper and lower surfaces of the cavity region; The radiative heat transfer is calculated based on the temperatures of the upper and lower surfaces, and the equivalent thermal conductivity is determined based on the equivalence between radiative heat transfer and thermal conductivity. The equivalent thermal conductivity is substituted into the thermal conductivity equation for iterative calculation. The relative changes in cavity surface temperature and equivalent thermal conductivity before and after the iteration are compared to determine whether the convergence condition is met. If the condition is met, the iteration is terminated; otherwise, the equivalent thermal conductivity is updated and the calculation is repeated.

2. The method according to claim 1, characterized in that, The calculation of radiative heat transfer based on the temperatures of the upper and lower surfaces includes: Assume that the upper and lower surfaces of the cavity satisfy the radiation angle coefficient condition that they are fully visible to each other; Based on the equal surface areas of the upper and lower surfaces and the surface emissivity parameters, the radiative heat transfer is calculated using the fourth-power temperature difference formula.

3. The method according to claim 1, characterized in that, The step of determining whether the convergence condition is met by comparing the relative changes in the cavity surface temperature and equivalent thermal conductivity before and after iteration includes: Calculate the relative errors of the upper and lower surface temperatures and equivalent thermal conductivity of the cavity before and after the iteration; When all relative errors are less than the preset threshold, the process is considered convergent.

4. The method according to claim 1, characterized in that, The mesh generation and solution of the heat conduction equation based on the core heat conduction calculation model includes: Discretize the core energy conservation equation in cylindrical coordinates; The temperature gradient at the grid interface is calculated by integrating the computational grid by volume and taking into account the assumption that the temperature is linearly distributed between adjacent grids.

5. The method according to claim 1, characterized in that, The acquisition of the temperature distribution and interphase heat transfer coefficient of the fluid within the reactor core includes: Gas flow parameters are dynamically corrected using a multiphysics coupling model; An empirical correction factor is introduced based on the ratio of the contact area between particles and gas in the reactor core to adjust the calculation results of the interphase heat transfer coefficient.

6. The method according to claim 1, characterized in that, Also includes: Set boundary conditions for the cavity region, including top isothermal boundary, bottom isothermal boundary, axisymmetric boundary condition and adiabatic boundary condition, to simulate actual operating conditions.

7. A calculation device for radiative heat transfer in a reactor top cavity, characterized in that, include: The acquisition unit is used to acquire the temperature distribution and interphase heat transfer coefficient of the fluid inside the reactor core. The solver element is used to solve the heat conduction equation based on the core heat conduction calculation model, and obtain the temperature of the upper and lower surfaces of the cavity region. The determining unit is used to calculate the radiative heat transfer based on the temperatures of the upper and lower surfaces, and to determine the equivalent thermal conductivity based on the equivalence relationship between radiative heat transfer and thermal conductivity. The judgment unit is used to substitute the equivalent thermal conductivity into the thermal conductivity equation for iterative calculation. It judges whether the convergence condition is met by comparing the relative changes in cavity surface temperature and equivalent thermal conductivity before and after the iteration. If the condition is met, the iteration is terminated; otherwise, the equivalent thermal conductivity is updated and the calculation is repeated.

8. An electronic device, characterized in that, include: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6.

9. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method according to any one of claims 1-6.

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