Method and device for calculating physical and thermal coupling numerical value of reactor, medium and equipment

Abstract

The invention relates to the technical field of nuclear reactor core calculation, and discloses a method and a device for calculating a physical and thermal coupling numerical value of a reactor, a medium and equipment. In the process of calculating the physical and thermal coupling numerical value of the reactor, a neutron space-time dynamic model is subjected to time discretization by adopting a diagonal implicit Runge-Kutta format; in the transient analysis process, coupling calculation is carried out through a simple operator splitting method and a Picard iteration method to obtain a calculation value, coupling global solution variables are selected based on a Newton method, a global solution residual equation is established, solving is carried out through a Krylov subspace solution method based on the coupling global solution variables and the global solution residual equation, a JFNK iteration process is constructed, and a transient analysis result is obtained. And finally, taking the calculated value as an initial value, establishing a hybrid iteration process according to the initial value and the JFNK iteration process, and calculating to obtain a reactor transient physical thermal full-coupling numerical solution. According to the method, excessive solution is avoided, the convergence speed is increased, and stable and rapid convergence calculation is realized.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor core calculation technology, and in particular to a reactor physical thermal coupling numerical calculation method and device, medium and equipment. Background Art

[0002] To accurately, quickly and realistically simulate the operation of complex coupled systems in nuclear power plants, it is necessary to carry out coupled calculations of multiple physical fields such as physics and thermal engineering. For example, the coupling effect between physics and thermal engineering specifically refers to the fission power calculated by the physics major affecting the fuel temperature, moderator density and related physical properties calculated by the thermal engineering major, while the fuel temperature and moderator density calculated by the thermal engineering major will affect the cross-sectional parameters of the physics major, thereby affecting the fission power calculated by the physics major. The specific coupling process is as follows: Figure 1 As shown, one of the core tasks of multi-physics field coupling calculation is to explore and develop high-precision coupled iterative calculation methods suitable for solving the multi-physics fields of nuclear reactors.

[0003] The multi-physics field coupling iterative solution strategy can be divided into tight coupling and loose coupling. The basic coupling solution feature of tight coupling is that each physical field reaches complete convergence under the coupling time iteration step; while the loose coupling solution method is to decouple the coupled system and split it into different subsystems, and realize the coupling solution by transferring the coupling boundary information of the decoupled subsystems. Under the coupling time iteration step, each physical field usually cannot reach complete convergence. The coupling problem solution strategy is as follows Figure 2 As shown, loosely coupled OS and OSSI methods are usually used under the external coupling strategy, while OS, OSSI, Picard, Newton iterative methods, etc. can be used under the internal coupling strategy.

[0004] The calculation programs for nuclear energy coupling systems developed in the early days generally adopted the external coupling mode. At the beginning of this century, nuclear energy coupling problems began to adopt the internal coupling mode, and each sub-physical field gradually adopted more accurate models and more efficient numerical calculation methods, which greatly improved the calculation ability of coupling problems. However, the various existing coupling methods have different limitations. For example, the Picard iteration method has a slow convergence rate, and it is necessary to study methods such as relaxation factor acceleration. In addition, under the Picard iteration idea, the physical fields may have problems of excessive convergence and mutual pulling. The JFNK method has local second-order convergence and needs to rely on good initial values ​​or global convergence technology to ensure its convergence. At the same time, the establishment of the residual equation requires certain skills, and the original physical field program needs to be greatly modified. Therefore, no matter what coupling method is used, it is impossible to achieve the effect of rapid convergence while ensuring the stability of the calculation. Summary of the invention

[0005] In view of this, the present application provides a method, device, storage medium and computer equipment for numerical calculation of reactor physics and thermal engineering coupling. The main purpose is to solve the technical problem that the coupling method of multi-physical field coupling calculations such as physics and thermal engineering in the prior art is single and cannot achieve rapid convergence while ensuring calculation stability.

[0006] According to a first aspect of the present invention, a method for numerical calculation of reactor physical and thermal coupling is provided, the method comprising:

[0007] In the process of numerical calculation of reactor physics and thermal engineering coupling, the neutron space-time dynamics model is time discretized using the diagonal implicit Runge-Kutta format, and coupled calculations are performed using the simple operator splitting method and the Picard iteration method during transient analysis to obtain the calculated values;

[0008] Selecting coupled global solution variables based on Newton's method, establishing a global solution residual equation according to the coupled global solution variables, and solving the coupled global solution variables and the global solution residual equation using a Krylov subspace solution method to construct a JFNK iterative process;

[0009] The calculated value is used as an initial value, a hybrid iterative process is established according to the initial value and the JFNK iterative process, and a fully coupled numerical solution of reactor transient physical and thermal engineering is obtained by calculation.

[0010] Optionally, in the process of numerical calculation of reactor physical and thermal coupling, the neutron space-time dynamics model is time discretized using a diagonal implicit Runge-Kutta format, and coupled calculation is performed using a simple operator splitting method and a Picard iteration method during transient analysis to obtain calculated values, including:

[0011] In the numerical calculation process of reactor physics and thermal engineering coupling, the initial conditions are set and the continuous time process is defined. The neutron space-time dynamics model uses the diagonal implicit Runge-Kutta format to discretize the continuous time process into the first sub-time step and the second sub-time step.

[0012] In the first sub-time step, a physical transient calculation module is called to calculate the neutron physical field;

[0013] In the second sub-time step, based on the neutron physical field, the physical module and the thermal module are solved in turn using a simple operator splitting method, and Picard iteration is performed after the solution. After the calculation result meets the convergence standard, it is output to obtain the calculated value.

[0014] Optionally, before performing coupled calculation by simple operator splitting method and Picard iteration method in the transient analysis process, the method includes:

[0015] Based on the calculation function and calculation process, the calculation program of each physical field is split and encapsulated as a whole into a pre-processing module, a solution module and a post-processing module.

[0016] Optionally, before selecting coupled global solution variables based on Newton's method, the method includes:

[0017] Determine the basic principles for selecting coupled global solution variables, wherein the basic principles include that the coupled global solution variables are independent of each other and do not affect each other, the coupled global solution variables can directly or indirectly represent other variables in the model, and the coupled global solution variables are the smallest subset of all variables.

[0018] Optionally, the selecting coupled global solution variables based on Newton's method includes:

[0019] Determine the physical model and select the coupled global solution variables of the physical model;

[0020] Determining a thermal model, wherein the thermal model is a homogeneous flow model with a slip ratio;

[0021] Based on a preset selection strategy, coupled global solution variables of the thermal model are selected, wherein the main variables of the thermal model are mixing enthalpy, axial pressure drop, axial mass flow rate, lateral mass flow rate and lateral pressure drop.

[0022] Optionally, establishing a global solution residual equation according to the coupled global solution variable includes:

[0023] The residual equation is constructed based on mathematical preprocessing methods, or the global solution residual equation is established based on physical preprocessing methods of different physical fields.

[0024] Optionally, after the globally solving variables based on the coupling and the globally solving residual equation, the method further includes:

[0025] The inexact Newton method is used to solve the problem and the JFNK iterative process is constructed.

[0026] According to a second aspect of the present invention, there is provided a reactor physical thermal coupling numerical calculation device, the device comprising:

[0027] The module for establishing transient physical thermal iterative calculation process is used to discretize the neutron space-time dynamics model using the diagonal implicit Runge-Kutta format in the process of coupled numerical calculation of reactor physical thermal engineering, and to obtain the calculated value by coupling calculation through the simple operator splitting method and Picard iteration method in the process of transient analysis;

[0028] A JFNK iterative process establishment module is used to select coupled global solution variables based on Newton's method, establish a global solution residual equation according to the coupled global solution variables, and solve the coupled global solution variables and the global solution residual equation using a Krylov subspace solution method to construct a JFNK iterative process;

[0029] The hybrid iterative process establishment module is used to use the calculated value as the initial value, establish a hybrid iterative process according to the initial value and the JFNK iterative process, and calculate and obtain the fully coupled numerical solution of reactor transient physical and thermal engineering.

[0030] According to a third aspect of the present invention, there is provided a storage medium having a computer program stored thereon, which implements the above-mentioned reactor physical-thermal coupling numerical calculation method when the program is executed by a processor.

[0031] According to a fourth aspect of the present invention, there is provided a computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the above-mentioned reactor physical-thermal coupling numerical calculation method is implemented when the processor executes the program.

[0032] The present invention provides a reactor physics and thermal coupling numerical calculation method, device, medium and equipment. First, in the process of reactor physics and thermal coupling numerical calculation, a neutron space-time dynamics model is time discretized using a diagonal implicit Runge-Kutta format, and coupled calculation is performed by a simple operator splitting method and a Picard iteration method during transient analysis to obtain a calculated value. Then, based on the Newton method, coupled global solution variables are selected, a global solution residual equation is established according to the coupled global solution variables, and based on the coupled global solution variables and the global solution residual equation, a Krylov subspace solution method is used to solve the equation, a JFNK iterative process is constructed, and finally, the calculated value is used as an initial value, a hybrid iterative process is established according to the initial value and the JFNK iterative process, and a fully coupled numerical solution of the reactor transient physics and thermal engineering is obtained by calculation. The above method uses the coupled iteration of the simple operator splitting method and the Picard iteration method as the preprocessing process of the JFNK iterative process. It can effectively avoid the over-solving of the simple operator splitting method and the Picard iteration method and improve the convergence speed by controlling the number of iterations and the convergence accuracy. At the same time, it can provide a good preprocessing effect for the JFNK iterative process and realize a more stable and fast-converging calculation method. Combining the advantages of the simple operator splitting method, the Picard iteration method and the JFNK iterative process, it can establish a reactor steady-state physical thermal coupling according to the objective coupling law between reactor physics and thermal engineering. The nonlinear equations are solved to obtain the neutron flux, power, coolant temperature and fuel rod temperature, and the calculation method is flexible. For the accident condition coupling problem, the Picard iteration method can be used in a relatively flat time period with weak coupling to reduce the solution workload; for the strong coupling time period, the simple operator splitting method and Picard iteration method can be executed several times and then the JFNK iteration process can be used to improve the convergence and stability of the solution. The calculation process adaptively controls the iterative calculation process according to the number of iterations or convergence accuracy, effectively improving the efficiency and precision of the reactor physical and thermal coupling calculations.

[0033] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0035] Figure 1 The physical and thermal coupling process of the reactor in the prior art is shown;

[0036] Figure 2 A schematic diagram of the classification of coupling problem solving strategies in the prior art is shown;

[0037] Figure 3 A schematic flow chart of a reactor physical and thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0038] Figure 4 A flowchart of iteration based on a simple operator splitting method and a Picard iteration method in a reactor physical thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0039] Figure 5 A schematic diagram of a coupling process of iteration based on a simple operator splitting method and a Picard iteration method in a reactor physics-thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0040] Figure 6 A schematic flow chart of a physical-thermal Newton coupling residual based on physical preprocessing in a numerical calculation method for reactor physical-thermal coupling provided by an embodiment of the present invention is shown;

[0041] Figure 7 A schematic flow chart of a local elimination technology in a reactor physical thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0042] Figure 8 A schematic diagram of the calculation process of the reactor core physical thermal residual equation based on the local elimination technology and the physical preprocessing residual construction method in a reactor physical thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0043] Fig. 9 A schematic diagram of a JFNK iterative process in a reactor physics-thermal coupling numerical calculation method provided by an embodiment of the present invention is shown;

[0044] Fig.10 A mixed iterative calculation flow chart of physical-thermal coupling calculation in a numerical calculation method for reactor physical-thermal coupling provided by an embodiment of the present invention is shown;

[0045] Fig.11 A schematic diagram of the structure of a reactor physical and thermal coupling numerical calculation device provided by an embodiment of the present invention is shown;

[0046] Fig.12 A schematic diagram of the device structure of a computer device provided by an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0047] The exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present application are shown in the accompanying drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0048] The present application embodiment provides a method for numerical calculation of reactor physics and thermal engineering coupling, such as Figure 3 As shown, the method includes the following steps: first, in the process of numerical calculation of reactor physics and thermal engineering coupling, the neutron space-time dynamics model is time discretized by using the diagonal implicit Runge-Kutta format, and in the process of transient analysis, the coupling calculation is performed by the simple operator splitting method and the Picard iteration method to obtain the calculated value, and then the coupled global solution variable is selected based on the Newton method, the global solution residual equation is established according to the coupled global solution variable, and the Krylov subspace solution method is used to solve the coupled global solution variable and the global solution residual equation, and the JFNK iterative process is constructed, and finally the calculated value is used as the initial value, and a hybrid iterative process is established according to the initial value and the JFNK iterative process, and the fully coupled numerical solution of the reactor transient physics and thermal engineering is calculated.

[0049] The reactor physics and thermal engineering coupled numerical calculation method provided by the present invention uses the coupled iteration of the simple operator splitting method and the Picard iteration method as the preprocessing process of the JFNK iteration process, effectively controls the number of iterations and the convergence accuracy, can avoid the over-solving of the simple operator splitting method and the Picard iteration method, improve the convergence speed, and provide a good preprocessing effect for the JFNK iteration process, and realize a more stable and fast convergence calculation method; combining the advantages of the simple operator splitting method, the Picard iteration method and the JFNK iteration process, can establish a reactor according to the objective coupling law between the reactor physics and thermal engineering. The nonlinear equations of steady-state physical and thermal coupling are solved to obtain neutron flux, power, coolant temperature and fuel rod temperature, and the calculation method is flexible. For the coupling problem of accident conditions, the Picard iteration method can be used in a relatively flat time period with weak coupling to reduce the workload of solution; for the strong coupling time period, the simple operator splitting method and Picard iteration method can be executed several times and then the JFNK iteration process can be used to improve the convergence and stability of the solution. The calculation process adaptively controls the iterative calculation process according to the number of iterations or convergence accuracy, which effectively improves the efficiency and precision of the reactor physical and thermal coupling calculation.

[0050] Specifically, in the above embodiment, in the numerical calculation process of reactor physics and thermal engineering coupling, the neutron space-time dynamics model adopts the diagonal implicit Runge-Kutta format to discretize time, and in the transient analysis process, the coupled calculation is performed by the simple operator splitting method and the Picard iteration method to obtain the calculated value, including firstly setting the initial conditions and defining the continuous time process in the numerical calculation process of reactor physics and thermal engineering coupling, and the neutron space-time dynamics model adopts the diagonal implicit Runge-Kutta format to discretize the continuous time process into the first sub-time step and the second sub-time step; then, in the first sub-time step, the physical transient calculation module is called to calculate the neutron physical field; finally, in the second sub-time step, based on the neutron physical field, the simple operator splitting method is used to solve the physical module and the thermal module in turn, and the Picard iteration is performed after the solution, and the calculation result is output after the convergence criterion is met to obtain the calculated value.

[0051] In reactor transient analysis, the operator splitting method is a commonly used numerical technique for decomposing complex multi-physics field problems into multiple simpler sub-problems and solving them in sequence. There are many variants according to different implementation methods. Specifically, the simple operator splitting method (OS) and the operator splitting semi-implicit method (OS) are applied in this application. Semi-Implicit (OSSI), the simple operator splitting method is a basic operator splitting method, which decomposes the entire system into multiple subsystems and solves each subsystem in turn. In each time step, one physical field (such as neutron dynamics) is first solved separately, and then the result of this physical field is used as input to solve another physical field (such as thermal hydraulics). The whole process is repeated until convergence is reached or all time steps are completed; the operator splitting semi-implicit method is an improved operator splitting method, which uses implicit methods when dealing with certain physical fields to improve stability and convergence. Specifically, in each time step, an explicit method is first used to solve one physical field (such as neutron dynamics), and then an implicit method is used to solve another physical field (such as thermal hydraulics). The implicit method can better handle nonlinear effects and strong coupling situations; the Picard iteration method, also known as the simple iteration method or the successive approximation method, is an iterative method for solving nonlinear equations. It approximates the true solution of the equations by gradually improving the initial guess; the diagonally implicit Runge-Kutta format (Diagonally Implicit Runge-Kutta format) The DIRK method combines the advantages of the explicit and implicit Runge-Kutta methods and improves stability and accuracy by partially implicitizing them.

[0052] First, the application background of this application is introduced. The coupling program of the simple operator splitting method of core physics and thermal engineering and the Picard iteration method is used for transient analysis. The physical module needs to provide the thermal module with the heat release rate of the fuel elements, and the thermal module needs to provide the physical module with parameters such as fuel and coolant temperature to update the cross-section. On the one hand, the grid divisions between modules are inconsistent, and the transmitted data needs to be spatially grid-correlated. On the other hand, the time discretization methods and step sizes between modules are inconsistent, and the time synchronization of the physical module and the thermal module needs to be coordinated.

[0053] In this embodiment, the neutron space-time dynamics model of the physics specialty of the present invention adopts the diagonal implicit Runge-Kutta format (DIRK) in the time discrete format, which is divided into two sub-time steps in the transient coupling iteration. For the first sub-time step, only the physical transient calculation module needs to be called to calculate the neutron physical field, while in the second sub-time step, the physical thermal engineering needs to be called to couple based on the simple operator splitting method and the Picard iteration method. The overall calculation process is as follows: Figure 4 As shown, in the first sub-time step, first prepare the relevant parameters of this stage, update the control rod position based on this, then update the cross section, and use the source iteration method to calculate the transient neutron diffusion equation to update the precursor nuclear concentration, and then calculate the power distribution, and finally calculate the thermal parameters of the transient model. In the second sub-time step, based on the simple operator splitting method, determine whether repeated iterations are required. If not, it is necessary to determine whether all levels are solved. If required, confirm whether iterative convergence is required. If not, determine whether the maximum number of iterations is reached based on the operator splitting semi-implicit method. If not, return to the step of updating the cross section. If it has been reached, it is necessary to determine whether all levels are solved. After reaching iterative convergence, it is necessary to determine whether the convergence standard is met based on the Picard iteration method. If not, it is also necessary to re-update the cross section. If the convergence standard is met, it is necessary to determine whether all levels are solved. If all levels are not solved, prepare the relevant parameters of this level again. If all levels are solved, calculate the relevant parameters according to the results of each DIRK level.

[0054] Specifically, in the above embodiment, before performing coupling calculations through simple operator splitting method and Picard iteration method during transient analysis, the method includes splitting and encapsulating the calculation programs of each physical field as a whole into a pre-processing module, a solution module and a post-processing module based on the calculation function and calculation process.

[0055] In this embodiment, in order to realize the simple operator splitting method and Picard iteration method, it is necessary to perform good code splitting, encapsulation and process control on the original programs of each physical field of physical thermal engineering. The calculation program of each physical field can be split and encapsulated into three parts from the calculation function and calculation process: pre-processing module, solution module, and post-processing module. Among them, the pre-processing module usually encapsulates the pre-processing functions such as input card reading and writing, data initialization of the existing program framework, such as input card reading of neutron physical field program, calculation of geometric structure data and application and initialization of related data memory. This module usually only needs to be solved once in the coupling calculation. By splitting and encapsulating the pre-processing modules of each existing program, it will be helpful to avoid repeated calculations and avoid logical errors that may be caused by initialization in the coupling process; the post-processing module usually encapsulates the post-processing process of the existing program, mainly including the output and post-processing functions of the original program framework, such as the output confirmation of the neutron physical field program, the output of the final calculation results, and the visualization process of the program calculation results. This module is usually only required once in the process of physical field calculation or coupling solution. As the key to coupling packaging, the core solution module is the solution module of each physical field equation, such as the source iteration solution module of the neutron physical field calculation program. After splitting and packaging, according to Figure 4 The iterative flow chart of the simple operator splitting method and Picard iteration method is used to build the physical thermal coupling calculation module, such as Figure 5 As shown, in order to ensure the stability and convergence of the Picard iterative method coupling solution, an adaptive relaxation factor method is used to improve it.

[0056] Specifically, in the above embodiment, before selecting coupled global solution variables based on Newton's method, the method includes determining the basic principles for selecting coupled global solution variables, wherein the basic principles include that the coupled global solution variables are independent of each other and do not affect each other, the coupled global solution variables can directly or indirectly represent other variables in the model, and the coupled global solution variables are the smallest subset of all variables.

[0057] Among them, Newton's method is a powerful numerical method for solving nonlinear equations. It approximates the solution of the nonlinear equations through local linearization and has a quadratic convergence rate near the solution, and can converge to the exact solution very quickly.

[0058] In this embodiment, the global convergence solution of multi-physical field coupling is achieved based on Newton's method. The core task is to establish the residual equation corresponding to the coupled global solution variable, and the core of the residual system construction is to first select the coupled global solution variable for which the residual needs to be established. The selection of coupled global solution variables follows three principles: first, the coupled global solution variables are independent of each other and do not affect each other; second, other variables in the model can be directly or indirectly expressed by coupled global solution variables; third, the coupled global solution variables should be the smallest subset of all variables to ensure global convergence while minimizing the number of variables.

[0059] Specifically, in the above embodiment, the coupled global solution variables are selected based on Newton's method, including determining the physical model and selecting the coupled global solution variables of the physical model; determining the thermal model, wherein the thermal model is a homogeneous flow model with a slip ratio; based on a preset selection strategy, the coupled global solution variables of the thermal model are selected, wherein the main variables of the thermal model are mixing enthalpy, axial pressure drop, axial mass flow rate, lateral mass flow rate and lateral pressure drop.

[0060] In this embodiment, the coupled global solution variables of the physical model are first selected. The physical program uses the second-kind boundary condition block Green's function method to solve the three-dimensional space-time dynamics calculation model of the neutron diffusion equation. The core idea is to transform the three-dimensional neutron diffusion equation into three mutually coupled one-dimensional transverse integral equations through transverse integration, and solve the transverse integral equations in each direction separately through the second-kind boundary condition Green's function method, and then obtain the interface flow in each direction, and then the block average flux and keff can be obtained.

[0061] Specifically, the node balance equation is:

[0062]

[0063]

[0064] in, is the average neutron flux of the g-th group in node k, is the average source term, and the transverse integral equations in the three coordinate directions can be expressed as:

[0065]

[0066] in, is the partial neutron flux density in the u direction, which means the average value of the neutron flux density in the node in the direction perpendicular to u. It represents the neutron leakage rate of the node in the other two directions in the selected direction. Similarly, the one-dimensional partial neutron flux equations in the v and w directions can be obtained. These three one-dimensional partial neutron flux equations are coupled together through the transverse leakage term. The nodal Green's function method is based on the nodal method. By introducing the Green's function with certain boundary conditions, the equations are integrated term by term to obtain the neutron flux in the node and the net neutron flow on the surface of the node. Combined with the continuity conditions of the net flow and flux (including the discontinuity factor), the net neutron flow coupling equations of three adjacent nodes (k-1, k, k+1) can be established:

[0067]

[0068]

[0069] Among them, J gu is the net neutron flux on the node surface, is the block length, is the block discontinuity factor, and is the specific coefficient expression, is the Green function, The corresponding source term moment can be obtained by applying the Legendre orthogonal polynomial P to the transverse integral partial flux n Expand, and solve the value of each expansion coefficient through weighted integral and other ideas to get The corresponding source moment.

[0070]

[0071] Through a detailed analysis of the physical solution process, we can see that the key parameters for solving the equations mainly include the expansion coefficient of the source term, the net neutron flow of the block, the partial flux expansion coefficient (the 0th order term is the average neutron flux), the leakage term expansion coefficient, and the effective multiplication factor. There are terms that can be eliminated in these parameters. The expansion coefficient of the source term is calculated by the partial flux expansion coefficient, and the leakage term expansion coefficient is obtained by solving the net neutron flow. The 0th order partial flux expansion coefficient in each direction is actually the average neutron flux. The above parameters can be eliminated and removed from the variables for solving the residual equation to reduce the scale of JFNK solution. Therefore, based on the above analysis, the global main variables of the Newton method based on the block Green's function are selected as follows:

[0072]

[0073] Then the coupled global solution variables of the thermal model are selected. The thermal program adopts a homogeneous flow model with a slip ratio, which consists of a mixed continuity equation, a mixed momentum equation, and a mixed energy equation. The liquid phase energy equation determines the boiling condition. The subscript i represents the channel number, and the subscript j represents the axial layer number. The basic form of the conservation equation based on axial one-dimensional flow is as follows:

[0074] 1. Mixed continuity equation:

[0075]

[0076] The left term of the above equation is the mass change rate in the control body; the first term on the right is the mass change in and out of the control body in the axial direction; the second term on the right is the mass change in and out of the control body due to the influence of the lateral pressure difference in the lateral direction. Since the thermal model uses an equal mass mixing model in turbulent mixing, the continuity equation does not reflect the mass change of the control body caused by turbulent mixing. In the above equation, ρ (i) is the density, G (i) is the axial mass flow rate; g ik is the lateral mass flow rate; l ik is the distance between adjacent coupling channels; S (i) is the cross-sectional area of ​​the channel.

[0077] 2. Hybrid energy equation:

[0078]

[0079] The first term on the left side of the above formula is the rate of change of mixing enthalpy in the control body; the second term on the left side is the change of mixing enthalpy in and out of the control body in the axial direction; the third term on the left side is the change of mixing enthalpy in and out of the control body due to the influence of turbulent mixing; the fourth term on the left side is the change of mixing enthalpy in and out of the control body due to the influence of lateral mixing; the fifth term on the left side is the heat entering and exiting the control body through the guide tube wall when the research object is in the guide tube; the term on the right side is the nuclear heat source term, in the above formula, H i is the mixing enthalpy; k tik is the turbulent diffusion coefficient of the transverse flow; L ik is the distance between the centroids of adjacent coupling channels; H ik is the mixing enthalpy at the interface of the two coupled channels; l pik The distance from the center of mass of the fluid channel outside the guide tube to the wall of the guide tube; is the heat transfer coefficient; T p is the wall temperature; T l is the fluid temperature; φ i Heat flux on fuel rod surface; q i is the heat flux released directly into the fluid by radiation.

[0080] 3. Liquid phase energy equation:

[0081]

[0082] The liquid phase energy equation is based on the mixed energy equation and multiplies some terms by corresponding coefficients, such as (1-α i )、(1-x i ) and (1-x ci ). i is the empty package share; x i is the gas content; x ci The convective heat flux heats the gas phase. The other variables have the same meaning as in the mixed energy equation.

[0083] 4. Mixed axial momentum equation:

[0084]

[0085]

[0086] The left term of the above formula is the axial pressure difference of the control body; the first term on the right is the rate of change of axial momentum in the control body; the second term on the right is the gravity term; the third term on the right is the change of axial momentum in and out of the control body in the axial direction; the fourth term on the right is the change of axial momentum in and out of the control body due to the influence of lateral mixing; the fifth term on the right is the friction term; the sixth term on the right is the change of axial momentum in and out of the control body due to the influence of turbulent mixing. In the above formula, P i is the axial pressure; v′ i Momentum transport effective specific volume; v′ ik is the effective specific volume of momentum transport on the coupling channel interface; G ik is the axial mass flow rate on the coupling channel interface;

[0087] 5. Mixed lateral momentum equation:

[0088]

[0089] The left term of the above formula is the lateral pressure difference term; the first term on the right is the rate of change of lateral momentum in the control body; the second term on the right is the friction term during lateral mixing; the third term on the right is the gradient of lateral momentum in the lateral direction; and the fourth term on the right is the gradient of lateral momentum in the axial direction. ik is the lateral pressure; f ik is the lateral friction coefficient; for The average quantity on the coupling channel interface, combined with the main vector selection strategy, the main variables of the thermal model are determined as mixing enthalpy H, axial pressure drop dp, axial mass flow rate G, and transverse mass flow rate g. ik and lateral pressure drop dp ik .

[0090] Among them, the global main variable of the Newton method based on the nodal Green's function is the net neutron flux J on the nodal surface. gu , nodal neutron partial flux expansion coefficient The thermal program uses a homogeneous flow model with a slip ratio, and the main variables are set as mixing enthalpy H, axial pressure drop dp, axial mass flow rate G, and transverse mass flow rate g. ik and lateral pressure drop dp ik The coupled system residual construction can be expressed as:

[0091]

[0092] Specifically, in the above embodiments, a global solution residual equation is established based on coupled global solution variables, including constructing a residual equation based on a mathematical preprocessing method, or establishing a global solution residual equation based on a physical preprocessing method of different physical fields.

[0093] In this embodiment, the key to the implementation of the Newton coupling method is the construction of the Newton coupling residual equation, which mainly includes the following two construction ideas: residual equation construction based on mathematical preprocessing and physical preprocessing residual equation construction based on existing physical field / subsystem programs.

[0094] Specifically, the residual equation construction based on mathematical preprocessing is aimed at the physical field control equations and discrete variables that need to be studied. Through research, a residual equation that can correctly express this physical field and solve efficiently is constructed. For example, for discrete variables such as pressure, gas / liquid phase velocity, and cavitation fraction in the reactor two-phase flow control model, the corresponding residual equation is established. The established residual equation can be generally written as:

[0095]

[0096] in, for The coefficient matrix of is a discrete variable that can represent the entire physical field or system. is a known item;

[0097] When constructing the residual equation and solving it using the NK / JFNK method, a preprocessing method is usually required. The specific form of NK / JFNK preprocessing is as follows:

[0098]

[0099] Secondly, based on the physical preprocessing residual equation construction of different physical fields / subroutines, the key to the physical preprocessing idea is to regard the product of the inverse of the preprocessing matrix and the subspace vector as the research whole, so as to implicitly achieve the preprocessing effect. For a nonlinear equation system as shown in the following formula:

[0100]

[0101] Decomposing the coefficient matrix A yields the following formula:

[0102]

[0103] And the nonlinear equations can be transformed into the following formula:

[0104]

[0105] The converted formula can be regarded as the calculation process of the existing calculation model / subroutine, and the following formula is true:

[0106]

[0107] Multiply both sides of the equation by [M] -1 You can get the formula:

[0108]

[0109] in, out That is, the original calculation model / subroutine is Output when

[0110] The equation for Jacobian Free technology is converted to the following:

[0111]

[0112] Therefore, the Newton residual equation established by the physical thermal coupling of this application based on the physical preprocessing method can be expressed as follows:

[0113]

[0114] Among them, h k Indicates the enthalpy of the coolant, Tfm k represents the fuel temperature of the fuel rod, and the Newton coupled residual equation construction flow chart based on the physical preprocessing method can be expressed as Figure 6 In order to improve the development speed and accelerate engineering application, this application adopts a local elimination method, which is based on the coupling characteristics and equivalent relations between different physical fields to simplify the process of selecting global variable residuals, and establish a Newton coupling residual system based on the corrected global residuals, such as Figure 7 shown; Figure 8 The core physical and thermal residuals of the reactor core physical and thermal coupling based on the local elimination technology + physical preprocessing residual construction method are given.

[0115] Specifically, in the above embodiment, after globally solving the variables and globally solving the residual equation based on coupling, the method further includes solving using the inexact Newton method to construct a JFNK iterative process.

[0116] Among them, the JFNK (Jacobian-Free Newton-Krylov) method is a technology that combines the matrix-free form of the Newton method and the Krylov subspace method. It is particularly suitable for solving large-scale nonlinear equations and is very effective in dealing with complex multi-physics field coupling problems. It avoids explicit calculation and storage of the Jacobian matrix, thereby greatly reducing memory requirements and computational costs.

[0117] In this embodiment, the basic flow chart of the JFNK iteration process is as follows: Fig. 9 As shown in the figure, based on the global solution variable selection and residual equation construction in the previous steps, the Krylov subspace solution method, including GMRES(m) and BICGTAB, and the preprocessing method are used to solve and realize the Newton calculation process, as shown in the following table.

[0118]

[0119] Among them, you can also choose to use the inexact Newton method, which not only reduces the calculation amount of the exact Newton method, but also effectively maintains the local second-order convergence characteristics of the original exact Newton method, called η k is the mandatory item for the k-th iteration, For an inexact Newton step, the following is called the inexact Newton condition:

[0120]

[0121] In each iteration of the inexact Newton method, the Newton equation is solved inexactly. It is both a local linear model and the residual of the Newton equation, η k The size of is essentially the accuracy of solving Newton's equation. If all the η k =0, it is the exact Newton method.

[0122] Specifically, in the above embodiment, the calculated value is used as the initial value, a hybrid iterative process is established according to the initial value and the JFNK iterative process, and a fully coupled numerical solution of reactor transient physical and thermal engineering is calculated.

[0123] In this embodiment, according to the simple operator splitting method and Picard iteration method and the JFNK iteration process in the preamble, the calculated values ​​based on the simple operator splitting method and Picard iteration method are used to provide a good initial value selection for JFNK and establish a hybrid iteration process. The specific calculation process is as follows: Fig.10 During the coupling calculation, according to the input setting of the iterative algorithm related options, the program determines the selection of the adaptive control iterative algorithm based on the calculated number of iterations or convergence accuracy. For the accident condition coupling problem, the Picard iteration method can be used for coupling in a relatively flat time period with weak coupling to reduce the workload of solving. For the strong coupling time period, several iterations based on the simple operator splitting method and the Picard iteration method can be performed and then the JFNK coupling method can be used to improve the convergence and stability of the solution.

[0124] In particular, the convergence accuracy control uses scaling technology, which is essentially a preprocessing. For example, the following formula will be better than the original equation in terms of condition number and eigenvalue distribution:

[0125]

[0126] In program development, scaling technology can also be used implicitly. For example, in thermal flow field calculations, the pressure field (pressure difference) is usually in the order of 105-106Pa, and the temperature field is usually in the order of 102-103℃. Different orders of magnitude may lead to problems such as too many equation conditions, ill-conditioned linear equations, poor convergence of coupled iterations, and slow solutions in solving thermal flow field equations. In the program, using relative pressure or MPa as the pressure unit can improve the situation, which is equivalent to the scaling technology shown in the following formula:

[0127]

[0128] Further, as Figure 1 The specific implementation of the method, the embodiment of the present application provides a reactor physical thermal coupling numerical calculation device, such as Fig.11 As shown, the device includes: a transient physical thermal iterative calculation process establishment module, a JFNK iterative process establishment module and a mixed iterative process establishment module.

[0129] The module for establishing transient physical thermal iterative calculation process is used to discretize the neutron space-time dynamics model using the diagonal implicit Runge-Kutta format in the process of coupled numerical calculation of reactor physical thermal engineering, and to obtain the calculated value by coupling calculation through the simple operator splitting method and Picard iteration method in the process of transient analysis;

[0130] A JFNK iterative process establishment module is used to select coupled global solution variables based on the Newton method, establish a global solution residual equation based on the coupled global solution variables, and solve the coupled global solution variables and the global solution residual equation using the Krylov subspace solution method to build a JFNK iterative process;

[0131] The hybrid iterative process establishment module is used to take the calculated value as the initial value, establish the hybrid iterative process according to the initial value and the JFNK iterative process, and calculate the fully coupled numerical solution of reactor transient physics and thermal engineering.

[0132] In specific application scenarios, the transient physical thermal iterative calculation process establishment module can be used to set initial conditions and define continuous time processes in the reactor physical thermal coupling numerical calculation process. The neutron space-time dynamics model uses the diagonal implicit Runge-Kutta format to discretize the continuous time process into the first sub-time step and the second sub-time step.

[0133] In the first sub-time step, the physical transient calculation module is called to calculate the neutron physical field;

[0134] In the second sub-time step, based on the neutron physics field, the simple operator splitting method is used to solve the physical module and the thermal module in turn, and Picard iteration is performed after the solution. After the calculation results meet the convergence criteria, they are output to obtain the calculated values.

[0135] In specific application scenarios, the transient physics thermal iterative calculation process establishment module can also be used to split and encapsulate the calculation programs of various physical fields into pre-processing modules, solution modules and post-processing modules based on the calculation functions and calculation processes.

[0136] In specific application scenarios, the JFNK iterative process establishment module can be used to determine the basic principles for selecting coupled global solution variables, where the basic principles include that the coupled global solution variables are independent of each other and do not affect each other, the coupled global solution variables can directly or indirectly represent other variables in the model, and the coupled global solution variables are the smallest subset of all variables.

[0137] In specific application scenarios, the JFNK iterative process building module can be used to determine the physical model and select the coupled global solution variables of the physical model;

[0138] Determine a thermal model, wherein the thermal model is a homogeneous flow model with a slip ratio;

[0139] Based on the preset selection strategy, the coupled global solution variables of the thermal model are selected, where the main variables of the thermal model are mixing enthalpy, axial pressure drop, axial mass flow rate, lateral mass flow rate, and lateral pressure drop.

[0140] In specific application scenarios, the JFNK iterative process establishment module can be used to construct residual equations based on mathematical preprocessing methods, or to establish global solutions to residual equations based on physical preprocessing methods of different physical fields.

[0141] In specific application scenarios, the JFNK iterative process building module can also be used to solve using the inexact Newton method and build a JFNK iterative process.

[0142] It should be noted that for other corresponding descriptions of the functional units involved in the reactor physics and thermal engineering coupling numerical calculation device provided in this embodiment, reference can be made to Figure 1 The corresponding description in will not be repeated here.

[0143] Based on the above Figure 1 The method shown, accordingly, this embodiment also provides a storage medium, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned reactor physical thermal coupling numerical calculation method is implemented.

[0144] Based on this understanding, the technical solution of the present application can be embodied in the form of a software product. The software product to be identified can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), including a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the numerical calculation method of reactor physics and thermal engineering coupling in various implementation scenarios of the present application.

[0145] Based on the above Figure 1 The method shown, and Fig.11 In order to achieve the above-mentioned purpose, the reactor physics and thermal engineering coupling numerical calculation device embodiment shown in the figure is as follows: Fig.12 As shown, this embodiment also provides a physical device for numerical calculation of reactor physical thermal coupling, which includes a communication bus, a processor, a memory and a communication interface, and may also include an input and output interface and a display device, wherein each functional unit can communicate with each other through the bus. The memory stores a computer program, and the processor is used to execute the program stored in the memory and execute the numerical calculation method of reactor physical thermal coupling in the above embodiment.

[0146] Optionally, the physical device may also include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a WI-FI module, etc. The user interface may include a display, an input unit such as a keyboard, etc., and the optional user interface may also include a USB interface, a card reader interface, etc. The network interface may optionally include a standard wired interface, a wireless interface (such as a WI-FI interface), etc.

[0147] Those skilled in the art will appreciate that the reactor physics-thermal coupling numerical calculation entity device structure provided in this embodiment does not constitute a limitation on the entity device, and may include more or fewer components, or a combination of certain components, or different component arrangements.

[0148] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware of the physical device and the software resources to be identified, and supports the operation of the information processing program and other software and / or programs to be identified. The network communication module is used to realize the communication between the components inside the storage medium, and the communication with other hardware and software in the information processing physical device.

[0149] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary general hardware platforms, or by hardware. By applying the technical solution of the present application, first in the process of numerical calculation of reactor physics and thermal engineering coupling, the neutron space-time dynamics model adopts the diagonal implicit Runge-Kutta format for time discretization, and in the transient analysis process, the coupling calculation is performed by the simple operator splitting method and the Picard iteration method to obtain the calculated value, and then the coupled global solution variable is selected based on the Newton method, and the global solution residual equation is established according to the coupled global solution variable, and based on the coupled global solution variable and the global solution residual equation, the Krylov subspace solution method is used to solve, and the JFNK iterative process is constructed, and finally the calculated value is used as the initial value, and a mixed iterative process is established according to the initial value and the JFNK iterative process, and the reactor transient physics thermal engineering fully coupled numerical solution is calculated. The above method uses the coupled iteration of the simple operator splitting method and the Picard iteration method as the preprocessing process of the JFNK iterative process. It can effectively avoid the over-solving of the simple operator splitting method and the Picard iteration method and improve the convergence speed by controlling the number of iterations and the convergence accuracy. At the same time, it can provide a good preprocessing effect for the JFNK iterative process and realize a more stable and fast-converging calculation method. Combining the advantages of the simple operator splitting method, the Picard iteration method and the JFNK iterative process, it can establish a reactor steady-state physical thermal coupling according to the objective coupling law between reactor physics and thermal engineering. The nonlinear equations are solved to obtain the neutron flux, power, coolant temperature and fuel rod temperature, and the calculation method is flexible. For the accident condition coupling problem, the Picard iteration method can be used in a relatively flat time period with weak coupling to reduce the solution workload; for the strong coupling time period, the simple operator splitting method and Picard iteration method can be executed several times and then the JFNK iteration process can be used to improve the convergence and stability of the solution. The calculation process adaptively controls the iterative calculation process according to the number of iterations or convergence accuracy, effectively improving the efficiency and precision of the reactor physical and thermal coupling calculations.

[0150] Those skilled in the art will appreciate that the accompanying drawings are only schematic diagrams of a preferred implementation scenario, and the modules or processes in the accompanying drawings are not necessarily necessary for implementing the present application. Those skilled in the art will appreciate that the modules in the devices in the implementation scenario can be distributed in the devices of the implementation scenario according to the description of the implementation scenario, or can be changed accordingly and located in one or more devices different from the present implementation scenario. The modules of the above-mentioned implementation scenario can be combined into one module, or can be further split into multiple submodules.

[0151] The above serial numbers of this application are only for description and do not represent the advantages and disadvantages of the implementation scenarios. The above disclosure is only a few specific implementation scenarios of this application, but this application is not limited to them, and any changes that can be thought of by technicians in this field should fall within the scope of protection of this application.

Claims

1. A reactor physics-thermal coupling numerical calculation method, characterized in that: The method comprises: In the process of numerical calculation of reactor physics and thermal engineering coupling, the neutron space-time dynamics model is time discretized using the diagonal implicit Runge-Kutta format, and coupled calculations are performed using the simple operator splitting method and the Picard iteration method during transient analysis to obtain the calculated values; Selecting coupled global solution variables based on Newton's method, establishing a global solution residual equation according to the coupled global solution variables, and solving the coupled global solution variables and the global solution residual equation using a Krylov subspace solution method to construct a JFNK iterative process; The calculated value is used as an initial value, a hybrid iterative process is established according to the initial value and the JFNK iterative process, and a fully coupled numerical solution of reactor transient physical and thermal engineering is obtained by calculation.

2. The method according to claim 1, characterized in that In the process of numerical calculation of reactor physical and thermal coupling, the neutron space-time dynamics model adopts the diagonal implicit Runge-Kutta format for time discretization, and in the transient analysis process, the simple operator splitting method and the Picard iteration method are used for coupling calculation to obtain the calculated values, including: In the numerical calculation process of reactor physics and thermal engineering coupling, the initial conditions are set and the continuous time process is defined. The neutron space-time dynamics model uses the diagonal implicit Runge-Kutta format to discretize the continuous time process into the first sub-time step and the second sub-time step. In the first sub-time step, a physical transient calculation module is called to calculate the neutron physical field; In the second sub-time step, based on the neutron physical field, the physical module and the thermal module are solved in turn using a simple operator splitting method, and Picard iteration is performed after the solution. After the calculation result meets the convergence standard, it is output to obtain the calculated value.

3. The method according to claim 1, characterized in that Before performing coupled calculations by simple operator splitting method and Picard iteration method in the transient analysis process, the method includes: Based on the calculation function and calculation process, the calculation program of each physical field is split and encapsulated as a whole into a pre-processing module, a solution module and a post-processing module.

4. The method according to claim 1, characterized in that: Before selecting coupled global solution variables based on Newton's method, the method includes: Determine the basic principles for selecting coupled global solution variables, wherein the basic principles include that the coupled global solution variables are independent of each other and do not affect each other, the coupled global solution variables can directly or indirectly represent other variables in the model, and the coupled global solution variables are the smallest subset of all variables.

5. The method according to claim 1, characterized in that The method of selecting coupled global solution variables based on Newton's method includes: Determine the physical model and select the coupled global solution variables of the physical model; Determining a thermal model, wherein the thermal model is a homogeneous flow model with a slip ratio; Based on a preset selection strategy, coupled global solution variables of the thermal model are selected, wherein the main variables of the thermal model are mixing enthalpy, axial pressure drop, axial mass flow rate, lateral mass flow rate and lateral pressure drop.

6. The method according to claim 1, characterized in that The step of establishing a global solution residual equation according to the coupled global solution variable comprises: The residual equation is constructed based on mathematical preprocessing methods, or the global solution residual equation is established based on physical preprocessing methods of different physical fields.

7. The method according to claim 1, characterized in that After the globally solving variables and the globally solving residual equation based on the coupling, the method further comprises: The inexact Newton method is used to solve the problem and the JFNK iterative process is constructed.

8. A reactor physical thermal coupling numerical calculation device, characterized in that: The device comprises: The module for establishing transient physical thermal iterative calculation process is used to discretize the neutron space-time dynamics model using the diagonal implicit Runge-Kutta format in the process of coupled numerical calculation of reactor physical thermal engineering, and to obtain the calculated value by coupling calculation through the simple operator splitting method and Picard iteration method in the process of transient analysis; A JFNK iterative process establishment module is used to select coupled global solution variables based on Newton's method, establish a global solution residual equation according to the coupled global solution variables, and solve the coupled global solution variables and the global solution residual equation using a Krylov subspace solution method to construct a JFNK iterative process; The hybrid iterative process establishment module is used to use the calculated value as the initial value, establish a hybrid iterative process according to the initial value and the JFNK iterative process, and calculate and obtain the fully coupled numerical solution of reactor transient physical and thermal engineering.

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

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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