Method and apparatus for reactor core flow and heat transfer analysis

Abstract

The application provides a reactor core flow heat transfer analysis method and device, and relates to the technical field of nuclear power. The method comprises the following steps: obtaining a reduced order model corresponding to a reactor core, wherein the reduced order model is obtained by using a snapshot set, and the snapshot set is used to represent the flow heat transfer state of the reactor core under different working conditions; obtaining first information of the reactor core; inputting the first information into the reduced order model to obtain second information of the reactor core at each time step; inputting the second information of the reactor core at each time step into a POD basis function application equation respectively to obtain flow heat transfer analysis results of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow heat transfer analysis results comprise solutions of velocity, pressure, internal energy, turbulent flow fluctuation and dissipation rate. The application improves the calculation efficiency of flow heat transfer analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical simulation, in particular to a reactor core flow and heat transfer analysis method and device. BACKGROUND

[0002] As one of the most widely used nuclear power reactor types in the world, pressurized water reactor (PWR) plays an important role in energy supply, greenhouse gas emission reduction, and national energy security. The flow and heat transfer characteristics of the reactor core are closely related to the performance and safety of the reactor.

[0003] Traditional PWR core flow and heat transfer simulation mostly uses numerical methods based on detailed physical models, such as computational fluid dynamics (CFD) methods. However, such methods can obtain relatively accurate results, but face high computational cost. Especially for full-size PWR cores, the calculation time may be as long as several months or even years, and the calculation cost is very high, which is difficult to meet the needs of rapid analysis and optimization in actual engineering applications. SUMMARY

[0004] The purpose of the embodiments of the present application is to provide a reactor core flow and heat transfer analysis method and device, so that the calculation efficiency of reactor flow and heat transfer calculation in terms of computing resources is improved.

[0005] In a first aspect, the embodiments of the present application provide a reactor core flow and heat transfer analysis method, which comprises:

[0006] Obtaining a reduced-order model corresponding to the reactor core, wherein the reduced-order model is constructed using a snapshot set, and the snapshot set is used to represent the flow and heat transfer state of the reactor core under different operating conditions;

[0007] Obtaining first information of the reactor core, wherein the first information includes initial velocity coefficient, initial pressure coefficient, initial internal energy coefficient, initial turbulent fluctuation coefficient, and initial dissipation rate coefficient;

[0008] Inputting the first information into the reduced-order model to obtain second information of the reactor core at each time step, wherein the second information includes target velocity coefficient, target pressure coefficient, target internal energy coefficient, target turbulent fluctuation coefficient, and target dissipation rate coefficient;

[0009] Inputting the second information of the reactor core at each time step into a POD basis function application equation respectively to obtain flow and heat transfer analysis results of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis results include solutions of velocity, pressure, internal energy, turbulent fluctuation, and dissipation rate.

[0010] In some embodiments, the step of obtaining the reduced-order model corresponding to the reactor core comprises:

[0011] obtaining the snapshot set;

[0012] constructing a POD basis function and obtaining a POD basis function application equation using the snapshot set and a truncated singular value decomposition method;

[0013] performing a reduced-order processing on the POD basis function application equation to obtain a reduced-order operator;

[0014] obtaining a radial basis function interpolation, the radial basis function interpolation being obtained by using a radial basis function to fit an interpolation domain by known data points;

[0015] constructing the reduced-order model using the radial basis function interpolation and the reduced-order operator.

[0016] In some embodiments, the step of obtaining the radial basis function interpolation comprises:

[0017] determining a radial basis function;

[0018] determining a weight coefficient vector of the radial basis function according to a matrix composed of function values of the radial basis function and a vector composed of known data points, the known data points being data points in the snapshot set;

[0019] determining the radial basis function interpolation according to the radial basis function and the weight coefficient vector.

[0020] In some embodiments, the step of performing a reduced-order processing on the POD basis function application equation to obtain a reduced-order operator comprises:

[0021] projecting the POD basis function application equation to obtain a projected equation of the POD basis function application equation;

[0022] solving the projected equation of the POD basis function application equation using an eigen-orthogonal decomposition method to obtain a reduced-order operator.

[0023] In some embodiments, the step of obtaining the snapshot set comprises:

[0024] obtaining a porous medium related equation of the reactor core, the porous medium related equation being used to determine a flow and heat transfer state of the reactor core;

[0025] inputting a boundary condition of the reactor core into the porous medium related equation;

[0026] discretizing the porous medium related equation input with the boundary condition to obtain a full-order model;

[0027] solving the full order model to obtain the snapshot set.

[0028] In some embodiments, the step of obtaining the porous media related equations of the reactor core comprises:

[0029] obtaining a flow model, a conjugate heat transfer model and a turbulence model of the reactor core;

[0030] obtaining a source term of the porous media, updating the flow model according to the source term to obtain an updated flow model;

[0031] obtaining an updated conjugate heat transfer model according to the porous media and the conjugate heat transfer model;

[0032] wherein the porous media related equations comprise the updated flow model, the updated conjugate heat transfer model and the turbulence model.

[0033] In some embodiments, the reduced order model comprises the following equations:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] , , , and wherein (φn) represents the POD coefficients at time step n; , , , , and represent the solution fields v, p, E, the POD coefficients of the set at time step n-1 (φn-1) ; and ; represents the number of time steps in the calculation simulation; represents a radial basis function whose value depends on the distance from the data set point (φn-1) ; ; and represent the weight coefficients (wherein ), where M represents the number of POD basis functions.

[0040] In a second aspect, an embodiment of the present application provides a reactor core flow and heat transfer analysis device, the device comprising:

[0041] an obtaining model module configured to obtain a reduced order model corresponding to the reactor core, wherein the reduced order model is constructed by using a snapshot set, and the snapshot set is used to represent flow and heat transfer states of the reactor core under different working conditions;

[0042] an obtaining information module configured to obtain first information of the reactor core, wherein the first information comprises an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent fluctuation coefficient, and an initial dissipation rate coefficient;

[0043] a result obtaining module configured to input the first information into the reduced order model to obtain second information of the reactor core at each time step, wherein the second information comprises a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent fluctuation coefficient, and a target dissipation rate coefficient;

[0044] a result obtaining module configured to input the first information into the reduced order model to obtain second information of the reactor core at each time step, wherein the second information comprises a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent fluctuation coefficient, and a target dissipation rate coefficient;

[0045] In a third aspect, an embodiment of the present application provides an electronic device, comprising:

[0046] a memory configured to store instructions; and

[0047] a processor configured to call the instructions from the memory and implement the reactor core flow and heat transfer analysis method provided in the first aspect of the present application when the instructions are executed.

[0048] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, the computer readable storage medium storing instructions, and the instructions are executed by a processor to implement the method in the first aspect.

[0049] In the embodiment of the present application, a reduced order model corresponding to the reactor core is obtained, wherein the reduced order model is constructed by using a snapshot set, and the snapshot set is used to represent the flow and heat transfer state of the reactor core under different working conditions. Secondly, the first information of the reactor core is obtained, wherein the first information includes the initial velocity coefficient, the initial pressure coefficient, the initial internal energy coefficient, the initial turbulent fluctuation coefficient and the initial dissipation rate coefficient. Then, the first information is input into the reduced order model to obtain the second information of the reactor core at each time step, wherein the second information includes the target velocity coefficient, the target pressure coefficient, the target internal energy coefficient, the target turbulent fluctuation coefficient and the target dissipation rate coefficient. Finally, the second information of the reactor core at each time step is input into the POD basis function application equation respectively to obtain the flow and heat transfer analysis result of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis result includes the solutions of velocity, pressure, internal energy, turbulent fluctuation and dissipation rate. That is, by inputting the first information into the reduced order model constructed based on the snapshot set, the second information of the reactor core is obtained, and then the second information is input into the POD basis function application equation to obtain the flow and heat transfer analysis result. In this way, the flow and heat transfer analysis of the reactor core is quickly realized by the constructed reduced order model, which breaks through the limitation of traditional reactor flow and heat transfer calculation in terms of calculation resources and improves the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 FIG. 1 is a flowchart of a reactor core flow and heat transfer analysis method provided by an embodiment of the present application;

[0051] Figure 2 FIG. 2 is another flowchart of a reactor core flow and heat transfer analysis method provided by an embodiment of the present application;

[0052] Figure 3 FIG. 3 is a structural schematic diagram of a reactor core flow and heat transfer analysis device provided by an embodiment of the present application;

[0053] Figure 4 FIG. 4 is a structural schematic diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art belong to the scope of protection of the present application.

[0055] The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of a kind and do not limit the number of objects, for example, the first object can be one or more. In addition, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / ", generally indicates that the objects before and after are in an "or" relationship.

[0056] The reactor core flow heat transfer analysis method and device, electronic device and computer storage medium provided by the embodiments of the present application will be described in detail below in conjunction with the drawings, specific embodiments and application scenarios.

[0057] Please refer to Figure 1 , which is a flowchart of the reactor core flow heat transfer analysis provided by the embodiments of the present application, and the method is applied to an electronic device. As Figure 1 shown, the reactor core flow heat transfer analysis method includes the following steps S100 to S400.

[0058] Step S100: obtaining a reduced order model corresponding to the reactor core, wherein the reduced order model is constructed by using a snapshot set, and the snapshot set is used to represent the flow heat transfer state of the reactor core under different working conditions;

[0059] The reduced order model corresponding to the reactor core in the embodiments of the present application can be constructed by using the snapshot set reflecting the flow heat transfer state of the reactor core under different working conditions. Different working conditions can be different time points or different parameter device operating states. The snapshot set can be a set of flow heat transfer state data of the reactor core recorded at different time points or under different parameter conditions. The snapshot set can be a plurality of snapshots, and the snapshot can reflect the distribution of flow field, pressure field, temperature field or internal energy field, turbulent kinetic energy and turbulent dissipation in turbulent flow. Based on the snapshot, known data points can be obtained, including velocity, pressure, internal energy, turbulent fluctuation and dissipation rate. The flow heat transfer state can be the flow field and temperature state, which can be the flow field, pressure field, temperature field or internal energy field, and the distribution of turbulent kinetic energy and turbulent dissipation in turbulent flow. The reduced order model constructed by reflecting the flow heat transfer state of the reactor core under different working conditions can quickly obtain the flow heat transfer analysis result of the reactor core. In a multi-dimensional space, the reduced order model can be expressed as:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] wherein, , , , and wherein denote the POD coefficients at time step n; , , , and denote the POD coefficients of the solution field v, p, E, and at time step n-1 denote the number of time steps in the calculation of the simulation; denote the radial basis functions whose value depends on the distance to the data set points wherein ; and denote the weight coefficients wherein M denotes the number of POD basis functions.

[0066] Step S200: obtaining first information of the reactor core, wherein the first information comprises an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent fluctuation coefficient, and an initial dissipation rate coefficient;

[0067] In the embodiment of the present application, the first information can be initial Proper Orthogonal Decomposition (POD) coefficients, which can be a set of coefficients used to describe the main characteristics and behavior patterns of the reactor core process in the initial state.

[0068] The initial velocity coefficient can be a POD coefficient of fluid velocity in the initial state of the reactor core. The initial pressure coefficient can be a POD coefficient of pressure distribution in the initial state of the reactor core. The initial internal energy coefficient can be a distribution of internal energy of materials in the core in the initial state.

[0069] The initial turbulent fluctuation coefficient can be a main fluctuation mode in the initial state. Turbulent fluctuation is an important phenomenon in fluid dynamics, especially when fluid passes through the reactor core.

[0070] The initial dissipation rate coefficient can be a dominant mode of energy dissipation in the fluid at the initial state. The dissipation rate coefficient is related to the viscous dissipation of the fluid, and in the reactor core analysis, the dissipation rate coefficient helps to understand how the energy is dissipated in the fluid.

[0071] Exemplarily, before the reactor core simulation starts, the initial POD coefficients need to be set , , , and These coefficients represent the state of each variable (velocity, pressure, internal energy, turbulent fluctuation and dissipation rate) at the start of the simulation.

[0072] Step S300: inputting the first information into the reduced order model to obtain second information of the reactor core at each time step.

[0073] In the embodiment of the application, the second information can be a set of coefficients at a time step for describing the state of the flow dynamics variables, which can be a method of reducing dimensions to describe the high-dimensional state with fewer coefficients.

[0074] Step S300 further includes steps one to five, which are explained as follows: Step one, determining the state of the fluid dynamics variables of the reactor core at the start of the simulation, including the first information of the variables such as velocity, pressure, internal energy, turbulent fluctuation and dissipation rate. Step two, constructing a reduced order model, extracting main modes from the snapshot set, and constructing POD basis functions, wherein the basis functions describe the main characteristics of the reactor core behavior. Selecting appropriate radial basis functions for each fluid dynamics variable (velocity, pressure, internal energy, turbulent fluctuation and dissipation rate), and determining the corresponding weight coefficients for interpolation calculation. Step three, inputting the first information determined in step one into the reduced order model. Step four, using the reduced order model to predict the POD coefficients at the next time step at each time step. Step five, updating the second information at each time step using the prediction result obtained in step four. Step six, repeating steps four and five until M basis spaces are iterated, wherein M is the number of basis functions.

[0075] Exemplarily, first, at each time step n-1, the radial basis interpolation function is used to predict the POD coefficients at the current step:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Secondly, the POD coefficients of the current time step are calculated by radial basis function interpolation combined with the fluid state of the previous time step:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Further, the first and second steps are repeated until the space composed of M basis functions is iterated.

[0088] Step 400: input the second information of the reactor core at each time step into the POD basis function application equation respectively to obtain the flow and heat transfer analysis results of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis results include solutions of velocity, pressure, internal energy, turbulent fluctuation and dissipation rate.

[0089] In the embodiment of the application, the POD basis function application equation can be a POD basis function application equation obtained by constructing a POD basis function using a snapshot set and a truncated singular value decomposition method. The POD basis function application equation can be a mathematical expression of a method for approximating and analyzing an original data set using a basis function obtained by POD analysis. The POD basis function application equation can simplify a complex multi-dimensional data set into a set of low-dimensional basis functions that can describe the main variation characteristics and corresponding POD coefficients. The POD basis function application equation can be used to reconstruct or predict the flow and heat transfer state of the reactor core using selected POD basis functions and calculated coefficients. The flow and heat transfer analysis results can be the flow and heat transfer state of the reactor core under different operating conditions, and can be solutions of velocity, pressure, internal energy, turbulent fluctuation and dissipation rate.

[0090] Firstly, the second information is calculated, and secondly, the POD basis function application equation is applied. For each time step, the flow and heat transfer state is reconstructed using the POD basis function application equation, and then the required flow and heat transfer parameters such as velocity, pressure, internal energy, turbulent fluctuation and dissipation rate are extracted from the reconstructed state. That is, the reduced coefficients are mapped back to the original physical space to obtain more intuitive physical quantities. The above content is repeated until the entire simulation time range is covered to obtain the flow and heat transfer analysis results of the entire time sequence.

[0091] Exemplarily, the POD basis function application equation can be:

[0092] , , , and

[0093] wherein:

[0094] , , , and are the POD basis functions of , , , and respectively, which are extracted by the truncated singular value decomposition, and M is the number of the POD bases used in the model, , , , and represent the reduced variable vectors (POD coefficients) of the time level, , , , and are the variable vectors, and n is the time step.

[0095] Through the steps S100-S400, first, the reduced-order model corresponding to the reactor core is obtained, wherein the reduced-order model is constructed by using the snapshot set, and the snapshot set is used to represent the flow and heat transfer state of the reactor core under different working conditions; second, the first information of the reactor core is obtained, wherein the first information includes the initial velocity coefficient, the initial pressure coefficient, the initial internal energy coefficient, the initial turbulent fluctuation coefficient and the initial dissipation rate coefficient; third, the first information is input into the reduced-order model to obtain the second information of the reactor core at each time step, wherein the second information includes the target velocity coefficient, the target pressure coefficient, the target internal energy coefficient, the target turbulent fluctuation coefficient and the target dissipation rate coefficient; and finally, the second information of the reactor core at each time step is input into the POD basis function application equation respectively to obtain the flow and heat transfer analysis result of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis result includes the solutions of velocity, pressure, internal energy, turbulent fluctuation and dissipation rate. That is, by inputting the first information into the reduced-order model constructed based on the snapshot set, the second information of the reactor core is obtained, and then the second information is input into the POD basis function application equation to obtain the flow and heat transfer analysis result. In this way, the flow and heat transfer analysis of the reactor core is quickly realized through the constructed reduced-order model, which breaks through the limitation of traditional reactor flow and heat transfer calculation in terms of computing resources and improves the calculation efficiency.

[0096] In some embodiments, the step of obtaining the reduced-order model corresponding to the reactor core includes:

[0097] obtaining the snapshot set;

[0098] constructing the POD basis function and obtaining the POD basis function application equation by using the snapshot set and the truncated singular value decomposition method;

[0099] performing reduced-order processing on the POD basis function application equation to obtain a reduced-order operator;

[0100] obtaining a radial basis function interpolation, wherein the radial basis function interpolation is obtained by using a radial basis function to fit an interpolation domain through known data points;

[0101] constructing the reduced-order model by using the radial basis function interpolation and the reduced-order operator.

[0102] In this embodiment, by applying the equation to the POD basis function obtained based on the snapshot set, the reduced order operator is obtained, and the reduced order model is constructed according to the reduced order operator and the radial basis function interpolation. In this way, the use of the reduced order model greatly reduces the demand for computing resources, making the complex analysis and simulation more efficient and improving the computing efficiency. At the same time, using the POD basis function and the radial basis function interpolation, important data is retained and the model is simplified. In addition, the reduced order model is suitable for various types of systems and different working conditions, has good universality and adaptability, and has a wide range of applications.

[0103] In this embodiment, it should be noted that singular value decomposition can be a mathematical method of decomposing a matrix into three specific matrix products. Truncated singular value decomposition can be to retain only the first M largest singular values and their corresponding vectors in the decomposition process to achieve data dimensionality reduction. The POD basis function can be a set of orthogonal basis functions obtained by singular value decomposition. The reduced order operator can be a function used to approximate the high-order model in the reduced order model corresponding to the application of the equation to the POD basis function, with the purpose of reducing the complexity and computational cost of the model. Radial basis function (RBF) interpolation: an interpolation method based on radial basis functions, used for smooth interpolation between known data points to predict the values of unknown data points. The known data points can be velocity, pressure, internal energy, turbulent fluctuation and dissipation rate.

[0104] In an available embodiment, a snapshot set is obtained, which reflects the fluid heat transfer state data of the reactor core under different working conditions, such as velocity, pressure, internal energy, turbulent fluctuation and dissipation rate. Secondly, the snapshot set data is preprocessed, and the truncated singular value decomposition method is applied to extract the characteristic vectors as the POD basis function. Using the POD basis function, a low-dimensional equation describing the flow and heat transfer state of the reactor core is constructed. Thirdly, the eigen-orthogonal method is used to construct the eigen-orthogonal reduced order model, wherein the eigen-orthogonal reduced order model refers to the reduced order operator. Then, using the radial basis function method, the radial basis function interpolation is constructed according to the known data points. Wherein, the known data points correspond to the fluid heat transfer state data of the reactor core under different working conditions. Finally, the radial basis function interpolation and the reduced order operator are combined to construct the final reduced order model.

[0105] In another available embodiment, by artificially setting the fluid heat transfer state data of the reactor core under different working conditions, the reduced order operator is constructed, the radial basis function interpolation is constructed according to the set data points using the radial basis function method, and the final reduced order model is constructed by combining the radial basis function interpolation and the reduced order operator.

[0106] Exemplarily, firstly, a full-order model based on the porous media related equations corresponding to the reactor core is run once, and the required states are recorded by snapshots. The snapshots obtain the flow field and temperature states produced by the full-order model at different time points or under different parameter configurations, obtaining a snapshot set. For each snapshot set, the average values of the velocity field v, the pressure field p, the temperature field , the turbulent kinetic energy k, and the dissipation rate are calculated respectively , , , and , , , , and are variables respectively.

[0107] POD is a numerical technique for finding a set of optimal basis functions from snapshots of the original model solution. The optimal POD basis functions can be used to construct a system that contains the main features of the flow and heat transfer in the reactor core. Since the POD basis functions have optimal convergence, only a small number of bases (for example, 10-200) can be used to capture the main variable variation process of a large-dimensional process.

[0108] Truncated singular value decomposition can decompose the dimensionality reduction into a set of low-dimensional orthogonal basis vectors, and these basis vectors are sorted in order of importance, that is, the first basis vector contains most of the energy of the data, and the second basis vector contains the remaining part of the energy. Select the first M important basis vectors to form an M-dimensional POD subspace, and map the original data to this subspace to obtain a reduced data matrix.

[0109] Secondly, using the snapshot set and the truncated singular value decomposition method, the POD basis function is constructed and the POD basis function application equation is obtained, and the POD basis function application equation is projected into the reduced space, that is, the above-mentioned subspace, to obtain the projection equation. The reduced projection equation in this embodiment can be expressed as:

[0110]

[0111]

[0112]

[0113]

[0114] .

[0115] The projection equation of the POD basis function is solved by using the eigenvalue orthogonal decomposition method, and the reduced-order operator is obtained:

[0116]

[0117]

[0118]

[0119]

[0120] .

[0121] For initial conditions:

[0122]

[0123]

[0124]

[0125]

[0126] ,

[0127] where, , , , and denote the solution fields v, p, E, and the POD coefficients of the set of and at time step n-1 ( is the number of time steps in the computational simulation.

[0128] Again, the radial basis function interpolation fits an interpolation domain using radial basis functions through all data points. For a function defined at N data points where and radial basis functions with centers at points . With the Euclidean norm, the interpolated field can be defined as follows:

[0129]

[0130] where:

[0131] is the interpolation function;

[0132] is the radial basis function, depending on the distance between the point x and the center point xi;

[0133] is a weight coefficient associated with each center point xi;

[0134] N is the number of center points.

[0135] Then, the weight coefficients of the interpolation function are determined. The weight coefficients are determined by ensuring that the interpolation function can accurately reproduce the known data values at the given data points, where the known data values are obtained from the previous snapshots. The weight coefficients are determined by solving the following linear system of equations:

[0136] ,

[0137] where:

[0138] A is a matrix composed of radial basis function values, whose internal elements are:

[0139] ,

[0140] is a weight coefficient vector ;

[0141] y is a vector of known data values .

[0142] Exemplarily, if there are three data points, a quadratic polynomial can be selected as the interpolation function: .

[0143] Need to determine , , , such that , for all three data points. Thus, three equations are obtained,

[0144] The three unknown weight coefficients can be solved. Among them is the value of the independent variable, is the value of the corresponding dependent variable.

[0145] Finally, the radial basis function interpolation and the order reduction operator are used to construct the order reduction model.

[0146] In some embodiments, the above step of obtaining the radial basis function interpolation comprises:

[0147] determining the radial basis function;

[0148] determining a weight coefficient vector of the radial basis function according to a matrix composed of function values of the radial basis function and a vector composed of known data points, the known data points being data points in the snapshot set;

[0149] According to the radial basis function and the weight coefficient vector, the radial basis function interpolation is determined.

[0150] In this embodiment, first, a suitable radial basis function is selected and a weight coefficient vector of the radial basis function is determined, and then the radial basis function interpolation is determined. In this way, the radial basis function interpolation can provide high-precision data fitting and can also be used for prediction of unknown data points, and has good prediction ability and high-precision fitting ability.

[0151] In this embodiment, it should be noted that the radial basis function can be a function centered at the origin and changing with the distance from the origin. The weight coefficient vector can be a weight coefficient corresponding to each data point in the RBF interpolation, and the weight coefficient is determined through an optimization process and is used to adjust the influence degree of RBF at the data point. The radial basis function interpolation can be a method of interpolating data points using radial basis functions, and can predict data values at unknown positions according to known data points.

[0152] In an implementable embodiment, a suitable radial basis function is selected, for example, a Gaussian function where r is the Euclidean distance, is a shape parameter. For each pair of data points in the data set, the distance between them is calculated, and the function value between them is calculated using the selected radial basis function. These function values are organized into a matrix. The values of the known data points in the snapshot set are organized into a vector, which contains the actual observation values of all data points used for interpolation. Then, a linear system equation is solved to determine the weight coefficient vector. Where A is the matrix of radial basis function values, w is the weight coefficient vector, and y is the vector of known data points. Finally, the radial basis function interpolation is constructed using the determined weight coefficient vector and the radial basis function.

[0153] In another implementable embodiment, the weight coefficient vector can also be determined by least squares method, regularization method or other optimization algorithm, and the radial basis function interpolation is constructed using the determined weight coefficient vector and the radial basis function.

[0154] For example, the radial basis function can also be obtained in the following way: RBF network is a weighted linear combination of RBF kernel interpolation of scattered data in d-dimensional space. In the deformed mesh or displacement mesh, specifically, the quantity that needs to be interpolated is the three-dimensional displacement at the known K surface mesh nodes, or usually the three-dimensional displacement at N different source nodes. Define as a radial function, whose value only depends on the distance between the input and a certain fixed point c, then where denotes the Euclidean distance. Radial functions are often used as a set to form a basis for a function space, and the above function is called a radial basis function. It is very important how to define a proper radial basis function , and some commonly used radial basis functions are listed in Table 1, where is the radius, is the shape parameter. There are mainly two types of standard RBF, one is infinitely smooth, and the other is infinitely smooth except at the center point. As shown in Table 1, Type I contains infinitely smooth radial basis functions with infinite differentiability and dependence on the shape parameter , such as Gaussian (GA), Multiquadric (MQ), Inverse Quadratic (IQ), and Inverse Multiquadric (IMQ). Type II is infinitely smooth except at the center point, and is independent of the shape parameter and cannot be infinitely differentiated, such as thin-plate splines.

[0155] Table 1, Examples of radial basis functions:

[0156]

[0157] For example, a multiquadric function radial basis function is selected:

[0158] .

[0159] where, is the distance defined by norm, i.e. the Euclidean norm, and is the shape parameter used to control the smoothness and width of the function. The weight coefficients

[0160] and are determined to ensure that the interpolated function has the same value as the known data points , , and at the data set points .

[0161] .

[0162] where:

[0163]

[0164] .

[0165]

[0166] .​

[0167] is an element of the interpolation matrix . is the number of data points.

[0168] The weight coefficients of the radial basis functions are then determined by solving the linear system of equations:

[0169] , and .

[0170] In some embodiments, the step of applying the POD basis functions to the equation to obtain a reduced order operator comprises:

[0171] projecting the POD basis functions to the equation to obtain a projected equation of the POD basis functions to the equation;

[0172] solving the projected equation of the POD basis functions to the equation using a proper orthogonal decomposition method to obtain a reduced order operator.

[0173] In the present embodiment, the projected equation of the POD basis functions to the equation is solved using a proper orthogonal decomposition method to obtain a reduced order operator. In this way, the use of the reduced order operator reduces the demand for computational resources and improves computational efficiency.

[0174] In the present embodiment, it should be noted that the POD basis functions can be a set of orthogonal modes extracted from data that maximize the variance in the data. The projected equation can be a new equation obtained by projecting the POD basis functions to the equation to a low-dimensional space using the POD basis functions, which describes the evolution of the reactor core system in the dominant modes. The proper orthogonal decomposition method (POD) can be a statistical method used to analyze multi-dimensional data sets and extract orthogonal basis functions that describe the main characteristics of the data. The reduced order operator can be an operator in the reduced order model obtained by solving the projected equation based on the proper orthogonal decomposition method, which describes the main dynamics of the flow and heat transfer in the reactor core after reduction. Through reduction, the complexity of the calculation can be reduced while retaining the main characteristics of the flow and heat transfer.

[0175] In a feasible embodiment, first, a set of POD basis functions of the flow and heat transfer state of the reactor core is determined, which are the dominant modes extracted from snapshot data of the flow and heat transfer state of the reactor core. Then, the POD basis functions are applied to the equation to obtain a projected equation. The projected equation is solved in a low-dimensional space, and by solving the projected equation, an operator describing the evolution of the flow and heat transfer of the reactor core in the POD basis function space, i.e. a reduced order operator, can be obtained. This operator can be used to predict the behavior of the flow and heat transfer state of the reactor core in the future or under different conditions.

[0176] In another possible implementation, the POD basis function applied equation is projected by querying a preset projection table to obtain a projection equation, and the projection equation is solved to obtain the reduced order operator. The projection table contains the correspondence between the POD basis function applied equation and the projection equation.

[0177] In some embodiments, the step of obtaining the snapshot set comprises:

[0178] Obtaining a porous medium related equation of the reactor core, the porous medium related equation being used to determine the flow and heat transfer state of the reactor core;

[0179] Inputting the boundary condition of the reactor core into the porous medium related equation;

[0180] Discretizing the porous medium related equation inputted with the boundary condition to obtain a full order model;

[0181] Solving the full order model to obtain the snapshot set.

[0182] In this embodiment, the full order model is obtained by discretizing the porous medium related equation inputted with the boundary condition of the reactor core, and the snapshot set is obtained by solving the full order model. The snapshot set reflects the flow and heat transfer state of the reactor core under different operating conditions. In this way, through accurate flow and heat transfer analysis, possible overheating or insufficient cooling conditions can be predicted and prevented, thereby improving the safety of the reactor.

[0183] In this embodiment, it should be noted that the porous medium related equation can be an equation used to describe the flow and heat transfer behavior of fluid in a porous medium. The porous medium related equation includes equations in the updated flow model, the updated conjugate heat transfer model, and the turbulence model. The updated flow model can be obtained by updating the flow model with a porous medium source term, and the updated conjugate heat transfer model can be obtained by combining the porous medium and the conjugate heat transfer model. The boundary condition can be a mathematical condition describing the behavior of physical phenomena (velocity, pressure, internal energy, turbulent fluctuations, and dissipation rate) on the boundary, and the boundary condition can be a supplementary condition required when solving partial differential equations. Discretization can be a step in numerical analysis, involving converting continuous equations into discrete form for solving. The full order model can be a model containing all possible physical phenomena and details. The snapshot set can be a collection of flow and heat transfer states of the reactor core recorded at different times or under different conditions in numerical simulation.

[0184] In one possible implementation, porous media related equations of the reactor core are determined, which can describe the flow and heat transfer characteristics of fluid in the porous media. Boundary conditions of the reactor core are input into the porous media related equations, which include the velocity, pressure, internal energy, turbulent fluctuation and dissipation rate of the inlet and outlet. The porous media related equations with the input boundary conditions are discretized to obtain a full-order model that can be solved on a computer. The full-order model is solved by numerical methods to obtain the flow and heat transfer states inside the reactor core. After solving the full-order model, a series of snapshot sets describing the states of the reactor core can be obtained, which are used to analyze and verify the performance of the reactor core under different operating conditions.

[0185] In another possible implementation, the snapshot sets describing the states of the reactor core are obtained by artificially setting data points of the states of the reactor core.

[0186] Exemplarily, the step of obtaining the snapshot sets described above can be described by two steps: Step 1, the porous media related equations include equations in the updated flow model, equations in the updated conjugate heat transfer model and equations in the turbulent flow model. The equations in the updated flow model include equations corresponding to the continuity equation of thermal hydraulic flow and equations corresponding to the momentum equation of coolant flow. The equations in the updated conjugate heat transfer model include equations corresponding to the conjugate heat transfer model.

[0187] The equations corresponding to the continuity equation of thermal hydraulic flow can be expressed as:

[0188]

[0189] wherein, is the permeability.

[0190] The equations corresponding to the momentum equation of coolant flow can be expressed as:

[0191]

[0192] wherein, P is the pressure, is the stress tensor of the fluid, is the gravity volume force term, and F is the external volume force term.

[0193] The equations corresponding to the conjugate heat transfer model can be expressed as:

[0194]

[0195] wherein, represents the effective thermal diffusivity or effective thermal conductivity, represents the effective viscous stress tensor, represents the volume energy source term.

[0196] The equations in the turbulence model can be expressed as:

[0197] The CFD simulation can provide various turbulence models, such as 0-equation model, two-equation model (standard model, RNG model, model, SST model, Reynolds stress model (RSM) and large eddy model (LES). The present embodiment adopts turbulence model, the equations of turbulent kinetic energy k and dissipation rate are:

[0198]

[0199]

[0200] wherein, represents the density of the fluid, represents the turbulent kinetic energy, represents the turbulent dissipation rate, t represents time, represents the spatial coordinates, subscript i represents in three spatial directions x, y, z, represents the component of the fluid velocity in direction, represents the dynamic viscosity of the fluid, represents the turbulent kinetic energy generated by the laminar velocity gradient, represents the turbulent dissipation generated by the laminar velocity gradient, represents the turbulent kinetic energy generated by the buoyancy, represents the turbulent dissipation generated by the buoyancy, is a self-defined source term, represents the turbulent viscosity coefficient, , and , is a constant;

[0201] Step two, identify the porous medium related equations and the required boundary conditions, and perform numerical discretization on the porous medium related equations with input boundary conditions to generate a full order model, which is composed of discrete control equations at different time steps . .

[0202] The discretization of the variables in the equation at different time steps n can be written in the general form, wherein:

[0203]

[0204]

[0205]

[0206]

[0207] .

[0208] The general procedure of the finite volume method in numerical simulation includes spatial and temporal discretization, and solution of nonlinear equations. That is, in the present embodiment, the computational domain Ω is divided into non-overlapping cells Ωi (i = 1, …, N), each with a volume of Vi. The governing equations are integrated over each cell, and the solution is assumed to be constant within the cell and on the boundaries, which is solved by an iterative method. The temporal discretization is performed using the implicit Euler method, while the nonlinear terms are handled by a fixed-point iteration.

[0209] The full-order model in this way has high fidelity and can provide accurate distribution of physical quantities such as flow field, pressure field, temperature field, or internal energy field, turbulent kinetic energy and turbulent dissipation in turbulent flow. A snapshot set is obtained by simulating the full-order model once.

[0210] In some embodiments, the step of obtaining the porous medium related equation of the reactor core includes:

[0211] Obtaining a flow model, a conjugate heat transfer model, and a turbulent flow model of the reactor core;

[0212] Obtaining a source term of the porous medium, updating the flow model according to the source term to obtain an updated flow model;

[0213] Obtaining an updated conjugate heat transfer model according to the porous medium and the conjugate heat transfer model;

[0214] The porous medium related equation includes the updated flow model, the updated conjugate heat transfer model, and the turbulent flow model.

[0215] In the present embodiment, the porous medium model is obtained by obtaining the updated flow model, the updated conjugate heat transfer model, and the created turbulent flow model according to the source term of the porous medium and the porous medium update. In this way, by obtaining the flow model, the flow rate and direction of the coolant can be predicted and controlled, and after adjustment according to the source term of the porous medium, the flow resistance inside the core can be more accurately reflected. By obtaining the conjugate heat transfer model and updating it according to the characteristics of the porous medium, the heat transfer process inside the core can be more accurately simulated. The turbulent flow model can be used to describe the turbulent flow phenomenon in fluid flow, which can affect the accuracy and computational cost of the simulation. Through accurate flow and heat transfer simulation, the safety of the reactor can be improved. Meanwhile, updating the flow model, the updated conjugate heat transfer model, and the turbulent flow model can also help to evaluate the performance of the reactor under different conditions.

[0216] In this embodiment, it should be noted that the flow model can be a mathematical model used to describe the flow characteristics of a fluid under different conditions. The conjugate heat transfer model can be a model that considers the heat exchange phenomenon between the fluid and the solid interface at the same time when calculating the fluid flow. The conjugate heat transfer model is usually used to simulate the heat transfer problem involving the interaction of solid and fluid. The turbulence model can be a mathematical model used to describe the turbulence phenomenon in fluid flow. Turbulence is a disordered and irregular flow state in fluid motion. The source term of the porous medium can be an internal factor that can affect the fluid flow and heat transfer in the porous medium flow model, such as the friction between the fluid and the porous medium skeleton, the inertial effect, and the energy change caused by chemical reaction or heat source. The porous medium related equation can be a set of mathematical equations describing the flow and heat transfer behavior of fluid in porous medium.

[0217] In a feasible implementation, first, the flow model, the conjugate heat transfer model and the turbulence model for reactor core analysis need to be established. The source term of the porous medium, such as the resistance and the heat source term, is introduced into the flow model to reflect the influence of the porous medium on the fluid flow. The introduction of the source term can update the flow model to more accurately describe the actual situation inside the core. Combined with the characteristics of the porous medium and the conjugate heat transfer model, the conjugate heat transfer model is updated to more accurately simulate the heat exchange process between the solid and the fluid. The updated flow model, conjugate heat transfer model and turbulence model are combined to form a complete set of porous medium related equations, which can comprehensively describe the flow and heat transfer state inside the reactor core.

[0218] In another feasible implementation, the flow model, the conjugate heat transfer model and the turbulence model for reactor core analysis are established, and then the porous medium related equation is obtained by querying the pre-established mapping table, which contains the correspondence between the flow model, the conjugate heat transfer model and the turbulence model for reactor core analysis and the porous medium related equation.

[0219] Illustratively, before the flow and heat transfer geometric model of the reactor core assembly is established, that is, before the thermal-hydraulic and heat transfer calculation module of the reactor core is established, the flow and heat transfer geometric model of the reactor core assembly needs to be established first: the geometric model of the reactor assembly is imported into the grid generation software for grid partitioning to form a numerical calculation grid model of the reactor assembly suitable for thermal-hydraulic analysis and heat transfer calculation.

[0220] Then in the computational fluid dynamics software, the thermal-hydraulic and heat transfer calculation module of the reactor core is established, considering the flow condition of the coolant and the conjugate heat transfer between the coolant and the fuel rod. The established thermal-hydraulic analysis calculation module includes the flow model, the turbulence model and the conjugate heat transfer model of the coolant. The steps are as follows:

[0221] The equation corresponding to the flow model of the coolant:

[0222] 1) In the normal operation condition of the reactor, the flow condition of the coolant is single flow and turbulent flow in the internal core of the primary loop, and the continuity equation of the thermal hydraulic flow is:

[0223]

[0224] wherein: represents the coolant; is the density of the coolant, and the vector is the velocity field of the coolant;

[0225] 2) The momentum equation of the coolant flow can be described by the incompressible Navier-Stokes equation as:

[0226]

[0227] wherein: represents the pressure in the grid control body, represents the dynamic viscosity of the coolant, represents the volume force source term, such as gravity, buoyancy, etc.;

[0228] The equation of the turbulence model is as shown above, and will not be repeated in the present embodiment.

[0229] 3) The conjugate heat transfer model includes the energy conservation control equation of the coolant and the temperature control equation in the solid domain, and the energy conservation control equation of the coolant is:

[0230]

[0231] wherein, represents the density of the coolant, represents the total energy of the coolant, represents the pressure of the coolant, represents the temperature, represents the effective thermal conductivity, represents the diffusion flow of the coolant j'; represents the enthalpy of the jth component; represents the i-j component of the stress tensor, represents the user-defined volume heat source;

[0232] The temperature control equation of the solid region including the fuel pellets and the cladding is:

[0233]

[0234] wherein, the subscript s represents the solid region, is the density of the solid domain, is the constant-pressure specific heat capacity under the pressure p, temperature of the solid region, thermal conductivity of the solid region, volume heat release rate of the solid region;

[0235] The heat transfer equations for the fluid region and the solid region are solved coupled through the temperature and heat flux variables on the solid / fluid interface.

[0236] After the thermal analysis calculation module is established, the source term of the porous medium is defined, and the equations related to the porous medium are constructed.

[0237] The source term of the porous medium is defined, and the source term The form can be expressed as follows:

[0238]

[0239] where D and F represent the Darcy-Forchheimer equation viscous tensor and inertial tensor, respectively, denotes the dot product of the trace (i.e., the scalar of the velocity magnitude) of the velocity vector and the unit tensor;

[0240] The values inside the tensor are estimated according to the problem under calculation or directly input by the user in order to obtain the desired porosity effect in the calculation domain. The source term is in the form of resistance, and the value is negative as the core fluid flow moves from a state of higher pressure to a state of lower pressure.

[0241] The coolant fluid flow in the core is in the form of turbulent flow, . For the rod bundle in the reactor core, the fluid viscous loss value is small and can be ignored. Because the rod bundle of the core assembly is different from the typical porous medium with interconnected pores, the pressure drop caused by the coolant turbulent flow in the reactor core assembly is in the range of a problem physics in which inertial force dominates over viscous force. Therefore, the viscous tensor D of the Darcy-Forchheimer model can be ignored, and the source term is only the dominant F inertial tensor. The equation can be expressed as:

[0242]

[0243] For a general two-dimensional problem, the tensor is a 4-component square matrix. The force vector form is defined as:

[0244]

[0245] In the formula, V is the volume of the porous medium, and Fx and Fy are the coefficients in the inertial tensor. The dependence of the force on the flow direction can be expressed by the explicit velocity component, which is in the form of:

[0246] The last term in the above formula, a vector, also represents:

[0247]

[0248] θ represents the angle between the coolant flow direction and the rod bundle direction. The equation can then be expressed as:

[0249]

[0250] Similarly, a three-dimensional problem can be represented as:

[0251]

[0252] In some implementations, the equations of the reduced-order model described above can be expressed as:

[0253]

[0254]

[0255]

[0256]

[0257] .

[0258] , , , and (in () represents the POD coefficient at time step n; , , , and This indicates that at time step n-1 ( The solution field at time ) v, p, E, and The POD coefficient of the set; This indicates the number of time steps in the simulation. This represents the radial basis function, whose value depends on the distance from the data set points. (in ); and Represents the weighting coefficients (where ), where M represents the number of POD basis functions.

[0259] Please see Figure 2is another flowchart of a reactor core flow and heat transfer analysis method provided by the embodiment of the present application, the embodiment of the present application first determines a problem (control equation and variable), the control equation includes a porous medium related equation, and the variable includes velocity, pressure, internal energy, turbulent fluctuation and dissipation rate, and then enters an offline / training stage (high cost) and an online / evaluation stage (low cost), the offline / training stage includes creating a full order model (FOM), simulating a problem object using the full order model, and constructing a reduced order operator. The online / evaluation stage includes assembling a reduced order model (ROM) from the reduced order operator, solving the reduced order model, and evaluating a quantity of interest.

[0260] The contents of the offline / training stage and the online / evaluation stage correspond to discretize the porous medium related equation of the input boundary condition to obtain a full order model. The full order model is solved to obtain a snapshot set. The snapshot set and the truncated singular value decomposition method are used to construct a POD basis function and obtain a POD basis function application equation. The POD basis function application equation is reduced to obtain a reduced order operator. A radial basis function interpolation is obtained, and the radial basis function interpolation is obtained by fitting an interpolation domain using a radial basis function. The radial basis function interpolation and the reduced order operator are used to construct a reduced order model. First information of the reactor core is obtained, and the first information is input into the reduced order model to obtain second information of the reactor core at each time step. The second information of the reactor core at each time step is input into the POD basis function application equation to obtain a flow and heat transfer analysis result of the reactor core at each time step, that is, to obtain the evaluation quantity of interest. It should be noted that the reduced order model has been constructed in the construction of the reduced order operator in the offline / training stage.

[0261] See Figure 3 is a structural schematic diagram of a reactor core flow and heat transfer analysis device provided by the embodiment of the present application, the second aspect of the embodiment of the present application provides a reactor core flow and heat transfer analysis device 30, the device 30 includes:

[0262] The model acquisition module 31 is configured to acquire a reduced order model corresponding to the reactor core, wherein the reduced order model is constructed by using a snapshot set, and the snapshot set is used to represent the flow and heat transfer state of the reactor core under different working conditions.

[0263] The information acquisition module 32 is configured to acquire first information of the reactor core, wherein the first information includes an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent fluctuation coefficient and an initial dissipation rate coefficient.

[0264] An obtaining information module 33 is configured to input the first information into the reduced-order model to obtain second information of the reactor core at each time step, wherein the second information comprises a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent fluctuation coefficient, and a target dissipation rate coefficient.

[0265] An obtaining result module 34 is configured to input the second information of the reactor core at each time step into a POD basis function application equation respectively to obtain a flow and heat transfer analysis result of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis result comprises a solution of velocity, pressure, internal energy, turbulent fluctuation, and dissipation rate.

[0266] The reactor core flow and heat transfer device 20 provided by the second aspect of the embodiment of the present application can implement each process implemented by the method embodiments and achieve the same beneficial effects. To avoid repetition, details are not described herein.

[0267] Please refer to Figure 4 The electronic device 4000 provided by the third aspect of the embodiment of the present application comprises a processor 4100 and a memory 4200. The memory 4200 stores machine executable instructions capable of being executed by the processor 4100. The processor 4100 can execute the machine executable instructions to implement the nuclear reactor core control method described above.

[0268] The fourth aspect of the embodiment of the present application provides a computer readable storage medium, and the computer readable storage medium stores instructions. When the instructions are executed by a processor, the processor implements the reactor core flow and heat transfer analysis method described above.

[0269] In some embodiments, the embodiment of the present application further provides a computer program product comprising a computer program. When the computer program is executed by a processor, the computer program implements the reactor core flow and heat transfer analysis method according to the above embodiments.

[0270] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in 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.

[0271] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks.

[0272] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0273] The memory can include non-persistent memory, random access memory (RAM), and / or non-volatile memory, etc. in the form of a computer-readable medium, such as read only memory (ROM) or flash memory. The memory is an example of computer-readable media.

[0274] Computer-readable media includes permanent and non-permanent, movable and non-movable media that can implement information storage by any method or technology. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition herein, computer-readable media does not include transitory media such as modulated data signals and carriers.

[0275] It should also be noted that the terms "comprising", "containing", or any other variant thereof are intended to cover non-exclusive inclusions, so that a process, method, article or apparatus that includes a list of elements not only includes those elements, but also includes other elements not explicitly listed, or inherent to such a process, method, article or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0276] The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the scope of claims of the present application.

[0277] In addition, any combination of various embodiments of the present application can also be made, as long as it does not deviate from the idea of the present application, it should also be considered as disclosed by the present application.

Claims

1. A reactor core flow heat transfer analysis method, characterized by, The method comprises the following steps: obtaining a reduced-order model corresponding to the reactor core, wherein the reduced-order model is constructed by using a snapshot set, and the snapshot set is used to represent the flow and heat transfer state of the reactor core under different working conditions; obtaining first information of the reactor core, wherein the first information comprises an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent fluctuation coefficient and an initial dissipation rate coefficient; inputting the first information into the reduced-order model to obtain second information of the reactor core at each time step, wherein the second information comprises a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent fluctuation coefficient and a target dissipation rate coefficient; inputting the second information of the reactor core at each time step into a POD basis function application equation respectively to obtain flow and heat transfer analysis results of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis results comprise solutions of velocity, pressure, internal energy, turbulent fluctuation and dissipation rate; wherein the snapshot set is obtained in the following manner: obtaining a porous medium related equation of the reactor core, wherein the porous medium related equation is used to determine the flow and heat transfer state of the reactor core; inputting boundary conditions of the reactor core into the porous medium related equation; discretizing the porous medium related equation input with the boundary conditions to obtain a full-order model; solving the full-order model to obtain the snapshot set.

2. The method of claim 1, wherein, The step of obtaining the reduced-order model corresponding to the reactor core comprises: obtaining the snapshot set; constructing a POD basis function and obtaining a POD basis function application equation by using the snapshot set and a truncated singular value decomposition method; performing a reduced-order processing on the POD basis function application equation to obtain a reduced-order operator; obtaining a radial basis function interpolation, wherein the radial basis function interpolation is obtained by using a radial basis function to fit an interpolation domain through known data points; constructing the reduced-order model by using the radial basis function interpolation and the reduced-order operator.

3. The method of claim 2, wherein, The step of obtaining the radial basis function interpolation comprises: determining a radial basis function; determining a weight coefficient vector of the radial basis function according to a matrix formed by function values of the radial basis function and a vector formed by known data points, wherein the known data points are data points in the snapshot set; determining the radial basis function interpolation according to the radial basis function and the weight coefficient vector.

4. The method of claim 2, wherein, The step of performing a reduced-order processing on the POD basis function application equation to obtain a reduced-order operator comprises: projecting the POD basis function application equation to obtain a projection equation of the POD basis function application equation; solving the projection equation of the POD basis function application equation by using an eigen-orthogonal decomposition method to obtain a reduced-order operator.

5. The method of claim 1, wherein, The step of obtaining the porous medium related equation of the reactor core comprises: obtaining a flow model, a conjugate heat transfer model and a turbulent flow model of the reactor core; obtaining a source term of a porous medium, updating the flow model according to the source term to obtain an updated flow model; obtaining an updated conjugate heat transfer model according to the porous medium and the conjugate heat transfer model; The porous media related equations include the updated flow model, the updated conjugate heat transfer model, and the turbulence model.

6. The method of claim 1, wherein, The reduced order model includes the following equations: , , , and denote the POD coefficients at time step n, is the velocity, is the pressure, is the internal energy, is the turbulent fluctuation, is the dissipation rate, wherein ; , , , and denote the POD coefficients of the solution fields v, p, E, and at time step n-1, ; denotes the number of time steps in the calculation simulation; φ(r i ) denotes the radial basis functions, the value of which depends on the distance to the data set points , wherein ; and denote the weight coefficients, wherein , wherein M denotes the number of POD basis functions, and N is a positive integer.

7. A reactor core flow heat transfer analysis device characterized by comprising: The device includes: An acquisition model module is configured to acquire a reduced order model corresponding to the reactor core, wherein the reduced order model is constructed by using a snapshot set, and the snapshot set is used to represent flow and heat transfer states of the reactor core under different working conditions. An acquisition information module is configured to acquire first information of the reactor core, wherein the first information includes initial velocity coefficients, initial pressure coefficients, initial internal energy coefficients, initial turbulence fluctuation coefficients, and initial dissipation rate coefficients. A result obtaining module is configured to input the first information into the reduced order model to obtain second information of the reactor core at each time step, wherein the second information includes target velocity coefficients, target pressure coefficients, target internal energy coefficients, target turbulence fluctuation coefficients, and target dissipation rate coefficients. A result obtaining module is configured to input the second information of the reactor core at each time step into a POD basis function application equation respectively to obtain flow and heat transfer analysis results of the reactor core at each time step, wherein the POD basis function application equation is generated based on the snapshot set, and the flow and heat transfer analysis results include solutions of velocity, pressure, internal energy, turbulence fluctuation, and dissipation rate. The snapshot set is obtained in the following manner: A porous media related equation of the reactor core is acquired, and the porous media related equation is used to determine flow and heat transfer states of the reactor core. Boundary conditions of the reactor core are input into the porous media related equation. The porous media related equation input with the boundary conditions is discretized to obtain a full order model. The full order model is solved to obtain the snapshot set.

8. The reactor core flow heat transfer analysis apparatus according to claim 7, wherein The device is further configured to acquire the snapshot set, construct a POD basis function and obtain a POD basis function application equation by using the snapshot set and a truncated singular value decomposition method, perform a reduced order processing on the POD basis function application equation to obtain a reduced order operator, acquire a radial basis function interpolation, and construct the reduced order model by using the radial basis function interpolation and the reduced order operator.

9. The reactor core flow heat transfer analysis apparatus according to claim 8, characterized by, The device is further configured to determine a radial basis function, determine a weight coefficient vector of the radial basis function according to a matrix composed of function values of the radial basis function and a vector composed of known data points, and determine the radial basis function interpolation according to the radial basis function and the weight coefficient vector.

10. The reactor core flow heat transfer analysis apparatus of claim 8, wherein, The device is further configured to project the POD basis function application equation to obtain a projected equation of the POD basis function application equation, and solve the projected equation of the POD basis function application equation by using an eigenvalue orthogonal decomposition method to obtain a reduced order operator. The device is further configured to project the POD basis function application equation to obtain a projected equation of the POD basis function application equation, and solve the projected equation of the POD basis function application equation by using an eigenvalue orthogonal decomposition method to obtain a reduced order operator.

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