Multi-scale temperature acquisition method and device for pebble-bed high-temperature gas cooled reactor, electronic equipment and storage medium

Abstract

The invention discloses a pebble-bed high-temperature gas cooled reactor multi-scale temperature acquisition method and device, electronic equipment and a storage medium. According to the method provided by the invention, the to-be-solved variable of the established residual function equation only contains the macroscopic pebble bed temperature vector, the Newton iteration framework is adopted to solve the macroscopic temperature, and in each Newton iteration, the thermal power is calculated by simultaneously solving the mesoscopic fuel sphere and microscopic fuel particle temperature equation set, so that the thermal power is calculated. The method comprises the steps that firstly, a Newton main loop and a GMRES linear solving correction equation are adopted, so that mesoscopic and microcosmic temperature vectors are eliminated from the Newton main loop, a matrix-free technology is adopted to linearly solve the correction equation through GMRES to obtain a temperature correction value, the macroscopic temperature is updated, convergence is judged, and in the temperature equation set solving process, reordering according to scales and the Schur complementary technology are adopted for optimization calculation. According to the method, direct solving of a large-scale nonlinear system is avoided, meanwhile, accurate in-reactor fuel temperature distribution can be obtained, and a reliable basis is provided for nuclear safety evaluation.

Description

Technical Field

[0001] The present disclosure relates to the field of nuclear engineering thermohydraulics, and particularly to a method, device, electronic device, and storage medium for obtaining multi-scale temperatures of a pebble bed high-temperature gas-cooled reactor. Background Art

[0002] The pebble bed high-temperature gas-cooled reactor is a preferred reactor type for the fourth-generation advanced nuclear energy system and has good inherent safety characteristics. Different from reactor types such as pressurized water reactors, high-temperature reactors adopt spherical fuel elements and TRISO-coated particles design, which is an important safety barrier to prevent the release of radioactive fission products and ensure the safety of the public and staff.

[0003] There are tens of thousands to hundreds of thousands of fuel pebbles inside the core of the pebble bed high-temperature gas-cooled reactor, and tens of thousands of fuel particles are dispersed inside each fuel pebble. Due to the material inhomogeneity of the materials in the reactor, there are three ways to define the temperature in the reactor: the average temperature distribution of the pebble bed area (grid) (also called the macroscopic pebble bed temperature or macroscopic temperature), the temperature distribution inside the fuel pebble (also called the mesoscopic fuel pebble temperature or mesoscopic temperature), and the temperature inside the fuel particle (also called the microscopic fuel particle temperature or microscopic temperature), which evaluate the temperature at different spatial scales respectively.

[0004] The temperature distribution inside the fuel element and the highest temperature of the fuel core are the key factors affecting the performance of the fuel element and the coated particles. Therefore, the temperature results at the fuel pebble and particle scales are important parameters for evaluating the reactor safety. Currently, laboratories and universities in many countries have developed simulation programs and calculation methods for the multi-scale temperatures of the pebble bed high-temperature gas-cooled reactor.

[0005] Currently, the mainstream thermohydraulic calculation program for the pebble bed high-temperature gas-cooled reactor uses the Picard-type iterative algorithm to iteratively solve between different scales. For a system with strong nonlinearity such as the pebble bed high-temperature gas-cooled reactor, the convergence characteristics are poor or even non-convergent. Therefore, only the convergence criterion can be reduced, which will introduce a large truncation error. A few research scholars have considered using the Newton-type iterative algorithm to attempt to solve the multi-scale problems of the pebble bed high-temperature gas-cooled reactor. However, due to the different coupling characteristics between different scales, the computational cost brought by its solution method is unacceptable, and only the Newton-type solution of the macroscopic pebble bed - mesoscopic spherical fuel element two-level multi-scale temperature can be achieved.

[0006] Therefore, there is an urgent need for a new method to solve the above problems. Summary of the Invention

[0007] The purpose of the present disclosure is to provide a multi-scale temperature acquisition scheme for a pebble bed high-temperature gas-cooled reactor. By adopting the Newton iteration framework and combining with the non-linear elimination technique to solve the multi-scale temperature, the problem of poor convergence of the existing Picard iteration in a strongly non-linear system is solved, and the calculation cost is significantly reduced.

[0008] According to an embodiment of the present disclosure, a method for acquiring multi-scale temperature of a pebble bed high-temperature gas-cooled reactor is proposed, including:

[0009] Prepare input parameters;

[0010] Based on the input parameters, establish a residual function for solving the macroscopic pebble bed temperature:

[0011]

[0012] where x global is the macroscopic pebble bed temperature vector to be solved, ε represents the porosity of the pebble bed region, ρ b represents the pebble bed density, c p,b represents the pebble bed heat capacity, k b represents the equivalent thermal conductivity of the pebble bed, α represents the heat transfer coefficient between the pebble bed and the coolant, T f represents the coolant fluid temperature, represents the thermal power of the pebble bed region;

[0013] Use the residual function to construct a Newton correction equation, and adopt the Newton iteration framework to solve the macroscopic pebble bed temperature vector. Among them, in each round of Newton iteration:

[0014] Based on the current macroscopic pebble bed temperature vector, by simultaneously solving the mesoscopic fuel sphere temperature equation and the microscopic fuel particle temperature equation, obtain the mesoscopic temperature vector and the microscopic temperature vector, and calculate the thermal power of the pebble bed region;

[0015] Substitute the calculated thermal power and the current macroscopic pebble bed temperature vector and use the GMRES algorithm to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction;

[0016] Update the macroscopic pebble bed temperature vector based on the obtained macroscopic pebble bed temperature correction;

[0017] Based on the updated macroscopic pebble bed temperature vector, determine whether the Newton iteration converges. If it does not converge, enter the next round of Newton iteration. If it converges, end the Newton iteration, and determine the currently updated macroscopic pebble bed temperature vector as the finally obtained macroscopic pebble bed temperature vector.

[0018] In some embodiments, in each round of Newton iteration, based on the current macroscopic pebble bed temperature vector, by simultaneously solving the mesoscopic fuel sphere temperature equation and the microscopic fuel particle temperature equation, a mesoscopic temperature vector and a microscopic temperature vector are obtained, and the thermal power of the pebble bed region is calculated, including:

[0019] According to the boundary conditions and energy conservation relations determined by the current macroscopic pebble bed temperature vector, a temperature equation set of the mesoscopic fuel spheres and the microscopic fuel particles is established;

[0020] The following iterative calculations are performed on the temperature equation set:

[0021] The temperature equation set is linearly processed to obtain a coefficient matrix;

[0022] The coefficient matrix is reordered according to the scale to which the temperature vector belongs;

[0023] The reordered linear equation is solved using the Schur complement technique to obtain the mesoscopic temperature vector and the microscopic temperature vector;

[0024] It is judged whether the currently obtained mesoscopic temperature vector and microscopic temperature vector converge. If they do not converge, the currently obtained mesoscopic temperature vector and microscopic temperature vector are used as the initial temperature vectors to enter the next round of iteration until convergence. If convergence is achieved, the iterative calculation of the temperature equation set is ended;

[0025] The thermal power of the pebble bed region is calculated based on the converged mesoscopic temperature vector and microscopic temperature vector.

[0026] In some embodiments, solving the reordered linear equation using the Schur complement technique to obtain the mesoscopic temperature vector and the microscopic temperature vector includes:

[0027] The reordered coefficient matrix is partitioned;

[0028] The Schur complement operation is performed on the partitioned matrix to obtain a tridiagonal matrix;

[0029] The tridiagonal matrix equation is solved using the chasing method to obtain the mesoscopic temperature vector and the microscopic temperature vector.

[0030] In some embodiments, in each round of Newton iteration, the thermal power brought into the calculation and the current macroscopic pebble bed temperature vector are used, and the GMRES algorithm is used to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction amount, including:

[0031] Calculate Jv according to the following difference formula i :

[0032]

[0033] where J represents the Jacobian matrix, vi represents the orthogonal vectors of the Krylov subspace, and h represents the difference step size;

[0034] Based on Jv i obtain the new orthogonal vector v i+1 , and add the orthogonal vector v i+1 to the orthogonal vector sequence;

[0035] obtain an approximation of the macroscopic spherical pebble bed temperature correction based on the linear combination of the currently obtained orthogonal vector sequence;

[0036] Determine whether the linear solution of the current Newton correction equation converges. If it converges, end the linear solution and return the current approximation as the macroscopic spherical pebble bed temperature correction to the Newton iteration. If it does not converge, increment the value of i and return to calculate Jv i step, and re - execute the above process.

[0037] In some embodiments, determining whether the linear solution of the current Newton correction equation converges includes:

[0038] Determine whether the current linear solution converges according to whether the relative residual, absolute residual of the current approximation, and / or the update step of the correction amount satisfy a preset convergence condition.

[0039] According to an embodiment of the present disclosure, a multi - scale temperature acquisition device for a spherical pebble bed high - temperature gas - cooled reactor is proposed, including:

[0040] A parameter preparation unit for preparing input parameters;

[0041] A residual function establishment unit for establishing a residual function for solving the macroscopic spherical pebble bed temperature based on the input parameters:

[0042]

[0043] where x global is the macroscopic spherical pebble bed temperature vector to be solved, ε represents the porosity of the spherical pebble bed region, ρ b represents the spherical pebble bed density, c p,b represents the spherical pebble bed heat capacity, κ b represents the equivalent thermal conductivity of the spherical pebble bed, α represents the heat transfer coefficient between the spherical pebble bed and the coolant, T f represents the coolant fluid temperature, represents the thermal power of the spherical pebble bed region;

[0044] A Newton iteration calculation unit for constructing a Newton correction equation using the residual function and solving the macroscopic spherical pebble bed temperature vector using the Newton iteration framework. The Newton iteration calculation unit includes:

[0045] The meso-micro temperature and macro thermal power calculation subunit is used to obtain the meso-temperature vector and the micro-temperature vector by jointly solving the meso-fuel ball temperature equation and the micro-fuel particle temperature equation based on the current macro-spherical bed temperature vector, and calculate the thermal power of the pebble bed area;

[0046] GMRES linear solution subunit, used to bring in the calculated thermal power and the current macroscopic pebble bed temperature vector and use the GMRES algorithm to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction;

[0047] A macroscopic temperature correction subunit, used for updating the macroscopic ball bed temperature vector based on the obtained macroscopic ball bed temperature correction amount;

[0048] The main loop convergence judgment subunit is used to judge whether the Newton iteration has converged based on the updated macro ball bed temperature vector. If not, it enters the next round of Newton iteration. If it converges, it ends the Newton iteration and determines that the currently updated macro ball bed temperature vector is the final macro ball bed temperature vector.

[0049] In some embodiments, the mesoscopic microscopic temperature and macroscopic thermal power calculation subunit includes:

[0050] The temperature equation group simultaneous module is used to establish the temperature equation group of the mesoscopic fuel ball and microscopic fuel particle according to the boundary conditions and energy conservation relationship determined by the current macroscopic ball bed temperature vector;

[0051] The temperature equations iterative solution module is used to perform the following iterative calculations on the temperature equations:

[0052] Linearize the temperature equations to get the coefficient matrix;

[0053] Reorder the coefficient matrix according to the scale to which the temperature vector belongs;

[0054] The Schur complement technique is used to solve the rearranged linear equations to obtain the mesoscopic temperature vector and the microscopic temperature vector;

[0055] Determine whether the currently obtained mesoscopic temperature vector and microscopic temperature vector converge. If not, use the currently obtained mesoscopic temperature vector and microscopic temperature vector as initial temperature vectors to enter the next round of iteration until convergence. If convergence, end the iterative calculation of the temperature equation group.

[0056] The thermal power of the pebble bed region is calculated based on the converged mesoscopic temperature vector and microscopic temperature vector.

[0057] In some embodiments, the Schur complement technique is used to solve the reordered linear equation to obtain the mesoscopic temperature vector and the microscopic temperature vector, including:

[0058] Block the reordered coefficient matrix;

[0059] Perform Schur complement operation on the block matrix to obtain a tridiagonal matrix;

[0060] Use the chase method to solve the tridiagonal matrix equation to obtain the mesoscopic temperature vector and the microscopic temperature vector.

[0061] In some embodiments, the GMRES linear solver unit includes:

[0062] A difference calculation module for calculating Jv according to the following difference formula i :

[0063]

[0064] where J represents the Jacobian matrix, v i represents the orthogonal vector of the Krylov subspace, and h represents the difference step size;

[0065] An orthogonal vector sequence update module for obtaining a new orthogonal vector v i based on Jv i+1 and adding the orthogonal vector v i+1 to the orthogonal vector sequence;

[0066] A temperature correction amount calculation module for obtaining an approximation of the macroscopic spherical bed temperature correction amount based on the linear combination of the currently obtained orthogonal vector sequence;

[0067] A GMRES convergence judgment module for judging whether the linear solution of the current Newton correction equation converges. If it converges, end the linear solution and return the current approximation as the macroscopic spherical bed temperature correction amount to the Newton iteration. If it does not converge, increment the value of i and return to the step of calculating Jv i by the difference formula, and re - execute the above process.

[0068] In some embodiments, the GMRES convergence judgment module is used to determine whether the current linear solution converges according to whether the relative residual, absolute residual, and / or update step size of the correction amount of the current approximation satisfy a preset convergence condition.

[0069] According to an embodiment of the present disclosure, an electronic device is provided. The device includes a memory and a processor. The memory is used to store computer instructions that can run on the processor, and the processor is used to implement the method described in any one of the above when executing the computer instructions.

[0070] According to an embodiment of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the method described in any one of the above is implemented.

[0071] The multi-scale temperature acquisition method for the pebble bed high-temperature gas-cooled reactor proposed by the present disclosure has the following advantages:

[0072] (1) By using the Newton iteration framework instead of the conventional Picard iteration, superlinear convergence characteristics can be achieved. For the complex system characteristics of the pebble bed high-temperature gas-cooled reactor, a higher convergence rate can be achieved.

[0073] (2) At the same time, the temperature distributions in the pebble bed area, inside the fuel pebbles, and inside the fuel particles are provided, which can accurately evaluate the highest temperature of the fuel in the reactor and provide a reliable basis for the safety evaluation of the reactor core design scheme.

[0074] (3) By identifying the coupling characteristics of temperature variables at different scales, the Schur complement technique is specifically used for matrix decomposition and the chase method for solution. The decomposed matrix has excellent properties, and the computational complexity can be reduced by one order of magnitude compared with ordinary matrices. In addition, through the optimized processing of temperature variables at different scales and in cooperation with the Newton superlinear convergence rate, the overall solution efficiency of this solution is higher than that of the existing methods.

[0075] (4) The matrix-free technique is applied to solve the correction equation, avoiding the explicit construction of a large-scale Jacobian matrix. At the same time, the thermal power value is reused during the GMRES iteration, significantly reducing the storage overhead and computational cost.

[0076] Other features and advantages of the technical solution proposed by the present disclosure will be described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present specification, and are used together with the specification to explain the principles of the present specification.

[0078] Figure 1 The flowchart of the multi-scale temperature acquisition method for the pebble bed high-temperature gas-cooled reactor according to an embodiment of the present disclosure is shown.

[0079] Figure 2 The schematic flow diagram of the multi-scale temperature acquisition method for the pebble bed high-temperature gas-cooled reactor according to an exemplary embodiment of the present disclosure is shown.

[0080] Figure 3 The schematic structural diagram of the electronic device shown in at least one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0081] Exemplary embodiments will be described in detail herein, and examples thereof are shown in the accompanying drawings. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present disclosure. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present disclosure as detailed in the appended claims.

[0082] Embodiments of the present disclosure can be applied to a computer system / server, which can operate with many other general-purpose or special-purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations suitable for use with a computer system / server include, but are not limited to: personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, microprocessor-based systems, set-top boxes, programmable consumer electronics, network personal computers, minicomputer systems, mainframe computer systems, and distributed cloud computing technology environments including any of the above systems, and so on.

[0083] The computer system / server can be described in the general context of computer system-executable instructions, such as program modules, executed by the computer system. Generally, program modules can include routines, programs, object programs, components, logic, data structures, etc., which perform specific tasks or implement specific abstract data types. The computer system / server can be implemented in a distributed cloud computing environment, where tasks are executed by remote processing devices linked through a communication network. In a distributed cloud computing environment, program modules can be located on local or remote computing system storage media including storage devices.

[0084] The core concept of the present disclosure is to use the Newton iteration framework to solve the multi-scale temperature of the pebble bed high-temperature gas-cooled reactor. By solving the mesoscopic fuel pebble and microscopic fuel particle temperature equations in each round of Newton iteration to obtain the thermal power term, and reusing this thermal power during the process of solving the correction equation of the macroscopic pebble bed temperature by GMRES, the convergence problem of the traditional Picard iteration is avoided, and at the same time the computational cost is reduced. In addition, different aspects of the present disclosure also include using matrix-free technology for GMRES solution, and using Schur complement technology to optimize the solution process of the mesoscopic fuel pebble and microscopic fuel particle temperature equations.

[0085] Figure 1 A flowchart of an automated interactive large language model pipeline orchestration method for complex queries according to an embodiment of the present disclosure is shown. This method can be applied to complex queries of structured, semi-structured, and unstructured data in a data lake. As shown, the method includes steps 1 to 3.

[0086] Step 1, prepare input parameters.

[0087] The following input parameters can be prepared for this embodiment: grid size information, which is used to determine the spatial discretization of the reactor core and provide a geometric basis for subsequent calculations; the nuclear power density in the core pebble bed area, which is used to characterize the power distribution in the pebble bed area and is an important input parameter for calculating the temperature distribution; the proportion and operation history of fuel pebbles in different batches within the pebble bed grid, which reflect the distribution characteristics and burnup status of fuel assemblies in the pebble bed area, and this information will affect the calculation of local thermal power; the physical property library of thermal conductivity, which can include the thermophysical parameters required for the calculation, mainly including the porosity ε (characterizing the void characteristics of the pebble bed area), the pebble bed density ρ S (e.g., the pebble bed heat capacity c p 、the equivalent thermal conductivity κ of the pebble bed s 、the heat transfer coefficient α between the pebble bed and the coolant.

[0088] An initial macroscopic temperature distribution x global,0 can also be set as the starting point of the Newton iteration. The selection of the initial value may affect the number of Newton iterations.

[0089] The above parameters can be used as the basic conditions for multi-scale temperature calculation, providing necessary information for the construction and solution of the subsequent residual function.

[0090] Step 2, based on the input parameters, establish a residual function for solving the macroscopic pebble bed temperature:

[0091]

[0092] where x global is the vector of macroscopic pebble bed temperature to be solved, ε represents the porosity of the pebble bed area, ρ b represents the pebble bed density, c p,b represents the pebble bed heat capacity, κ b represents the equivalent thermal conductivity of the pebble bed, α represents the heat transfer coefficient between the pebble bed and the coolant, T f represents the coolant fluid temperature, represents the thermal power in the pebble bed area.

[0093] After obtaining the input parameters, a residual function for the macroscopic pebble bed temperature distribution as described above can be established according to this embodiment. This residual function reflects the energy conservation relationship in the pebble bed area, which is used to describe the rate of change of the pebble bed temperature over time, where (1 - ε) represents the actual volume fraction of the pebble bed, ρ b c p,b represents the heat capacity per unit volume; the conduction term describes the heat conduction inside the pebble bed, where represents the gradient of the vector x global of the macroscopic pebble bed temperature, represents the solution Divergence; the convective heat transfer term α(x global -T f ) is used to describe the heat transfer between the spherical pebble bed and the coolant. α is the heat transfer coefficient, and (x global -T f ) is the temperature difference driving force; the thermal power of the spherical pebble bed region is determined according to the temperature distributions of the mesoscopic fuel pebbles and the microscopic fuel particles.

[0094] The vector x to be solved of the residual function constructed according to this embodiment global only contains the macroscopic spherical pebble bed temperature.

[0095] Step 3: Use the residual function to construct a Newton correction equation, and adopt a Newton iteration framework to solve the macroscopic spherical pebble bed temperature vector. Among them, in each round of Newton iteration:

[0096] Based on the current macroscopic spherical pebble bed temperature vector, by simultaneously solving the mesoscopic fuel pebble temperature equation and the microscopic fuel particle temperature equation, obtain the mesoscopic temperature vector and the microscopic temperature vector, and calculate the thermal power of the spherical pebble bed region;

[0097] Substitute the calculated thermal power and the current macroscopic spherical pebble bed temperature vector and use the GMRES algorithm to solve the Newton correction equation to obtain the macroscopic spherical pebble bed temperature correction amount;

[0098] Update the macroscopic spherical pebble bed temperature vector based on the obtained macroscopic spherical pebble bed temperature correction amount;

[0099] Based on the updated macroscopic spherical pebble bed temperature vector, determine whether the Newton iteration converges. If it does not converge, enter the next round of Newton iteration. If it converges, end the Newton iteration, and determine the currently updated macroscopic spherical pebble bed temperature vector as the finally obtained macroscopic spherical pebble bed temperature vector.

[0100] According to this embodiment, solve the following Newton correction equation based on the Newton iteration framework to obtain the macroscopic spherical pebble bed temperature vector:

[0101] Jδx = -F(x global ),

[0102] where J is the Jacobian matrix, δx is the macroscopic spherical pebble bed temperature correction amount, and F(x global ) is the residual vector.

[0103] The Newton iteration process may include the following steps 31 to 34.

[0104] Step 31: Based on the current x global, by simultaneously solving the mesoscopic fuel sphere temperature equation and the microscopic fuel particle temperature equation, the mesoscopic temperature vector and the microscopic temperature vector are obtained, and then the thermal power is solved based on the obtained mesoscopic temperature vector and microscopic temperature vector The solved thermal power Substitute it into the subsequent GMRES solution and keep it unchanged during the entire GMRES solution process.

[0105] According to this embodiment, the thermal power is calculated only once in each round of Newton iteration, rather than updated in each GMRES iteration. After in-depth research, the inventor believes that reusing the same thermal power value during the GMRES iteration process will not affect the convergence rate, but can avoid repeated non-linear cancellation calculations, thus significantly reducing the computational cost.

[0106] Step 32, solve the Newton correction equation.

[0107] According to this embodiment, the GMRES algorithm is used to solve the correction equation, and the solution of this equation is based on the current x global and the already calculated thermal power The GMRES algorithm gradually approximates the solution by constructing a Krylov subspace, and the obtained temperature correction is used to update the macroscopic temperature.

[0108] Step 33, the macroscopic spherical bed temperature vector x can be updated based on the following formula global :

[0109]

[0110] Step 34, Newton convergence judgment. For example, relative residual convergence determination can be performed. If the two-norm of the current residual vector reaches the desired accuracy (for example, less than a preset threshold), it can be determined that the Newton iteration has converged, the Newton iteration is terminated, and the currently updated macroscopic spherical bed temperature vector is the finally obtained macroscopic spherical bed temperature vector; if does not reach the desired accuracy, it can be determined that the Newton iteration has not converged, then return to step 31 to perform the next round of Newton iteration.

[0111] According to the above embodiment, the Newton iteration framework is used for solution, decoupling the mesoscopic and microscopic temperatures from the Newton iteration system, and only iteratively solving the macroscopic temperature in the main loop, avoiding directly solving a large-scale non-linear system and reducing the computational complexity; only calculating the thermal power once in each Newton iteration, avoiding repeated non-linear cancellation calculations, and significantly reducing the computational cost.

[0112] In some embodiments, in step 3 above, in each round of Newton iteration, based on the current macroscopic pebble bed temperature vector, by simultaneously solving the mesoscopic fuel sphere temperature equation and the microscopic fuel particle temperature equation, the mesoscopic temperature vector and the microscopic temperature vector are obtained, and the thermal power of the pebble bed region is calculated, including:

[0113] According to the boundary conditions and energy conservation relations determined by the current macroscopic pebble bed temperature vector, establish the temperature equation of the mesoscopic fuel sphere and the temperature equation set of the microscopic fuel particles;

[0114] Perform the following iterative calculation on the temperature equation set:

[0115] Linearly process the temperature equation set to obtain the coefficient matrix;

[0116] Reorder the coefficient matrix according to the scale to which the temperature vector belongs;

[0117] Use the Schur complement technique to solve the reordered linear equation to obtain the mesoscopic temperature vector and the microscopic temperature vector;

[0118] Judge whether the currently obtained mesoscopic temperature vector and microscopic temperature vector converge. If they do not converge, use the currently obtained mesoscopic temperature vector and microscopic temperature vector as the initial temperature vector to enter the next round of iteration until convergence. If they converge, end the iterative calculation of the temperature equation set;

[0119] Calculate the thermal power of the pebble bed region based on the convergent mesoscopic temperature vector and microscopic temperature vector.

[0120] Specifically, first determine the boundary conditions according to the current macroscopic pebble bed temperature vector, and simultaneously establish the control equations describing the mesoscopic and microscopic temperature changes as follows:

[0121]

[0122] where, T sphere and T particle are the temperatures of the spherical fuel element (i.e., fuel sphere) and the fuel particle respectively, represents the core power of the fuel particle, represents the heat generation power of the fuel particles in the spherical fuel element, c p,s 、c p,p are the corresponding specific heat capacities respectively, ρ s 、ρ p are the corresponding densities respectively, λ s 、λ p are the corresponding thermal conductivities respectively.

[0123] The above temperature equation is non - linear, and it is relatively complex to solve directly with a high computational cost. However, research shows that the non - linearity between the temperature vectors of these two scales is weak. Based on this characteristic, the inventor considered using linearization to reduce the computational cost. After linearization, a meso - micro coupled coefficient matrix is obtained. Due to the coupling of different scales, the properties of the matrix are poor. To optimize the solution process, in this embodiment, the coefficient matrix is reordered according to the scale of the temperature vector (i.e., meso - scale or micro - scale) to make it more suitable for subsequent Schur complement decomposition.

[0124] The Schur complement technique is used to solve the reordered coefficient matrix, and the meso - scale and micro - scale temperature distributions can be obtained. To ensure the calculation accuracy, convergence judgment can be performed on the obtained meso - scale and micro - scale temperature vectors. If the convergence criterion is not met, the current obtained meso - scale / micro - scale temperature vector is used as the new initial temperature vector and the steps of linearizing the temperature equation system are returned, and the iterative calculation continues until the meso - scale and micro - scale temperature distributions meet the corresponding convergence requirements.

[0125] The fuel in the reactor is the fission heat generated by nuclear fuel fission. Although there are concepts such as fuel spheres in the pebble - bed high - temperature gas - cooled reactor, the actual internal component directly containing nuclear fuel is the fuel particle. The heat generated by fission will pass through the particle - fuel sphere - pebble bed, and then the heat is carried out by the convective heat transfer of the coolant helium gas to drive the steam turbine to generate electricity.

[0126] For the macroscopic temperature of the pebble bed, its thermal power represents the heat flux on the surface of the fuel sphere. Therefore, after obtaining the convergent meso - scale and micro - scale temperatures, the heat flux on the sphere surface can be calculated according to the temperature gradient and used as the thermal power of the pebble bed area in the macroscopic temperature calculation. Calculating the thermal power of the pebble bed area through the meso - scale temperature vector and the micro - scale temperature vector is a common technique in the art and will not be elaborated here.

[0127] As mentioned above, the calculated thermal power value will remain unchanged in this round of Newton iteration and be used to construct the residual function and calculate the macroscopic pebble bed temperature correction. This design avoids the repeated calculation of thermal power in the GMRES solution process, significantly reducing the computational cost while ensuring the calculation accuracy.

[0128] Through linearization and non - linear elimination, this embodiment avoids taking the meso - scale and micro - scale temperatures as variables to be solved in the main loop of Newton iteration, significantly reducing the overall computational complexity.

[0129] In some embodiments, the above use of the Schur complement technique to solve the temperature vector includes:

[0130] Partition the reordered coefficient matrix;

[0131] Perform Schur complement operation on the partitioned matrix to obtain a tridiagonal matrix;

[0132] The mesoscopic temperature vector and the microscopic temperature vector are obtained by using the chasing method to solve the tridiagonal matrix equation.

[0133] According to this embodiment, the reordered coefficient matrix is subjected to Schur complement decomposition, which can be transformed into a tridiagonal matrix. The obtained tridiagonal structure has excellent computational properties, and the distribution law of its elements significantly reduces the computational complexity. On the basis of Schur complement decomposition, the chasing method is further used for solution. The chasing method is an efficient algorithm specifically for tridiagonal matrix equations, and the calculation is completed through two processes of forward substitution and back substitution. Compared with dealing with ordinary matrices, its computational complexity can be reduced by one order of magnitude. In particular, the aforementioned coefficient matrix reordering based on scale, when used in conjunction with Schur complement technology, ensures that the decomposed matrix still has good computational properties, significantly improving the solution efficiency while ensuring computational accuracy.

[0134] In some embodiments, in step 3 above, the GMRES solution can be implemented using matrix-free technology to further improve the computational efficiency. Matrix-free technology calculates the product of the Jacobian matrix J and the orthogonal vector v through a difference formula, avoiding the explicit construction of the complete Jacobian matrix, and can significantly reduce the storage overhead and computational cost. i

[0135] The GMRES solution of the Newton correction equation using matrix-free technology includes:

[0136] Calculating Jv according to the following difference formula i :

[0137]

[0138] where J represents the Jacobian matrix, v i represents the orthogonal vector of the Krylov subspace, and h represents the difference step size;

[0139] Based on Jv i a new orthogonal vector v i+1 is obtained, and the orthogonal vector v i+1 is added to the orthogonal vector sequence;

[0140] An approximate value of the macroscopic spherical bed temperature correction is obtained based on the linear combination of the currently obtained orthogonal vector sequence;

[0141] Determine whether the linear solution of the current Newton correction equation converges. If it converges, end the linear solution and return the current approximate value as the macroscopic spherical bed temperature correction to the Newton iteration. If it does not converge, increment the value of i and return the calculation of Jv through the difference formula iStep, re - execute the above process.

[0142] According to this embodiment, in the GMRES solution process, the product Jv is first approximately calculated using the difference formula i . First, based on the existing macroscopic spherical - bed temperature vector x global and the thermal power calculate the residual F(x global ), and at the same time calculate the residual F(x global + hv i ). Then, through the difference formula approximately obtain Jv i . Here, the thermal power remains unchanged throughout the GMRES solution process. Among them, in the difference calculation step of each iteration, due to the update of v i , it is necessary to recalculate F(x global + hv i ), while F(x global ) remains unchanged throughout the GMRES solution process. Therefore, it only needs to be calculated in the first - round GMRES iteration.

[0143] After obtaining Jv i , perform orthogonalization processing on it to obtain a new orthogonal vector v i+1 . Add this orthogonal vector to the existing sequence to expand the Krylov subspace. As the GMRES iteration progresses, the orthogonal vector sequence continuously grows, providing a better approximation space for the solution.

[0144] Based on the currently obtained orthogonal vector sequence, perform a linear combination to obtain an approximate value of the macroscopic spherical - bed temperature correction. The solution of this approximate value can be achieved by minimizing the residual.

[0145] Finally, perform a convergence judgment on the current approximate value. If the linear solution converges, use this approximate value as the correction to return to the Newton iteration to update the macroscopic spherical - bed temperature vector; if it does not converge, increment i by 1 and return to the difference calculation step to continue the GMRES iteration.

[0146] Through the above - mentioned embodiment, explicit construction of a large - scale Jacobian matrix is avoided, and at the same time, the thermal power value is reused throughout the GMRES solution, effectively reducing the storage and calculation overhead.

[0147] In some embodiments, determining whether the linear solution of the current Newton correction equation converges includes:

[0148] Determine whether the current linear solution converges according to whether the relative residual, absolute residual, and / or the update step of the correction of the current approximate value satisfy the preset convergence condition.

[0149] The residual refers to the Newton correction equation Jδx = -F(x global ) is the solution error under the current approximate solution. The relative residual can use the second norm of the current iteration residual. The absolute residual can refer to the absolute value of the current iteration residual, providing an absolute benchmark for convergence judgment. The correction update step size can refer to the difference between the approximate solutions obtained in two adjacent iterations, reflecting the stability of the iteration process.

[0150] Appropriate convergence conditions can be selected according to the characteristics of the specific problem, such as using the above three judgment criteria alone or in combination. When the preset convergence conditions are met, it can be considered that the linear solution of the current Newton correction equation has reached the required accuracy, and the current approximate solution can be returned as the macroscopic pebble bed temperature correction amount.

[0151] Figure 2 A schematic flow chart of a multi-scale temperature acquisition method for a pebble bed high temperature gas-cooled reactor according to an exemplary embodiment of the present disclosure is shown.

[0152] The upper left part is the pre-processing, including parameter preparation and determination of the vector x to be solved global , the vector x to be solved global Only macroscopic pebble bed temperature is included.

[0153] The lower left part describes the Newton iteration framework as the main loop, constructing the Newton correction equation and calling the linear solution process to obtain the macroscopic ball bed temperature correction δx to update the macroscopic ball bed temperature vector x according to the following formula global :

[0154]

[0155] Then make a convergence judgment. If convergence occurs, the Newton iteration ends and the current updated As the final macroscopic pebble bed temperature vector; if it does not converge, enter the next round of Newton iteration.

[0156] The middle part shows the linear solution process in detail. First, the thermal power of the ball bed area is calculated by micro-temperature and meso-temperature, and then the correction equation is solved by matrix-free technology and Krylov subspace construction. If the linear equation system converges, the linear solution is jumped out and the macroscopic ball bed temperature correction is returned to the Newton main loop, otherwise the next round of GMRES iteration continues.

[0157] The right part shows the nonlinear elimination process, which combines the mesoscale and microscale temperature equations and uses the Schur complement technique to quickly solve and judge the convergence.

[0158] An embodiment of the present disclosure further provides a multi-scale temperature acquisition device for a pebble bed high temperature gas-cooled reactor, comprising:

[0159] A parameter preparation unit for preparing input parameters;

[0160] A residual function establishment unit for establishing a residual function for solving the macroscopic spherical bed temperature based on the input parameters:

[0161]

[0162] where x global is the macroscopic spherical bed temperature vector to be solved, ε represents the porosity of the spherical bed region, ρ b represents the spherical bed density, c p,b represents the heat capacity of the spherical bed, κ b represents the equivalent thermal conductivity of the spherical bed, α represents the heat transfer coefficient between the spherical bed and the coolant, T f represents the coolant fluid temperature, represents the thermal power of the spherical bed region;

[0163] A Newton iteration calculation unit for constructing a Newton correction equation using the residual function and solving the macroscopic spherical bed temperature vector using a Newton iteration framework. The Newton iteration calculation unit includes:

[0164] A mesoscopic and microscopic temperature and macroscopic thermal power calculation sub-unit for obtaining a mesoscopic temperature vector and a microscopic temperature vector and calculating the thermal power of the spherical bed region by simultaneously solving a mesoscopic fuel sphere temperature equation and a microscopic fuel particle temperature equation based on the current macroscopic spherical bed temperature vector;

[0165] A GMRES linear solution sub-unit for substituting the calculated thermal power and the current macroscopic spherical bed temperature vector and using the GMRES algorithm to solve the Newton correction equation to obtain a macroscopic spherical bed temperature correction;

[0166] A macroscopic temperature correction sub-unit for updating the macroscopic spherical bed temperature vector based on the obtained macroscopic spherical bed temperature correction;

[0167] A main loop convergence judgment sub-unit for judging whether the Newton iteration converges based on the updated macroscopic spherical bed temperature vector. If it does not converge, enter the next round of Newton iteration. If it converges, end the Newton iteration and determine the currently updated macroscopic spherical bed temperature vector as the finally obtained macroscopic spherical bed temperature vector.

[0168] For other details and features of this embodiment, please refer to the relevant descriptions above.

[0169] Figure 3An electronic device provided by at least one embodiment of the present disclosure, the device includes a memory and a processor, the memory is used to store computer instructions that can run on the processor, and the processor is used to implement the multi-scale temperature acquisition method of the pebble bed high-temperature gas-cooled reactor described in any embodiment or implementation manner of the present disclosure when executing the computer instructions.

[0170] At least one embodiment of the present disclosure also provides a computer-readable storage medium, on which a computer program is stored, and the program implements the multi-scale temperature acquisition method of the pebble bed high-temperature gas-cooled reactor described in any embodiment or implementation manner of the present disclosure when executed by a processor.

[0171] Those skilled in the art should understand that one or more embodiments of this specification can be provided as a method, a system, or a computer program product. Therefore, one or more embodiments of this specification can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, one or more embodiments of this specification can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0172] The various embodiments in this specification are described in a progressive manner. For the parts that are the same or similar among the various embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the embodiment of the data processing device, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0173] The above describes specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the acts or steps recited in the claims can be executed in a different order than in the embodiments and still achieve the desired results. Additionally, the processes depicted in the figures do not necessarily require the particular order or sequential order shown to achieve the desired results. In certain implementations, multitasking and parallel processing are also possible or may be advantageous.

[0174] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware including the structures disclosed in this specification and their structural equivalents, or in one or more of them in combination. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non-transitory program carrier to be executed by, or to control the operation of, data processing apparatus. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode and transmit information to the appropriate receiver apparatus for execution by the data processing apparatus. A computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0175] The processes and logical flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform the functions by operating on input data and generating output. The processes and logical flows can also be performed by, or the apparatus can be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0176] Suitable computers for executing a computer program include, by way of example, general and / or special purpose microprocessors, or any other type of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory and / or a random access memory. Basic components of a computer include a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include one or more mass storage devices for storing data, such as magnetic disks, magneto-optical disks, or optical disks, etc., or the computer will be operatively coupled to such mass storage devices to receive data therefrom or to transfer data thereto, or both. However, a computer need not have such devices. In addition, a computer may be embedded in another device, such as a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive, to name just a few.

[0177] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and memory devices, including, for example, semiconductor memory devices (such as EPROM, EEPROM, and flash memory devices), magnetic disks (such as internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks. The processor and the memory may be supplemented by, or incorporated in, special purpose logic circuitry.

[0178] Although this specification contains many specific implementation details, these should not be construed as limiting the scope of any invention or the scope of what is claimed, but rather as mainly describing the features of specific embodiments of particular inventions. Certain features that are described in multiple embodiments in this specification may also be implemented in combination in a single embodiment. On the other hand, the various features described in a single embodiment may also be implemented separately in multiple embodiments or in any suitable sub-combination. Additionally, although features may operate in certain combinations as described above and even be claimed as such initially, one or more features from a claimed combination may in some cases be removed from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination.

[0179] Similarly, although operations are depicted in the figures in a particular order, this should not be understood as requiring that the operations be performed in the particular order shown or sequentially, or that all illustrated operations be performed, to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Additionally, the separation of various system modules and components in the above embodiments should not be understood as required in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0180] Thus, particular embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the acts recited in the claims may be performed in a different order and still achieve the desired result. Additionally, the processes depicted in the figures are not necessarily in the particular order or sequential order shown to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.

[0181] The above description is only the preferred embodiment of one or more embodiments of this specification and is not intended to limit one or more embodiments of this specification. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of one or more embodiments of this specification shall be included within the scope protected by one or more embodiments of this specification.

Claims

1. A multi-scale temperature acquisition method for a pebble bed high temperature gas-cooled reactor, characterized in that: include: Prepare input parameters; Based on the input parameters, a residual function for solving the macroscopic pebble bed temperature is established: Among them, x global is the temperature vector of the macroscopic pebble bed to be solved, ε represents the porosity of the pebble bed area, ρ b represents the density of the pebble bed, c p,b represents the heat capacity of the pebble bed, κ b represents the equivalent thermal conductivity of the pebble bed, α represents the heat transfer coefficient between the pebble bed and the coolant, T f represents the coolant fluid temperature, Indicates the thermal power of the pebble bed area; The Newton correction equation is constructed using the residual function, and the macroscopic pebble bed temperature vector is solved using the Newton iteration framework, wherein in each round of Newton iteration: Based on the current macroscopic ball bed temperature vector, the mesoscopic temperature vector and microscopic temperature vector are obtained by solving the mesoscopic fuel ball temperature equation and the microscopic fuel particle temperature equation simultaneously, and the thermal power of the ball bed area is calculated; Substitute the calculated thermal power and the current macroscopic pebble bed temperature vector and use the GMRES algorithm to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction value; Update the macroscopic ball bed temperature vector based on the obtained macroscopic ball bed temperature correction; Based on the updated macroscopic ball bed temperature vector, determine whether the Newton iteration converges. If not, enter the next round of Newton iteration. If converged, end the Newton iteration and determine the currently updated macroscopic ball bed temperature vector as the final macroscopic ball bed temperature vector.

2. The method according to claim 1, characterized in that: In each round of Newton iteration, based on the current macroscopic pebble bed temperature vector, the mesoscopic fuel ball temperature equation and the microscopic fuel particle temperature equation are solved simultaneously to obtain the mesoscopic temperature vector and the microscopic temperature vector, and calculate the thermal power of the pebble bed area, including: According to the boundary conditions and energy conservation relationship determined by the current macroscopic ball bed temperature vector, the temperature equations of the mesoscopic fuel ball and microscopic fuel particle are established; The temperature equations are iterated as follows: Linearize the temperature equations to get the coefficient matrix; Reorder the coefficient matrix according to the scale to which the temperature vector belongs; The Schur complement technique is used to solve the rearranged linear equations to obtain the mesoscopic temperature vector and the microscopic temperature vector; Determine whether the currently obtained mesoscopic temperature vector and microscopic temperature vector converge. If not, use the currently obtained mesoscopic temperature vector and microscopic temperature vector as initial temperature vectors to enter the next round of iteration until convergence. If convergence, end the iterative calculation of the temperature equation group. The thermal power of the pebble bed region is calculated based on the converged mesoscopic temperature vector and microscopic temperature vector.

3. The method according to claim 2, characterized in that The Schur complement technique is used to solve the reordered linear equations to obtain the mesoscopic temperature vector and microscopic temperature vector, including: Divide the reordered coefficient matrix into blocks; Perform Schur complement operation on the block matrix to obtain a tridiagonal matrix; The mesoscopic temperature vector and microscopic temperature vector are obtained by solving the tridiagonal matrix equation using the pursuit method.

4. The method according to claim 1, characterized in that: In each round of Newton iteration, the calculated thermal power and the current macroscopic pebble bed temperature vector are introduced and the GMRES algorithm is used to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction, including: Calculate Jv according to the following difference formula i : Where J represents the Jacobian matrix, v i represents the orthogonal vector of the Krylov subspace, and h represents the difference step size; Based on Jv i Get the new orthogonal vector v i+1 , and the orthogonal vector v i+1 Add orthogonal vector sequence; Based on the linear combination of the orthogonal vector sequence currently obtained, the approximate value of the macroscopic pebble bed temperature correction is obtained; Determine whether the linear solution of the current Newton correction equation converges. If it converges, end the linear solution and return the current approximate value as the macroscopic ball bed temperature correction to the Newton iteration. If it does not converge, add 1 to the i value and return the Jv calculated by the difference formula. i Step 1, and execute the above process again.

5. The method according to claim 4, characterized in that Determine whether the linear solution of the current Newton correction equation converges, including: Whether the current linear solution converges is determined based on whether the relative residual, absolute residual and / or update step of the current approximation value meets the preset convergence condition.

6. A multi-scale temperature acquisition device for a pebble bed high temperature gas-cooled reactor, characterized in that: include: A parameter preparation unit, used for preparing input parameters; The residual function establishment unit is used to establish a residual function for solving the macroscopic pebble bed temperature based on the input parameters: Among them, x global is the temperature vector of the macroscopic pebble bed to be solved, ε represents the porosity of the pebble bed area, ρ b represents the density of the pebble bed, c p,b represents the heat capacity of the pebble bed, κ b represents the equivalent thermal conductivity of the pebble bed, α represents the heat transfer coefficient between the pebble bed and the coolant, T f represents the coolant fluid temperature, Indicates the thermal power of the pebble bed area; A Newton iterative calculation unit is used to construct a Newton correction equation using the residual function and solve the macroscopic pebble bed temperature vector using a Newton iterative framework. The Newton iterative calculation unit includes: The meso-micro temperature and macro thermal power calculation subunit is used to obtain the meso-temperature vector and the micro-temperature vector by jointly solving the meso-fuel ball temperature equation and the micro-fuel particle temperature equation based on the current macro-spherical bed temperature vector, and calculate the thermal power of the pebble bed area; GMRES linear solution subunit, used to bring in the calculated thermal power and the current macroscopic pebble bed temperature vector and use the GMRES algorithm to solve the Newton correction equation to obtain the macroscopic pebble bed temperature correction; A macroscopic temperature correction subunit, used for updating the macroscopic ball bed temperature vector based on the obtained macroscopic ball bed temperature correction amount; The main loop convergence judgment subunit is used to judge whether the Newton iteration has converged based on the updated macro ball bed temperature vector. If not, it enters the next round of Newton iteration. If it converges, it ends the Newton iteration and determines that the currently updated macro ball bed temperature vector is the final macro ball bed temperature vector.

7. The device according to claim 6, characterized in that The mesoscopic microscopic temperature and macroscopic thermal power calculation subunit includes: The temperature equation group simultaneous module is used to establish the temperature equation group of the mesoscopic fuel ball and microscopic fuel particle according to the boundary conditions and energy conservation relationship determined by the current macroscopic ball bed temperature vector; The temperature equations iterative solution module is used to perform the following iterative calculations on the temperature equations: Linearize the temperature equations to get the coefficient matrix; Reorder the coefficient matrix according to the scale to which the temperature vector belongs; The Schur complement technique is used to solve the rearranged linear equations to obtain the mesoscopic temperature vector and the microscopic temperature vector; Determine whether the currently obtained mesoscopic temperature vector and microscopic temperature vector converge. If not, use the currently obtained mesoscopic temperature vector and microscopic temperature vector as initial temperature vectors to enter the next round of iteration until convergence. If convergence, end the iterative calculation of the temperature equation group. The thermal power of the pebble bed region is calculated based on the converged mesoscopic temperature vector and microscopic temperature vector.

8. The device according to claim 7, characterized in that The Schur complement technique is used to solve the reordered linear equations to obtain the mesoscopic temperature vector and microscopic temperature vector, including: Divide the reordered coefficient matrix into blocks; Perform Schur complement operation on the block matrix to obtain a tridiagonal matrix; The mesoscopic temperature vector and microscopic temperature vector are obtained by solving the tridiagonal matrix equation using the pursuit method.

9. The device according to claim 6, characterized in that GMRES linear solver subunits include: The difference calculation module is used to calculate Jv according to the following difference formula i : Where J represents the Jacobian matrix, v i represents the orthogonal vector of the Krylov subspace, and h represents the difference step size; Orthogonal vector sequence update module for Jv-based i Get the new orthogonal vector v i+1 , and the orthogonal vector v i+1 Add orthogonal vector sequence; A temperature correction calculation module is used to obtain an approximate value of the macroscopic pebble bed temperature correction based on a linear combination of the currently obtained orthogonal vector sequence; GMRES convergence judgment module is used to judge whether the linear solution of the current Newton correction equation converges. If it converges, the linear solution is terminated and the current approximate value is returned to the Newton iteration as the macroscopic ball bed temperature correction value. If it does not converge, the i value is increased by 1, and Jv calculated by the difference formula is returned. i Step 1, and execute the above process again.

10. The device according to claim 9, characterized in that The GMRES convergence judgment module is used to determine whether the current linear solution converges according to whether the relative residual, absolute residual and / or update step of the current approximation value meets the preset convergence condition.

11. An electronic device, characterized in that: The device comprises a memory and a processor, wherein the memory is used to store computer instructions executable on the processor, and the processor is used to implement the method according to any one of claims 1 to 5 when executing the computer instructions.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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