Reactor core flow heat transfer analysis method, device and equipment and storage medium

Abstract

The invention provides a reactor core flow heat transfer analysis method, device and equipment and a storage medium, 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, the reduced-order model being constructed by using a snapshot set, and the snapshot set being used for representing the flow heat transfer state of the reactor core under different working conditions; acquiring first information of a reactor core; inputting the first information into a reduced-order model to obtain second information of the reactor core on each time step; the second information of the reactor core on each time step is input into a POD primary function application equation, a flow heat transfer analysis result of the reactor core on each time step is obtained, the POD primary function application equation is generated based on the snapshot set, and the flow heat transfer analysis result comprises solutions of the speed, the pressure, the internal energy, the turbulence pulsation and the dissipation rate. The calculation efficiency of flow heat transfer analysis is improved.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation, and in particular to a reactor core flow heat transfer analysis method, device, equipment and storage medium. Background Art

[0002] As one of the most widely used nuclear power reactor types in the world, pressurized water reactors play a vital role in energy supply, greenhouse gas emission reduction, and national energy security. Among them, the flow and heat transfer characteristics of the core are closely related to the performance and safety of the reactor.

[0003] Traditional PWR core flow and heat transfer simulations mostly use numerical methods based on detailed physical models, such as computational fluid dynamics (CFD). However, although such methods can produce relatively accurate results, they face high computational costs. Especially for a full-scale PWR core, the calculation time may be as long as several months or even years, and the computational cost is very high, which is difficult to meet the needs of rapid analysis and optimization in actual engineering applications. Summary of the invention

[0004] The purpose of the embodiments of the present application is to provide a reactor core flow and heat transfer analysis method, device, equipment and storage medium, so as to improve the computational efficiency of reactor flow and heat transfer calculations in terms of computing resources.

[0005] In a first aspect, an embodiment of the present application provides a method for analyzing flow and heat transfer in a reactor core, the method comprising:

[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 characterize the flow and heat transfer state of the reactor core under different operating conditions;

[0007] Acquiring 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 turbulence pulsation coefficient, and an 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 a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulence pulsation coefficient, and a target dissipation rate coefficient;

[0009] The second information of the reactor core at each time step is respectively input into the POD basis function application equation to obtain the flow 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 heat transfer analysis result includes solutions of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

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

[0011] Obtaining the snapshot set;

[0012] Using the snapshot set and a truncated singular value decomposition method, a POD basis function is constructed and an application equation of the POD basis function is obtained;

[0013] Applying equations to the POD basis functions to perform order reduction processing to obtain a reduced-order operator;

[0014] Obtaining a radial basis function interpolation, wherein the radial basis function interpolation is obtained by fitting an interpolation domain through known data points using a radial basis function;

[0015] The reduced-order model is constructed by using the radial basis function interpolation and the reduced-order operator.

[0016] In some implementations, the step of obtaining radial basis function interpolation includes:

[0017] Determine radial basis functions;

[0018] Determine 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;

[0019] The radial basis function interpolation is determined according to the radial basis function and the weight coefficient vector.

[0020] In some implementations, the step of applying an equation to the POD basis function to perform order reduction processing to obtain a reduced-order operator comprises:

[0021] Projecting the POD basis function application equation to obtain a projection equation of the POD basis function application equation;

[0022] The projection equation of the POD basis function application equation is solved by using the eigenorthogonal decomposition method to obtain a reduced-order operator.

[0023] In some implementations, the step of obtaining the snapshot set includes:

[0024] Acquiring a porous medium correlation equation of the reactor core, wherein the porous medium correlation equation is used to determine a flow heat transfer state of the reactor core;

[0025] Inputting the boundary conditions of the reactor core into the porous medium related equations;

[0026] Discretizing the porous medium related equations inputting the boundary conditions to obtain a full-order model;

[0027] The full-order model is solved to obtain the snapshot set.

[0028] In some embodiments, the step of obtaining the porous medium correlation equation of the reactor core includes:

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

[0030] Acquire a source term of the porous medium, and update the flow model according to the source term to obtain an updated flow model;

[0031] According to the porous medium and the conjugate heat transfer model, an updated conjugate heat transfer model is obtained;

[0032] Wherein, the porous medium related equations include 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 equation:

[0034]

[0035]

[0036] and (where j∈{1,2,…,M}) represents the POD coefficient at time step n; and Indicates that at time step n-1 (n∈{1,2,…,N t}) The solution field v, p, E, k and POD coefficient of ε set; N t represents the number of time steps in the computational simulation; φ(r i ) represents the radial basis function, whose value depends on the distance from the data set point (where i∈1,2,…,N); w v,i,j ,w p,i,j ,w E,i,j ,w k,i,j and w ε,i,jrepresents the weight coefficient (where j∈{1,2,…,M}), where M represents the number of POD basis functions.

[0037] In a second aspect, an embodiment of the present application provides a reactor core flow heat transfer analysis device, the device comprising:

[0038] An acquisition model module is used to acquire 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 characterize the flow and heat transfer state of the reactor core under different operating conditions;

[0039] An information acquisition module, 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 turbulence pulsation coefficient, and an initial dissipation rate coefficient;

[0040] an information 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 includes a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulence pulsation coefficient, and a target dissipation rate coefficient;

[0041] A result obtaining module is used to input the second information of the reactor core at each time step into the POD basis function application equation respectively, to obtain the flow 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 heat transfer analysis result includes the solution of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

[0042] In a third aspect, an embodiment of the present application provides an electronic device, including:

[0043] a memory configured to store instructions; and

[0044] The processor is configured to call the instructions from the memory and implement the reactor core flow heat transfer analysis method provided in the first aspect of the embodiment of the present application when executing the instructions.

[0045] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores instructions, and when the instructions are executed by a processor, the method described in the first aspect is implemented.

[0046] In an embodiment of the present application, a reduced-order model corresponding to a reactor core is obtained, wherein the reduced-order model is constructed using a snapshot set, and the snapshot set is used to characterize the flow and heat transfer state of the reactor core under different operating conditions; secondly, first information of the reactor core is obtained, wherein the first information includes an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent pulsation coefficient, and an initial dissipation rate coefficient; then, the first information is input into the reduced-order model to obtain second information of the reactor core at each time step, wherein the second information includes a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent pulsation coefficient, and a 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 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 includes solutions of velocity, pressure, internal energy, turbulent pulsation, 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 heat transfer analysis result. In this way, the flow heat transfer analysis of the reactor core is quickly realized through the constructed reduced-order model, breaking through the limitations of traditional reactor flow and heat transfer calculations in computing resources and improving computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic flow chart of a reactor core flow heat transfer analysis method provided in an embodiment of the present application;

[0048] Figure 2 is another schematic flow chart of the reactor core flow heat transfer analysis method provided in an embodiment of the present application;

[0049] Figure 3 It is a structural schematic diagram of a reactor core flow heat transfer analysis device provided in an embodiment of the present application;

[0050] Figure 4 It is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present application to clearly describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the present application belong to the scope of protection of this application.

[0052] 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 are interchangeable where appropriate, 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 one type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0053] The reactor core flow and heat transfer analysis method and device, electronic device, and computer storage medium provided in the embodiments of the present application are described in detail below in conjunction with the accompanying drawings through specific embodiments and their application scenarios.

[0054] See also Figure 1 , is a schematic diagram of the flow chart of reactor core flow heat transfer analysis provided by the embodiment of the present application, and the method is applied to electronic equipment. Figure 1 As shown, the reactor core flow heat transfer analysis method includes the following steps S100 to S400.

[0055] Step S100: 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 characterize the flow and heat transfer state of the reactor core under different operating conditions;

[0056] The reduced-order model corresponding to the reactor core in the embodiment of the present application can be constructed by a set of snapshots reflecting the flow heat transfer state of the reactor core under different operating conditions. Different operating conditions can be equipment operating states at different time points or under different parameters. A 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. A snapshot set can be a plurality of groups of snapshots. The snapshots can reflect the distribution of flow field, pressure field, temperature field or internal energy field, turbulent kinetic energy in turbulence and turbulent dissipation. Based on the snapshots, known data points can be obtained. The known data points include velocity, pressure, internal energy, turbulent pulsation and dissipation rate. The flow heat transfer state can be a flow field and temperature state, and can be a flow field, pressure field, temperature field or internal energy field, turbulent kinetic energy in turbulence and turbulent dissipation distribution. The reduced-order model constructed by a set of snapshots reflecting the flow heat transfer state of the reactor core under different operating conditions can quickly obtain the flow heat transfer analysis results of the reactor core. In multidimensional space, the reduced-order model can be expressed as:

[0057]

[0058] in, and (where j∈{1,2,…,M}) represents the POD coefficient at time step n; and Indicates that at time step n-1 (n∈{1,2,…,N t}) The solution field v, p, E, k and POD coefficient of ε set; N t represents the number of time steps in the computational simulation; φ(r i ) represents the radial basis function, whose value depends on the distance from the data set point (where i∈1,2,…,N); w v,i,j ,w p,i,j ,w E,i,j ,w k,i,j and w 3,i,j represents the weight coefficient (where j∈{1,2,…,M}), where M represents the number of POD basis functions.

[0059] Step S200: 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 turbulence pulsation coefficient, and an initial dissipation rate coefficient;

[0060] In an embodiment of the present application, the first information may be an initial proper orthogonal decomposition (POD) coefficient, which may be a set of coefficients used to describe the main characteristics and behavior patterns of the reactor core process in the initial state.

[0061] The initial velocity coefficient may be a POD coefficient of the fluid velocity at the initial state of the reactor core. The initial pressure coefficient may be a POD coefficient of the pressure distribution at the initial state of the reactor core. The initial internal energy coefficient may be the distribution of the internal energy of the material in the core at the initial state.

[0062] The initial turbulence pulsation coefficient may be the main pulsation mode in the turbulent flow at the initial state. Turbulence pulsation is an important phenomenon in fluid dynamics, especially when the fluid passes through the reactor core.

[0063] The initial dissipation rate coefficient can be the dominant mode of energy dissipation in a fluid at the initial state. The dissipation rate coefficient is related to the viscous dissipation of the fluid and in reactor core analysis, the dissipation rate coefficient helps understand how energy is dissipated in a fluid.

[0064] For example, before the reactor core simulation begins, the initial POD coefficient needs to be set and These coefficients represent the state of the various variables (velocity, pressure, internal energy, turbulence fluctuations and dissipation rate) at the beginning of the simulation.

[0065] Step S300: inputting the first information into the reduced-order model to obtain second information of the reactor core at each time step.

[0066] In an embodiment of the present application, the second information may be a set of coefficients for describing the state of flow dynamics variables at a time step, and may provide a dimensionality reduction method to describe a high-dimensional state with fewer coefficients.

[0067] Step S300 includes multiple steps, namely, step 1 to step 5. The following is a specific explanation of step 1 to step 5: Step 1, determine the state of the fluid dynamic variables of the reactor core at the beginning of the simulation, and the state of the fluid dynamic variables includes the first information of variables such as velocity, pressure, internal energy, turbulent pulsation and dissipation rate. Step 2, construct a reduced-order model, extract the main modes from the snapshot set, and construct POD basis functions, where these basis functions describe the main characteristics of the behavior of the reactor core. Select an appropriate radial basis function for each fluid dynamic variable (velocity, pressure, internal energy, turbulent pulsation and dissipation rate), and determine the corresponding weight coefficient, which is used for interpolation calculation. Step 3, use the first information determined in step 1 as input and load it into the reduced-order model. Step 4, at each time step, use the reduced-order model to predict the POD coefficient of the next time step, step 5, use the prediction results obtained in step 4 to update the second information of each time step, step 6, repeat steps 4 and 5 until M basis spaces are iterated, where M is the number of basis functions.

[0068] Exemplarily, first, at each time step n-1, the radial basis interpolation function is used to predict the POD coefficient of the current step:

[0069]

[0070] Secondly, the POD coefficient of the current time step is calculated by radial basis function interpolation combined with the fluid state of the previous time step:

[0071]

[0072] Then, repeat the first and second steps until the space formed by M basis functions is iterated.

[0073] 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 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 heat transfer analysis result includes solutions of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

[0074] In an embodiment of the present application, the POD basis function application equation may 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 may be a mathematical expression of a method for approximating and analyzing an original data set using a basis function obtained by POD analysis, and a complex multidimensional data set may be simplified into a set of low-dimensional basis functions and corresponding POD coefficients that can describe the main change characteristics. The POD basis function application equation may be a method of reconstructing or predicting the flow and heat transfer state of a reactor core using selected POD basis functions and calculated coefficients. The flow heat transfer analysis result may be the flow heat transfer state of the reactor core under different operating conditions, and may be a solution of velocity, pressure, internal energy, turbulent pulsation, and dissipation rate.

[0075] First, calculate the second information, then apply the POD basis function application equation, for each time step, use the POD basis function application equation to reconstruct the flow and heat transfer state, then extract the required flow and heat transfer parameters such as velocity, pressure, internal energy, turbulent pulsation and dissipation rate from the reconstructed state. That is, remap the coefficients after dimensionality reduction to the original physical space to obtain more intuitive physical quantities. Repeat the above content until the entire simulation time range is covered to obtain the flow heat transfer analysis results of the entire time series.

[0076] Exemplarily, the POD basis function application equation may be:

[0077]

[0078] in:

[0079] Φ v =(Φ v，1 ,...,Φ v,M ), Φ p =(Φ p，1 ,...,Φ p,M ), Φ E =(Φ E，1 ,...,Φ E,M ), Φ k =(Φ k，1 ,...,Φ k,M )

[0080] and Φ ε =(Φ ε，1 ,...,Φ ε,M ) are v n 、p n , T n , k n and ε n The POD basis functions are extracted by the intercept singular value decomposition, and M is the number of POD basis used in the model. and represents the vector of reduced variables (POD coefficients) at the time level, v n 、p n 、T n , k n and ε n is the variable vector and n is the time step.

[0081] Through the above steps S100 to S400, first, a reduced-order model corresponding to the reactor core is obtained, wherein the reduced-order model is constructed using a snapshot set, and the snapshot set is used to characterize the flow and heat transfer state of the reactor core under different operating conditions; secondly, first information of the reactor core is obtained, wherein the first information includes an initial velocity coefficient, an initial pressure coefficient, an initial internal energy coefficient, an initial turbulent pulsation coefficient, and an initial dissipation rate coefficient; then, the first information is input into the reduced-order model to obtain second information of the reactor core at each time step, wherein the second information includes a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulent pulsation coefficient, and a 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 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 includes solutions of velocity, pressure, internal energy, turbulent pulsation, 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 heat transfer analysis result. In this way, the flow heat transfer analysis of the reactor core is quickly realized through the constructed reduced-order model, breaking through the limitations of traditional reactor flow and heat transfer calculations in computing resources and improving computing efficiency.

[0082] In some embodiments, the step of obtaining the reduced-order model corresponding to the reactor core comprises:

[0083] Obtaining the snapshot set;

[0084] Using the snapshot set and a truncated singular value decomposition method, a POD basis function is constructed and an application equation of the POD basis function is obtained;

[0085] Applying equations to the POD basis functions to perform order reduction processing to obtain a reduced-order operator;

[0086] Obtaining a radial basis function interpolation, wherein the radial basis function interpolation is obtained by fitting an interpolation domain through known data points using a radial basis function;

[0087] The reduced-order model is constructed by using the radial basis function interpolation and the reduced-order operator.

[0088] In this embodiment, the POD basis function obtained based on the snapshot set is applied to the equation for order reduction to obtain the reduced-order operator, and the reduced-order model is constructed based on the reduced-order operator and radial basis function interpolation. In this way, the use of the reduced-order model greatly reduces the demand for computing resources, making complex analysis and simulation more efficient and improving computing efficiency. At the same time, the use of POD basis functions and radial basis function interpolation not only retains important data but also simplifies the model. In addition, the reduced-order model is applicable to various types of systems and different operating conditions, has good versatility and adaptability, and has a wide range of applications.

[0089] In this embodiment, it should be noted that singular value decomposition can be a mathematical method for decomposing a matrix into the product of three specific matrices. Truncated singular value decomposition can be that only the first M largest singular values ​​and their corresponding vectors are retained during 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 a high-order model in a reduced order model corresponding to the POD basis function application equation, in order to reduce 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 pulsation and dissipation rate.

[0090] In one feasible implementation, a snapshot set is obtained, which reflects the fluid heat transfer state data of the reactor core under different operating conditions, such as velocity, pressure, internal energy, turbulent pulsation and dissipation rate. Secondly, the snapshot set data is preprocessed, and the truncated singular value decomposition method is applied to extract the eigenvector as the POD basis function. Using the POD basis function, a low-dimensional equation describing the flow heat transfer state of the reactor core is constructed. Thirdly, the intrinsic orthogonal method is used to construct an intrinsic orthogonal reduced-order model, where the intrinsic orthogonal reduced-order model refers to the reduced-order operator. Then, the radial basis function method is used to construct a radial basis function interpolation based on known data points. Among them, the known data points correspond to the fluid heat transfer state data of the reactor core under different operating conditions. Finally, the radial basis function interpolation and the reduced-order operator are combined to construct the final reduced-order model.

[0091] In another feasible implementation, the fluid heat transfer state data of the reactor core under different operating conditions is artificially set to construct a reduced-order operator, and the radial basis function method is used to construct a radial basis function interpolation according to the set data points. The radial basis function interpolation and the reduced-order operator are then combined to construct the final reduced-order model.

[0092] For example, first, a simulation is run on the full-order model built on the basis of the porous media correlation equations corresponding to the reactor core, and the required states are recorded through snapshots. The snapshots obtain the flow field and temperature states generated by the full-order model at different time points or different parameter configurations to obtain a set of snapshots. For each set of snapshots, the average values ​​of the velocity field v, pressure field p, temperature field E, turbulent kinetic energy k, and dissipation rate ε are calculated respectively. and v n 、p n 、E n , k n and ε U are variables respectively.

[0093] POD is a numerical technique that finds a set of optimal basis functions from a snapshot of the original model solution. The optimal POD basis functions can be used to construct the main characteristic system containing flow and heat transfer in the reactor core. Since the POD basis functions have optimal convergence, only a small number of bases (e.g., 10-200) can be used to capture the main variable changes of large-dimensional processes.

[0094] The truncated singular value decomposition can be decomposed and reduced 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 energy. Select the first M important basis vectors to form an M-dimensional POD subspace, map the original data into this subspace, and obtain the reduced-dimensional data matrix.

[0095] Secondly, the snapshot set and the truncated singular value decomposition method are used to construct the POD basis function and obtain the POD basis function application equation, and the POD basis function application equation is projected to the reduced space, that is, the above-mentioned subspace, to obtain the projection equation. In this embodiment, the projection equation after dimensionality reduction can be expressed as:

[0096]

[0097] The projection equation of the POD basis function is solved by the eigenorthogonal decomposition method to obtain the reduced-order operator:

[0098]

[0099] For the initial conditions:

[0100]

[0101] in, and Indicates that at time step n-1 (n∈{1,2,…,N t}) The solution field v, p, E, k and POD coefficient of ε set, Nt is the number of time steps in the computational simulation.

[0102] Again, radial basis function interpolation uses radial basis functions to fit the interpolation domain through all data points. For a function f:R d →R is defined at N data points where i∈{1,...,N} and the radial basis function φ:R + →R, centered at point Using the Euclidean norm, the interpolation field of f can be defined as follows:

[0103]

[0104] in:

[0105] f(x) is the interpolation function;

[0106] φ is the radial basis function, which depends on the distance between point x and the center point xi

[0107] ω i is the weight coefficient associated with each center point xi;

[0108] N is the number of center points.

[0109] 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 value at a given data point, where the known data value is obtained from the previous snapshot. Determining the weight coefficients is done by solving the following linear system equations:

[0110] Aω=y,

[0111] in:

[0112] A is a matrix consisting of radial basis function values, and its internal elements are:

[0113]

[0114] ω is the weight coefficient vector ω=[ω1,ω2,...,ω N ] T ;

[0115] y is a vector of known data values ​​y = [y1, y2, ..., y N ] T .

[0116] For example, if there are three data points, one might choose a quadratic polynomial as the interpolation function:

[0117] f(x)=a0+a1x+a2x 2 .

[0118] We need to determine a0, a1, a3 so that f(x i )=y i , which is true for all three data points. This gives us three equations that can be used to solve for the three unknown weight coefficients. i is the value of the independent variable, y i is the value of the corresponding dependent variable.

[0119] Finally, radial basis function interpolation and order reduction operators are used to construct the reduced-order model.

[0120] In some implementations, the step of obtaining radial basis function interpolation includes:

[0121] Determine radial basis functions;

[0122] Determine 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;

[0123] The radial basis function interpolation is determined according to the radial basis function and the weight coefficient vector.

[0124] In this implementation, firstly, 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 the prediction of unknown data points, with good prediction ability and high-precision fitting ability.

[0125] In this embodiment, it should be noted that the radial basis function can be a type of function centered at the origin that changes as the distance from the origin increases. The weight coefficient vector can be that in RBF interpolation, each data point has a corresponding weight coefficient, and these weight coefficients are determined by an optimization process to adjust the degree of influence of the RBF at the data point. Radial basis function interpolation can be a method of interpolating data points using radial basis functions, and data values ​​at unknown locations can be predicted based on known data points.

[0126] In one possible implementation, a suitable radial basis function is selected, such as Gaussian φ(r)=e -(r / σ)2, where r is the Euclidean distance and σ is the 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, and these function values ​​are organized into a matrix. The values ​​of the known data points in the snapshot set are then organized into a vector that contains the actual observed values ​​of all data points used for interpolation. Then, a linear system equation Aω=y 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 radial basis function.

[0127] In another feasible implementation, the weight coefficient vector may also be determined by a least square method, a regularization method or other optimization algorithms, and a radial basis function interpolation is constructed using the determined weight coefficient vector and radial basis function.

[0128] For example, the radial basis function can also be obtained in the following way: the RBF network is a weighted linear combination of RBF kernels interpolating scattered data in d-dimensional space. In a deformed grid or a displacement grid, specifically, the quantity to be interpolated is the three-dimensional displacement at the known K surface grid nodes, or usually the three-dimensional displacement at N different source nodes. Define φ as a radial function whose value depends only on the distance between the input and a fixed point c, then Where ||·|| represents the Euclidean distance. Radial functions are often used as a set to form the basis of a function space, so the above function φ(x) is called a radial basis function. How to define a suitable radial basis function φ is very important. Table 1 lists some commonly used radial basis functions, where r is the radius and σ is the shape parameter. There are two main types of standard RBFs, one is infinitely smooth and the other is infinitely smooth except for the center point. As shown in Table 1, type I contains infinitely smooth radial basis functions with infinite differentiability and depends on the shape parameter σ, such as Gaussian (GA), multi-quadratic (MQ), inverse quadratic (IQ) and inverse multi-quadratic (IMQ). Type II is a radial basis that is infinitely smooth except for the center point and is independent of the shape parameter and cannot be infinitely differentiable, such as the thin plate spline.

[0129] Table 1, radial basis function example:

[0130]

[0131] Exemplarily, multiple quadratic radial basis functions are selected:

[0132]

[0133] in, It is the distance defined by the L2 norm, which is the Euclidean norm, σ>0 and σ is the shape parameter used to control the smoothness and width of the function.

[0134] Weight coefficient w v,i ,w p,i ,w E,i ,w k,i and w ε,i is determined to ensure that the interpolation function is at the data set point The value of f v,m , f p,m , f E,m , f k,m and f ε,m Match. Represented as: Aw v,i =f v,i ,Aw p,i =f p,i ,Aw E,i =f E,i ,Aw k,i =f k,i ,Aw ε,i =f ε,i i∈{1,2,…,N}.

[0135] in:

[0136]

[0137] A is the element of the interpolation matrix m,l∈{1,2,…,N}, N is the number of data points.

[0138] The weight coefficients of the radial basis function are then determined by solving the linear system equations:

[0139] (w k,i,j ) j＝1,…,N and (w ε,i,j ) j＝1,…,N .

[0140] In some implementations, the step of applying an equation to the POD basis function to reduce the order to obtain a reduced-order operator includes:

[0141] Projecting the POD basis function application equation to obtain a projection equation of the POD basis function application equation;

[0142] The projection equation of the POD basis function application equation is solved by using the eigenorthogonal decomposition method to obtain a reduced-order operator.

[0143] In this embodiment, the projection equation of the POD basis function application equation is solved by using the eigenorthogonal decomposition method to obtain a reduced-order operator. In this way, the use of the reduced-order operator reduces the demand for computing resources and improves computing efficiency.

[0144] In this embodiment, it should be noted that the POD basis function can be a set of orthogonal modes extracted from the data, which can maximize the variance in the data. The projection equation can be a new equation obtained by projecting the POD basis function application equation into a low-dimensional space through the POD basis function, which describes the evolution of the reactor core system in the main mode. The proper orthogonal decomposition method (POD) can be a statistical method for analyzing multidimensional data sets and extracting orthogonal basis functions that can describe the main characteristics of the data. The reduced-order operator can be an operator in the reduced-order model obtained by solving the projection equation based on the proper orthogonal decomposition method, which describes the main dynamics of the flow heat transfer in the reactor core after the order reduction. By reducing the order, the complexity of the calculation can be reduced while retaining the main characteristics of the flow heat transfer.

[0145] In one feasible implementation, first, determine the POD basis function set of the flow heat transfer state of the reactor core, which are the main modes extracted from the snapshot data of the flow heat transfer state of the reactor core. Then, the POD basis function application equations are projected onto these basis functions to obtain the projection equations. The projection equations are solved in a low-dimensional space. By solving the projection equations, an operator that describes the evolution of the flow heat transfer of the reactor core in the POD basis function space can be obtained, that is, a reduced-order operator. This operator can be used to predict the future behavior of the flow heat transfer state of the reactor core or the response under different conditions.

[0146] In another feasible implementation, the POD basis function application 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 corresponding relationship between the POD basis function application equation and the projection equation.

[0147] In some implementations, the step of obtaining the snapshot set includes:

[0148] Acquiring a porous medium correlation equation of the reactor core, wherein the porous medium correlation equation is used to determine a flow heat transfer state of the reactor core;

[0149] Inputting the boundary conditions of the reactor core into the porous medium related equations;

[0150] Discretizing the porous medium related equations inputting the boundary conditions to obtain a full-order model;

[0151] The full-order model is solved to obtain the snapshot set.

[0152] In this embodiment, the porous medium-related equations of the boundary conditions of the input reactor core are discretized to obtain a full-order model, and a 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 working conditions. In this way, through accurate flow and heat transfer analysis, possible overheating or insufficient cooling can be predicted and prevented, thereby improving the safety of the reactor.

[0153] In this embodiment, it should be noted that the porous medium related equations can be equations used to describe the flow and heat transfer behavior of the fluid in the porous medium. The porous medium related equations include 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 after the porous medium source term is updated, and the updated conjugate heat transfer model can be obtained by combining the porous medium and the conjugate heat transfer model. Boundary conditions can be mathematical conditions that describe the behavior of physical phenomena (velocity, pressure, internal energy, turbulent pulsation, and dissipation rate) on the boundary, and boundary conditions can be supplementary conditions required for solving partial differential equations. Discretization can be a step in numerical analysis, involving converting continuous equations into discrete forms for solving. A full-order model can be a model that includes all possible physical phenomena and details. A snapshot set can be a collection of reactor core flow and heat transfer states recorded at different times or under different conditions in a numerical simulation.

[0154] In one feasible implementation, it is necessary to determine the porous media correlation equations of the reactor core, which can describe the flow and heat transfer characteristics of the fluid in the porous medium. The boundary conditions of the reactor core are input into the porous media correlation equations, which include the velocity, pressure, internal energy, turbulent pulsation and dissipation rate at the inlet and outlet. The porous media correlation equations of 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 state inside the reactor core. After solving the full-order model, a series of snapshots describing the state of the reactor core can be obtained, which can be used to analyze and verify the performance of the reactor core under different operating conditions.

[0155] In another feasible implementation manner, a snapshot set describing the state of the reactor core is obtained by artificially setting data points of the state of the reactor core.

[0156] Exemplarily, the step of obtaining the snapshot set can be described by two steps: Step 1, the porous medium related equations include updating the flow model, updating the conjugate heat transfer model, and the equations in the turbulence 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.

[0157] Then the equation corresponding to the continuity equation of thermal hydraulic flow can be expressed as:

[0158]

[0159] Here, γ is the permeability.

[0160] The equation corresponding to the momentum equation for coolant flow can be expressed as:

[0161]

[0162] Where P is the pressure, is the stress tensor of the fluid, is the gravitational body force term, and F is the external body force term; the equation corresponding to the conjugate heat transfer model can be expressed as:

[0163]

[0164] Among them, λ eff represents the effective thermal diffusivity or effective thermal conductivity, represents the effective viscous stress tensor, S e Represents the volume energy source term.

[0165] The equations in the turbulence model can be expressed as:

[0166] CFD simulation can provide a variety of turbulence models, such as 0-equation model, two-equation model (standard k-ε model, RNGk-ε model, k-ω model, k-ωSST model, etc.), Reynolds stress model (RSM) and large eddy model (LES). This embodiment adopts k-ε turbulence model, and the equations of turbulent kinetic energy k and dissipation rate ε are:

[0167]

[0168] Where ρ represents the density of the fluid, k represents the turbulent kinetic energy, ε represents the turbulent dissipation rate, t represents the time, and x i Represents spatial coordinates, and the subscript i represents the three spatial directions x, y, z, and u i represents the fluid velocity at x i The component in the direction, μ represents the dynamic viscosity of the fluid, P k represents the turbulent kinetic energy generated by the laminar velocity gradient, P ε represents the turbulent dissipation caused by the laminar velocity gradient, P kb represents the turbulent kinetic energy generated by buoyancy, P εb represents the turbulent dissipation caused by buoyancy, S k is a custom source term, μ t represents the turbulent viscosity coefficient, C ε1 , C ε2 and σk , σ z is a constant;

[0169] Step 2: Identify the porous media related equations and the required boundary conditions, and numerically discretize the porous media related equations of the input boundary conditions to generate a full-order model. The full-order model consists of discrete control equations. The discrete control equations at different time steps n∈{1,2,…,N} are:

[0170] The discretization of the variables in the equation at different time steps n can be written in the general form, where:

[0171]

[0172]

[0173] The general process of the finite volume method in numerical simulation includes the discretization of space and time, and the solution of nonlinear equations. That is, in this embodiment, the computational domain Ω is divided into non-overlapping units Ωi (i = 1, ..., N), and the volume of each unit is Vi. The control equation is integrated in each unit, and the solution is assumed to be constant inside the unit and on the boundary, and solved by an iterative method. The time discretization uses the implicit Euler method, and the nonlinear terms are handled by fixed point iteration.

[0174] 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 in turbulence and turbulent dissipation. A full-order model is simulated once to obtain a set of snapshots.

[0175] In some embodiments, the step of obtaining the porous medium correlation equation of the reactor core includes:

[0176] Obtaining a flow model, a conjugate heat transfer model, and a turbulence model of the reactor core;

[0177] Acquire a source term of the porous medium, and update the flow model according to the source term to obtain an updated flow model;

[0178] According to the porous medium and the conjugate heat transfer model, an updated conjugate heat transfer model is obtained;

[0179] Wherein, the porous medium related equations include the updated flow model, the updated conjugate heat transfer model and the turbulence model.

[0180] In this embodiment, the porous medium model is obtained by updating the updated flow model, updating the conjugate heat transfer model and creating the turbulence 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 flow direction of the coolant can be predicted and controlled. 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 turbulence model can be used to describe the turbulent phenomenon in the fluid flow, which can affect the accuracy and computational cost of the simulation. The safety of the reactor can be improved through accurate flow and heat transfer simulation. At the same time, updating the flow model, the conjugate heat transfer model and the turbulence model can also help evaluate the performance of the reactor under different conditions.

[0181] In this embodiment, it should be noted that the flow model can be a mathematical model used to describe the flow characteristics of the fluid under different conditions. The conjugate heat transfer model can be a heat exchange phenomenon between the fluid and the solid interface that is considered when calculating the fluid flow. The conjugate heat transfer model is usually used to simulate heat transfer problems involving the interaction between solids and fluids. The turbulence model can be a mathematical model used to describe turbulent phenomena in fluid flow. Turbulence is a disordered and irregular flow state in fluid motion. The source term of the porous medium can be in the porous medium flow model, and the source term can be an internal factor that can affect the fluid flow and heat transfer, such as friction between the fluid and the porous medium skeleton, inertial effects, and energy changes caused by chemical reactions or heat sources. The porous medium related equations can be a set of mathematical equations that describe the flow and heat transfer behavior of the fluid in the porous medium.

[0182] In one feasible implementation, first, it is necessary to establish a flow model, a conjugate heat transfer model, and a turbulence model for reactor core analysis. Source terms of porous media, such as resistance and heat source terms, are introduced into the flow model to reflect the influence of porous media on fluid flow. The introduction of source terms can update the flow model to more accurately describe the actual situation inside the core. Combining the characteristics of porous media and the conjugate heat transfer model, the conjugate heat transfer model is updated to more accurately simulate the heat exchange process between solids and fluids. The updated flow model, conjugate heat transfer model, and turbulence model are combined to form a complete set of porous media related equations, which can fully describe the flow and heat transfer state inside the reactor core.

[0183] In another feasible implementation, a flow model, a conjugate heat transfer model and a turbulence model for reactor core analysis are established, and then the porous medium related equations are obtained by querying a preset mapping table. The preset mapping table 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 equations.

[0184] For example, before establishing the flow model, conjugate heat transfer model and turbulence model for reactor core analysis, that is, before establishing the reactor core thermal-hydraulic and heat transfer calculation modules, it is necessary to first establish the flow and heat transfer geometric model of the reactor core assembly: import the geometric model of the reactor assembly into the mesh generation software for meshing, and form a numerical calculation mesh model of the reactor assembly suitable for thermal-hydraulic analysis and heat transfer calculation.

[0185] Then, in the computational fluid dynamics software, the reactor core thermal hydraulic and heat transfer calculation module is established, considering the flow conditions of the coolant and the conjugate heat transfer between the coolant and the fuel rods. The established thermal analysis calculation module includes the coolant flow model, turbulence model and conjugate heat transfer model. The steps are as follows:

[0186] The equation corresponding to the coolant flow model is:

[0187] 1) Under normal operating conditions of the reactor, the flow condition of the coolant inside the primary core is a unidirectional flow and a turbulent flow, and the continuity equation of its thermal hydraulic flow is:

[0188]

[0189] Where: l represents the coolant; ρ l is the coolant density, vector is the coolant velocity field;

[0190] 2) The momentum equation of coolant flow can be described by the incompressible Navier-Stokes equations:

[0191]

[0192] Where: p represents the pressure in the grid control volume, μ represents the dynamic viscosity of the coolant, and f represents the body force source term, such as gravity, buoyancy, etc.;

[0193] The equation of the turbulence model is as described above and will not be repeated in this embodiment.

[0194] 3) The conjugate heat transfer model includes the energy conservation control equation of the coolant and the temperature control equation in the solid domain. The energy conservation control equation of the coolant is:

[0195]

[0196] Where, ρ represents the density of the coolant, E represents the total energy of the coolant, P represents the coolant pressure, T represents the temperature, k eff represents the effective heat transfer coefficient, J j′ represents the diffusion flow rate of coolant j'; h j′ represents the enthalpy of the jth component; τ ijrepresents the ij component of the stress tensor, S h Represents a user-defined volume heat source;

[0197] The temperature control equation for the solid region including the fuel pellets and cladding is:

[0198]

[0199] Where the subscript s represents the solid area, ρ s is the solid domain density, c p is the constant pressure specific heat capacity at pressure p, T s is the temperature of the solid region, k eff is the thermal conductivity of the solid region, q″ s is the volume heat release rate of the solid area;

[0200] The heat transfer equations for the fluid and solid regions are solved by coupling the temperature and heat flux variables at the solid / fluid interface.

[0201] After establishing the thermal analysis calculation module, define the source term of the porous medium and construct the porous medium related equations.

[0202] Define the source term of porous media, source term S m The expressible forms are as follows:

[0203]

[0204] Where D and F represent the viscosity tensor and inertia tensor of the Darcy-Forchheimer equation (Darcy-Forchheimer), respectively. represents the velocity vector The dot product of the trace of (i.e., the scalar magnitude of velocity) and the unit tensor;

[0205] The values ​​inside the tensor are either estimated based on the problem being solved or directly input by the user in order to obtain the desired porosity effect within the computational domain. The source term is in the form of a drag force and appears negative as the core fluid flow moves from a higher pressure regime to a lower pressure regime.

[0206] The coolant fluid flow in the core is turbulent, Re>10 5 . For the rod bundles in the reactor core, the fluid viscosity loss is very small and can be ignored. Because the core assembly rod bundle is different from the typical porous medium with interconnected pores, the pressure drop caused by the coolant turbulence in the reactor core assembly is in a range where the inertial force dominates the problem physics relative to the viscous force. Therefore, the viscosity tensor D of the Darcy-Forchheimer model can be ignored, and the only source term left is the inertia tensor F. The equation can be expressed as:

[0207]

[0208] For ordinary two-dimensional problems, the tensor is a square matrix with 4 components. The vector form of the force is defined as:

[0209]

[0210] Where V is the volume of the porous medium, and Fx and Fy are coefficients in the inertia tensor. The dependence of the force on the flow direction can be expressed by an explicit velocity component in the form of:

[0211]

[0212] The last vector in the above formula also represents:

[0213]

[0214] θ represents the angle between the coolant flow direction and the rod bundle direction. The equation can be expressed as:

[0215]

[0216] Similarly, the three-dimensional problem can be expressed as:

[0217]

[0218] In some embodiments, the equation of the reduced-order model can be expressed as:

[0219]

[0220] and (where j∈{1,2,…,M}) represents the POD coefficient at time step n; and Indicates that at time step n-1 (n∈{1,2,…,N t}) The solution field v, p, E, k and POD coefficient of ε set; N t represents the number of time steps in the computational simulation; φ(r i ) represents the radial basis function, whose value depends on the distance from the data set point (where i∈1,2,…,N); w v,i,j ,w p,i,j ,w E,i,j ,w k,i,j and w ε,i,j represents the weight coefficient (where j∈{1,2,…,M}), where M represents the number of POD basis functions.

[0221] See also Figure 2 , is another flow diagram of the reactor core flow heat transfer analysis method provided by the embodiment of the present application. The embodiment of the present application first determines the problem (control equations and variables), the control equations include porous media related equations, and the variables include velocity, pressure, internal energy, turbulent pulsation and dissipation rate, and then enters the offline / training stage (high cost) and the online / evaluation stage (low cost). The offline / training state includes creating a full order model (Full Order Model, FOM), using the full order model to simulate the problem object, and constructing a reduced order operator. The online / evaluation stage includes assembling a reduced order model (Reduced Order Model, ROM) from the reduced order operator, solving the reduced order model, and evaluating the amount of interest.

[0222] The contents of the offline / training phase and the online / evaluation phase correspond to discretizing the porous media-related equations for the input boundary conditions to obtain a full-order model. Solve the full-order model to obtain a snapshot set. Using the snapshot set and the truncated singular value decomposition method, construct the POD basis function and obtain the POD basis function application equation, and reduce the order of the POD basis function application equation to obtain a reduced-order operator. Obtain radial basis function interpolation, which is obtained by fitting the interpolation domain through known data points using radial basis functions. Use radial basis function interpolation and reduced-order operators to construct a reduced-order model. Obtain the first information of the reactor core, and input the first information into the reduced-order model to obtain the second information of the reactor core at each time step. Input the second information of the reactor core at each time step into the POD basis function application equation respectively, and obtain the flow and heat transfer analysis results of the reactor core at each time step, that is, the evaluation focus. It should be noted that the construction of a reduced-order model has already been done in the construction of a reduced-order operator in the offline / training phase.

[0223] See also Figure 3 , is a schematic diagram of the structure of a reactor core flow heat transfer analysis device provided in an embodiment of the present application. In a second aspect of an embodiment of the present application, a reactor core flow heat transfer analysis device 30 is provided. The device 30 includes:

[0224] An acquisition model module 31 is used 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 characterize the flow and heat transfer state of the reactor core under different operating conditions;

[0225] An information acquisition module 32 is used 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 turbulence pulsation coefficient, and an initial dissipation rate coefficient;

[0226] An information obtaining module 33 is used 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 a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulence pulsation coefficient and a target dissipation rate coefficient;

[0227] A result obtaining module 34 is used to input the second information of the reactor core at each time step into the POD basis function application equation respectively, to obtain the flow 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 heat transfer analysis result includes solutions of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

[0228] The reactor core flow heat transfer device 20 provided in the second aspect of the embodiment of the present application can implement each process implemented in the above-mentioned method embodiment and achieve the same beneficial effects. To avoid repetition, it will not be described here.

[0229] See also Figure 4 , is a structural diagram of an electronic device provided in an embodiment of the present application. The third aspect of an embodiment of the present application provides an electronic device 4000, including a processor 4100 and a memory 4200, the memory 4200 stores machine executable instructions that can be executed by the processor 4100, and the processor 4100 can execute the machine executable instructions to implement the above-mentioned nuclear reactor core control method.

[0230] A fourth aspect of an embodiment of the present application provides a computer-readable storage medium, on which instructions are stored. When the instructions are executed by a processor, the processor implements the above-mentioned reactor core flow heat transfer analysis method.

[0231] In some embodiments, the embodiments of the present application also provide a computer program product, including a computer program, which, when executed by a processor, implements the reactor core flow heat transfer analysis method according to the above-mentioned embodiment.

[0232] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0233] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0234] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0235] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0236] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. 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 technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0237] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0238] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

[0239] In addition, various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A reactor core flow heat transfer analysis method, characterized in that: The method comprises the following steps: 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 characterize the flow and heat transfer state of the reactor core under different operating conditions; Acquiring 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 turbulence pulsation 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 includes a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulence pulsation coefficient, and a target dissipation rate coefficient; The second information of the reactor core at each time step is respectively input into the POD basis function application equation to obtain the flow 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 heat transfer analysis result includes solutions of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

2. The method according to claim 1, characterized in that The step of obtaining the reduced-order model corresponding to the reactor core comprises: Obtaining the snapshot set; Using the snapshot set and a truncated singular value decomposition method, a POD basis function is constructed and an application equation of the POD basis function is obtained; Applying equations to the POD basis functions to perform order reduction processing to obtain a reduced-order operator; Obtaining a radial basis function interpolation, wherein the radial basis function interpolation is obtained by fitting an interpolation domain through known data points using a radial basis function; The reduced-order model is constructed by using the radial basis function interpolation and the reduced-order operator.

3. The method according to claim 2, characterized in that The steps to obtain radial basis function interpolation include: Determine radial basis functions; Determine 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; The radial basis function interpolation is determined according to the radial basis function and the weight coefficient vector.

4. The method according to claim 2, characterized in that The step of applying an equation to the POD basis function to reduce the order 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; The projection equation of the POD basis function application equation is solved by using the eigenorthogonal decomposition method to obtain a reduced-order operator.

5. The method according to claim 2, characterized in that The step of obtaining the snapshot set comprises: Acquiring a porous medium correlation equation of the reactor core, wherein the porous medium correlation equation is used to determine a flow heat transfer state of the reactor core; Inputting the boundary conditions of the reactor core into the porous medium related equations; Discretizing the porous medium related equations inputting the boundary conditions to obtain a full-order model; The full-order model is solved to obtain the snapshot set.

6. The method according to claim 5, characterized in that 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 turbulence model of the reactor core; Acquire a source term of the porous medium, and update the flow model according to the source term to obtain an updated flow model; According to the porous medium and the conjugate heat transfer model, an updated conjugate heat transfer model is obtained; Wherein, the porous medium related equations include the updated flow model, the updated conjugate heat transfer model and the turbulence model.

7. The method according to claim 1, characterized in that The reduced order model includes the following equations: and (where j∈{1,2,…,M}) represents the POD coefficient at time step n; and Indicates that at time step n-1 (n∈{1,2,…,N t }) The solution field v, p, E, k and POD coefficient of ε set; N t represents the number of time steps in the computational simulation; φ(r i ) represents the radial basis function, the value of which depends on the distance from the data set point (where i∈1,2,…,N); w v,i,j ,w p,i,j ,w E,i,j ,w k,A,j and w ε,i,j represents the weight coefficient (where j∈{1,2,…,M}), where M represents the number of POD basis functions.

8. A reactor core flow heat transfer analysis device, characterized in that: The device comprises: An acquisition model module is used 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 characterize the flow and heat transfer state of the reactor core under different operating conditions; An information acquisition module, 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 turbulence pulsation coefficient, and an initial dissipation rate coefficient; an information 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 includes a target velocity coefficient, a target pressure coefficient, a target internal energy coefficient, a target turbulence pulsation coefficient, and a target dissipation rate coefficient; A result obtaining module is used to input the second information of the reactor core at each time step into the POD basis function application equation respectively, to obtain the flow 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 heat transfer analysis result includes the solution of velocity, pressure, internal energy, turbulent pulsation and dissipation rate.

9. An electronic device, characterized in that: include: a memory configured to store instructions; as well as A processor is configured to call the instructions from the memory and implement the reactor core flow heat transfer analysis method according to any one of claims 1 to 7 when executing the instructions.

10. A computer-readable storage medium storing instructions, characterized in that: When the instructions are executed by a processor, the reactor core flow and heat transfer analysis method according to any one of claims 1 to 7 is implemented.

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