Reactor core thermal hydraulic numerical solution method and system based on data assimilation

Abstract

The invention provides a data assimilation-based reactor core thermal-hydraulic numerical solution method and system, and the method comprises the steps: building a control equation set according to a to-be-analyzed thermal-hydraulic problem, carrying out the sealing and discretization processing, and forming a complete linear control equation set; determining a solving area; establishing data transmission modes of different-scale thermal hydraulic methods; selecting a data assimilation algorithm and a CFD (computational fluid dynamics) algorithm according to the thermal hydraulic problem to be analyzed, and performing joint calculation; judging whether iteration meets a convergence requirement or not; if the CFD simulation data and / or experimental data in the current time layer exist, updating a prior covariance matrix of the temperature and the speed to obtain a posterior covariance matrix; and judging whether the numerical solution process is finished or not. According to the method, observation information of different sources and different resolutions can be fused, rapid thermal hydraulic calculation is carried out on the reactor core, the coolant flow and heat exchange model prediction capacity is improved, and the precision of the fine lattice cell sub-channel calculation method is improved.

Description

Technical Field

[0001] The invention relates to the technical field of reactor thermal hydraulic design, and in particular to a method and system for numerically solving core thermal hydraulics based on data assimilation. Background Art

[0002] The purpose of reactor thermal hydraulic design is to clarify the core's heat transfer capacity and coolant flow characteristics, and to ensure that the heat generated by the reactor core can be safely and reliably removed through the coolant. In order to ensure the safety and economy of the reactor, it is necessary to understand the changes in its thermal hydraulic parameters and ensure that the thermal parameters do not exceed the design limits of the thermal design criteria. At present, the core thermal hydraulic calculation and analysis methods mainly include single-channel analysis method, sub-channel analysis method and computational fluid dynamics (CFD) analysis method.

[0003] Low-resolution and medium-resolution thermal-hydraulic analysis methods represented by the subchannel analysis method are currently the reference tools for rapid core thermal-hydraulic analysis and safety review. However, when using this type of analysis method for thermal-hydraulic analysis, a large number of coolant flow and heat transfer models are required to describe the flow and heat transfer behavior of the core coolant in order to make the control equations closed and solvable. The coolant flow and heat transfer models used are mostly empirical correlations obtained through experiments, and their applicability to thermal-hydraulic calculations under different boundary conditions and different operating conditions is also different, which makes the numerical calculation results of local thermal-hydraulic parameters generally have great uncertainty and error. On the other hand, computational fluid dynamics (CFD) methods have become tools for refined thermal-hydraulic calculation analysis and design of reactor cores because they can simulate complex thermal-hydraulic phenomena with high resolution. However, its main limitation is that even if there are sufficient computing resources, CFD still takes a long time to perform thermal-hydraulic calculations on large core basins, which is difficult to meet the requirements of engineering applications.

[0004] In order to comprehensively utilize the advantages of the two different analysis methods, domestic and foreign scholars have proposed a variety of thermal hydraulic multi-scale coupling calculation methods, such as regional decomposition method and regional overlap method. However, they have problems such as high data transmission complexity, low calculation stability, high algorithm convergence difficulty, and low calculation time economy.

[0005] In view of the characteristics of the above two different thermal-hydraulic analysis methods and the shortcomings of the existing thermal-hydraulic multi-scale coupling method, it is urgent to provide a more complete core thermal-hydraulic numerical solution method to overcome at least one technical problem existing in the prior art. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for numerical solution of core thermal hydraulics based on data assimilation. On the basis of considering the simulation field obtained by medium and low resolution thermal hydraulic analysis methods and the simulation field or (and) experimental measurement field errors obtained by high-precision CFD methods, the observation information from different sources and different resolutions is integrated to perform rapid thermal hydraulic calculations on the core, improve the prediction capability of coolant flow and heat transfer models, and enhance the accuracy of fine gate element sub-channel calculation methods.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for numerically solving core thermal hydraulics based on data assimilation comprises the following steps:

[0009] S1, according to the thermal hydraulic problem to be analyzed, a control equation group is established, and the control equation group is closed and discretized to form a complete linear control equation group for numerical solution, wherein the complete linear control equation group includes a mass conservation equation, an energy conservation equation, and a momentum conservation equation;

[0010] S2, determine the solution area according to the geometric structure of the object to be analyzed and the thermal hydraulic problem;

[0011] S3, establish data transfer methods for thermal-hydraulic methods of different scales according to the type of observation data and the thermal-hydraulic calculation method used;

[0012] S4, according to the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected, and joint calculations are performed to obtain the core thermal-hydraulic values ​​of the solution area, wherein the data assimilation algorithm is a data assimilation algorithm with a prediction-correction two-step structure, and the CFD algorithm is a CFD algorithm with a solution-correction two-step structure;

[0013] S5, iteratively updating the core thermal hydraulic values ​​in the solution area and judging whether the iteration meets the convergence requirement, if not, repeating step S4 until the convergence requirement is met;

[0014] S6, if CFD simulation data and / or experimental data in the current time layer exist, then updating the prior covariance matrix of temperature and velocity to obtain a posterior covariance matrix;

[0015] S7, based on the set conditions, determine whether the numerical solution process is completed. If so, output the core thermal hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

[0016] Furthermore, the S1, according to the thermal hydraulic problem to be analyzed, establishes a control equation group, closes and discretizes the control equation group, and forms a complete linear control equation group for numerical solution, specifically including:

[0017] According to the boundary conditions and initial conditions of the thermal-hydraulic problem to be analyzed, a group of control equations describing the thermal-hydraulic phenomena is established. The coolant flow and heat transfer model is used to close the group of control equations. The group of control equations is discretized using space and time discrete formats to obtain a complete linear group of control equations for numerical solution.

[0018] Furthermore, the step S2, determining the area to be solved according to the geometric structure of the object to be analyzed and the thermal hydraulic problem, specifically includes:

[0019] According to the thermal-hydraulic problem to be analyzed, the solution area to be calculated using the data assimilation algorithm is divided, and the divided solution area is the overall solution domain or a partial area of ​​the thermal-hydraulic problem to be analyzed.

[0020] Furthermore, the S3, according to the type of observation data and the thermal hydraulic calculation method used, establishes a data transmission method of thermal hydraulic methods of different scales, specifically including:

[0021] For the data obtained by CFD simulation, experimental measurement data or actual operation data of the unit, which have different data sizes, data sources and data resolutions, data transmission methods of thermal-hydraulic methods at different scales are established to realize data transmission in time and space.

[0022] Further, the S4, according to the thermal hydraulic problem to be analyzed, selects a data assimilation algorithm and a CFD algorithm, and performs joint calculations to obtain the core thermal hydraulic values ​​of the solution area, specifically including:

[0023] S41, according to the boundary conditions and initial conditions of the thermal hydraulic problem to be analyzed, setting the initial values ​​of various physical field parameters in the physical field of the solution area under steady-state conditions or transient conditions of the reactor system;

[0024] S42, using the time marching method to solve the transient physical field of the outer layer, updating the solution on each time layer and judging whether the numerical solution time has ended;

[0025] S43, in each time layer, solving the energy conservation equation to obtain a predicted value of the temperature of the coolant, assembling and solving the linearized momentum conservation equation to obtain a predicted value of the speed of the coolant;

[0026] S44, calculating a velocity priori covariance matrix and a temperature priori covariance matrix of the current time layer according to the velocity transfer matrix and the temperature transfer matrix in the current time layer;

[0027] S45, determining whether there is observation data in the solution area, wherein the observation data includes at least one of CFD simulation data and experimental measurement data; if not, performing the numerical calculation process of the selected CFD algorithm to solve the interface flow velocity of the control body without performing the thermal hydraulic calculation based on the selected data assimilation algorithm; if yes, performing the thermal hydraulic calculation based on the selected data assimilation algorithm to solve the interface flow velocity of the control body without performing the numerical calculation process of the selected CFD algorithm;

[0028] S46, assembling and solving the mass conservation equation using the interface flow velocity to obtain a pressure correction value;

[0029] S47, using the pressure correction value to correct the pressure and velocity, and using the corrected pressure field and velocity field to update the flow velocity at the interface of the control volume using Rhie-Chow interpolation.

[0030] Furthermore, in S45, the numerical calculation process of the selected CFD algorithm includes:

[0031] The velocity prediction value is used to solve the control volume interface flow velocity through Rhie-Chow interpolation.

[0032] Furthermore, in S45, the thermal hydraulic calculation based on the selected data assimilation algorithm includes:

[0033] S4501, calculating the velocity Kalman gain and the temperature Kalman gain in the current time layer taking into account the measurement error according to the velocity prior covariance matrix and the temperature prior covariance matrix, the velocity transfer matrix and the temperature transfer matrix in the current time layer;

[0034] S4502, updating the velocity field and the temperature field according to the calculated Kalman gain, the velocity prediction value and the temperature prediction value, and obtaining a gain velocity prediction value and a gain temperature prediction value;

[0035] S4503, using the gain velocity prediction value, solve the control volume interface flow velocity through Rhie-Chow interpolation.

[0036] Furthermore, the step S5 iteratively updates the core thermal hydraulic values ​​in the solution area and determines whether the iteration meets the convergence requirement. If not, repeat step S4 until the convergence requirement is met. Specifically, the step S5 includes:

[0037] Iteratively update the obtained gain temperature prediction value and gain speed prediction value and determine whether the iteration meets the convergence requirement;

[0038] If the convergence requirements are met, exit the loop and proceed to step S6 to update the time layer. If the convergence requirements are not met, assign the gain speed prediction value and the gain speed prediction value to the speed prediction value and the temperature prediction value, and return to step S4502 for a new round of loop until the convergence requirements are met.

[0039] Furthermore, the step S7, based on the set conditions, determines whether the numerical solution process is finished, specifically includes:

[0040] It is determined whether the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, the converged velocity field, velocity field and pressure field obtained in the current time layer are assigned as the initial field to the next time layer, and the process returns to step S43 to start a new time layer cycle.

[0041] Otherwise, the numerical solution process is terminated, and the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field are output.

[0042] The present invention also provides a core thermal hydraulic numerical solution system based on data assimilation, which is used to execute the above-mentioned core thermal hydraulic numerical solution method based on data assimilation, comprising:

[0043] A control equation group construction module is used to establish a control equation group according to the thermal hydraulic problem to be analyzed, close and discretize the control equation group, and form a complete linear control equation group for numerical solution, wherein the complete linear control equation group includes a mass conservation equation, an energy conservation equation, and a momentum conservation equation;

[0044] A solution region determination module is used to determine the solution region according to the geometric structure of the object to be analyzed and the thermal hydraulic problem;

[0045] The data transfer equation establishment module is used to establish data transfer methods of thermal hydraulic methods of different scales according to the type of observation data and the thermal hydraulic calculation method used;

[0046] An algorithm selection module is used to select a data assimilation algorithm and a CFD algorithm according to the thermal hydraulic problem to be analyzed, and perform joint calculations to obtain the core thermal hydraulic values ​​of the solution area, wherein the data assimilation algorithm is a data assimilation algorithm with a prediction-correction two-step structure, and the CFD algorithm is a CFD algorithm with a solution-correction two-step structure;

[0047] A convergence judgment module is used to iteratively update the core thermal hydraulic values ​​in the solution area and judge whether the iteration meets the convergence requirements;

[0048] The observation data judgment module is used to judge whether there is CFD simulation data and / or experimental data in the current time layer. If so, the prior covariance matrix of temperature and velocity is updated to obtain the posterior covariance matrix;

[0049] The solution completion judgment module is used to judge whether the numerical solution process is completed based on the set conditions. If so, it outputs the core thermal hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

[0050] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0051] (1) The present invention uses a data assimilation method to enable high-resolution CFD calculation methods and medium- and low-resolution thermal-hydraulic calculation methods, two different-scale thermal-hydraulic calculation methods, to exchange and fuse data during the solution process. Compared with the traditional coupling method, this method has a simple calculation process, low data transfer complexity, high calculation stability, low algorithm convergence difficulty, and high calculation time economy; it supports thermal-hydraulic calculation analysis based on the data assimilation algorithm for reactor types containing open fuel assemblies. This method supports the joint solution of multi-scale thermal-hydraulic calculation methods, which can solve the problems of high data transfer complexity, low calculation stability, high algorithm convergence difficulty, and low calculation time economy in the existing multi-scale thermal-hydraulic coupling method;

[0052] (2) The present invention integrates data from different sources and resolutions into the numerical solution process, reducing the errors and uncertainties introduced by direct modeling of complex thermal-hydraulic phenomena (such as turbulent mixing and directional crossflow). Compared with the use of thermal-hydraulic calculation methods with medium and low resolutions alone, this method can improve the accuracy of numerical calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0054] Figure 1 It is a schematic diagram of a flow chart of a core thermal hydraulic numerical solution method based on data assimilation according to an embodiment of the present invention;

[0055] Figure 2 Schematic diagram of the solution region division for applying the data assimilation algorithm according to an embodiment of the present invention, wherein (a) is the overall solution domain and (b) is the local area of ​​interest. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] As stated in the background technology, the sub-channel analysis method has the characteristics of low fidelity and can quickly perform thermal and hydraulic calculations and analysis. The CFD method can provide a detailed description of complex flow and heat transfer phenomena in the core, but it requires a long calculation time. The existing multi-scale coupling methods have problems such as high data transmission complexity, low calculation stability, high algorithm convergence difficulty, and low calculation time economy.

[0058] In view of the characteristics of the above-mentioned two different-scale thermal-hydraulic analysis methods and the shortcomings of the existing thermal-hydraulic multi-scale coupling methods, the present invention, on the basis of considering the errors of the simulation field obtained by the medium and low resolution thermal-hydraulic analysis method and the simulation field or (and) the experimental measurement field obtained by the high-precision CFD method, integrates observation information from different sources and different resolutions to use a multi-scale thermal-hydraulic calculation method to perform rapid thermal-hydraulic calculations on the core, improve the prediction capability of the coolant flow and heat transfer model, and enhance the accuracy of the medium and low resolution thermal-hydraulic analysis method.

[0059] The present invention provides a core thermal hydraulic numerical solution method based on data assimilation, which is used to solve the technical problems in the prior art.

[0060] The present invention integrates observation information from different sources and with different resolutions, taking into account the errors of simulated fields obtained by medium and low resolution thermal-hydraulic analysis methods and simulated fields or (and) experimental measurement fields obtained by high-precision CFD methods, and uses a thermal-hydraulic calculation method based on data assimilation to perform rapid thermal-hydraulic calculations on the core, thereby improving the prediction capabilities of coolant flow and heat transfer models and enhancing the accuracy of fine gate element sub-channel calculation methods.

[0061] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] like Figure 1 As shown, the core thermal hydraulic numerical solution method based on data assimilation provided by the present invention includes the following steps:

[0063] S1. Analyze the core type and solution scale. According to the boundary conditions and initial conditions of the thermal hydraulic problem to be analyzed, establish the control equations describing the thermal hydraulic phenomena. Use the coolant flow and heat transfer model to close the control equations. Use the space and time discrete format to discretize the control equations to obtain a complete linear control equation for numerical solution. Specifically, it may include:

[0064] Step S11: According to the core type, boundary conditions and initial conditions, a control equation group describing the thermal hydraulic phenomenon is established. The core type that can be numerically simulated by this method is an open channel reactor without box wall components, such as a pressurized water reactor, a sodium-cooled fast reactor, a lead-bismuth fast reactor, etc.

[0065] Taking the analysis of the fine grid element subchannel of the pressurized water reactor core and the establishment of the three-dimensional fine grid element subchannel control equation group as an example, the following is explained:

[0066] The mass conservation equation:

[0067]

[0068] Momentum conservation equation:

[0069]

[0070] Energy conservation equation:

[0071]

[0072] Where, symbol ρ is the density of the coolant, unit: kg / m 3 ; Symbols u, v, w are the speed of the coolant in the x, y, z directions respectively, unit: m / s; symbol p is the pressure, unit: Pa; symbol g x , g y , g z They are the gravitational acceleration in the x, y, and z directions, in m / s 2 ; Symbol T is the temperature of the coolant, unit: K; Symbol k represents the thermal conductivity, unit: W / (m·K); Symbol M Mx 、M My 、M Mz are the turbulent mixing quantities of momentum in the x, y, and z directions, respectively, in kg / (m·s); symbol M E is the energy of turbulent mixing, unit: J / (m 2 ·s); symbol S Mx , S My , S Mz The momentum sources in the x, y, and z directions are formed by friction and form resistance pressure drop introduced by the fuel bundle, assembly box wall, and spacer grid, respectively. Unit: kg / (m 2 ·s 2); symbol S E is the energy source term, unit: J / (m 3 ·s).

[0073] Step S12: Close the control equation group and discretize it to obtain a complete linear control equation group.

[0074] S in the control equation M , S E 、M M 、M E They all need to be described using flow and heat transfer models to form a closed set of control equations. By discretizing the closed set of control equations, a complete set of linear control equations that can ultimately be solved numerically can be obtained.

[0075] The selection of coolant flow and heat transfer models is explained using the PWR lateral flow resistance coefficient model and the cladding surface heat transfer model.

[0076] The lateral flow resistance coefficient f in the rod bundle area can be calculated using the Gaddis-Gnielinski correlation, which is expressed as follows:

[0077]

[0078] Among them, f l is the influence factor of laminar flow on flow resistance, dimensionless; f t is the factor affecting turbulence on flow resistance, dimensionless.

[0079] Convective heat transfer coefficient between fuel rod surface and coolant h c The following model can be used for calculation:

[0080]

[0081] Where: λ is the thermal conductivity of the coolant, unit: W / (m·K); D e It is the equivalent hydraulic diameter, in m.

[0082] The resulting complete set of linear temperature and speed control equations has the following form:

[0083]

[0084] Among them, the superscript "0" represents the value of the previous time step; dimensionless; a represents the coefficient of the coefficient matrix, dimensionless; φ represents flux, which can represent temperature T, unit: K. When representing temperature, the above equation ▽p 0=0; it can represent the three components of velocity u, v, w, in units of m / s; f represents the time layer weight factor, which takes values ​​in the interval [0,1]. When f = 0, it represents the time explicit format, and when f = 1, it represents the time implicit format, dimensionless; ΔV represents the volume of the control body, in units of m 3 ; S C represents the constant part of the source term; S P represents the non-constant part of the source term; Δt represents the time step, unit: s; F e 、F w 、F n 、F s 、F t 、F b Respectively represent the mass flow rate of the east, west, north, south, upper and lower interfaces of the control body, unit: kg / s.

[0085] S2, according to the thermal hydraulic analysis problem to be analyzed, divide the solution area that needs to be calculated using the data assimilation algorithm. The divided solution area can be the overall solution domain of the thermal hydraulic problem to be analyzed, or it can be a partial area of ​​concern, such as the downstream of the mixing wing and other areas with strong turbulent mixing.

[0086] Take a typical fuel assembly of a pressurized water reactor as an example to illustrate:

[0087] like Figure 2 As shown, the solution area is divided according to the grid division. If the numerical calculation of the solution method of the present invention is used only in the area of ​​interest, the grid index is marked, and the calculation method of the present invention is selected to calculate the discrete equations of this part of the grid. If the calculation method of the present invention is used for the entire solution domain, there is no need to mark the grid index.

[0088] S3, establish data transmission methods for thermal hydraulic methods of different scales. For data obtained by CFD algorithm simulation, experimental measurement data or actual operation data of the unit, these data have different sizes, data sources and data resolutions. It is necessary to establish an efficient and accurate data transmission method based on the control coordinate position to achieve accurate data transmission in time and space.

[0089] Take the data transfer between the PWR fine gate element sub-channel analysis method and the CFD method as an example to illustrate:

[0090] Take the coordinate value of the central node of the fine grid element sub-channel control body, find the grid containing this coordinate value in the CFD grid as the mapping grid, and use the physical field value of the grid as the observation data for data assimilation.

[0091] S4, according to the thermal-hydraulic problem to be analyzed, select the data assimilation algorithm and the CFD algorithm, and perform joint calculations to obtain the core thermal-hydraulic values ​​of the solution area;

[0092] Among them, when selecting the appropriate data assimilation algorithm and the appropriate CFD algorithm, the following selection principles should be followed: For the selection of the data assimilation algorithm, a data assimilation algorithm with a two-step structure of prediction-correction should be selected, including but not limited to sequential data assimilation algorithms such as Kalman filtering, ensemble Kalman filtering, and particle filtering. For the selection of the CFD algorithm, a CFD algorithm with a two-step structure of solution-correction should be selected, including but not limited to SIMPLE algorithms such as SIMPLE algorithm, SIMPLEC algorithm, PISO algorithm, and PPIME algorithm.

[0093] Specifically, the S4, according to the thermal hydraulic problem to be analyzed, selects a data assimilation algorithm and a CFD algorithm, and performs joint calculations to obtain the core thermal hydraulic values ​​of the solution area, specifically including:

[0094] S41, according to the boundary conditions and initial conditions of the thermal hydraulic problem to be analyzed, the initial values ​​of various physical field parameters in the physical field of the solution area under the steady-state condition or transient condition of the reactor system are set; in order to be able to iteratively solve, the initial field needs to be given, and for the initial moment iteration, the temperature field, velocity field, and pressure field can be set to zero field, and for non-initial moments, the temperature field, velocity field, and pressure field in the current time layer are initialized to the field values ​​obtained by iterative convergence in the previous time layer;

[0095] S42, for transient thermal hydraulic problems, using the time stepping method to solve the transient physical field, updating the solution at each time layer, updating the Kalman gain (if data assimilation is performed), and determining whether the set numerical calculation time has ended;

[0096] S43, in each time layer, solving the energy conservation equation to obtain a predicted value of the temperature of the coolant, assembling and solving the linearized momentum conservation equation to obtain a predicted value of the speed of the coolant;

[0097] Taking the solution of the energy conservation equation and momentum conservation in the fine grid element sub-channel analysis method of a pressurized water reactor and the use of Kalman filtering as an example, the following is explained:

[0098] Using the physical fields (temperature field, velocity field, pressure field) obtained at the previous time layer k-1 or the previous iteration k-1, the predicted values ​​of the physical fields (predicted values ​​of the temperature field, predicted values ​​of the velocity field, predicted values ​​of the pressure field) at the time layer k or the current iteration k are obtained by solving the following momentum state prediction equation and energy state prediction equation;

[0099] Momentum state prediction equation:

[0100]

[0101] Energy state prediction equation:

[0102]

[0103] in: and are the velocity prediction values ​​in the x, y, and z directions, in m / s and the temperature prediction value, in K; x , Η y , Η z , Η T They represent the state transfer matrix of velocity u in the x direction, the state transfer matrix of velocity v in the y direction, the state transfer matrix of velocity w in the z direction, and the state transfer matrix of temperature T, dimensionless; and p k-1,k-1 They are the velocity values ​​in the x, y, and z directions of the previous time layer or iteration, in m / s; the temperature value, in K; and the pressure value, in Pa;

[0104] S44, calculating a velocity priori covariance matrix and a temperature priori covariance matrix of the current time layer according to the velocity transfer matrix and the temperature transfer matrix in the current time layer;

[0105] Take the calculation of the prior covariance matrix of Kalman filtering as an example to illustrate:

[0106] The velocity transfer matrix and temperature transfer matrix of the current time layer are used to calculate the velocity prior covariance matrix and temperature prior covariance matrix of the current time layer through the velocity and temperature covariance prediction matrix;

[0107] Speed ​​covariance prediction matrix:

[0108]

[0109] Temperature covariance prediction matrix:

[0110] P Tk,k-1 =H T P Tk-1,k-1 (H T ) T +Q Tk

[0111] Among them, P xk,k-1 , P yk,k-1 , P zk,k-1 , P Tk,k-1 They represent the prior covariance matrix of the three velocity components in the x, y, and z directions at the k time layer and the prior covariance matrix of the temperature at the k time layer respectively; P xk-1,k-1 , P yk-1,k-1 , P zk-1,k-1 , P Tk-1,k-1They represent the posterior covariance matrix of the three velocity components in the x, y, and z directions at the k-1 time layer and the posterior covariance matrix of the temperature at the k-1 time layer respectively; the superscript “T” represents the transpose operation of the matrix; Q xk , Q yk , Q zk , Q Tk They represent the prior covariance matrix of the components of the three momentum conservation equations in the x, y, and z directions at the k time layer, and the prior covariance matrix of the energy conservation equation at the k time layer respectively;

[0112] S45, judging whether there is observation data in the solution area, wherein the observation data includes at least one of CFD simulation data and experimental measurement data; if not, performing the numerical calculation process of the selected CFD algorithm, for example, using SIMPLE-type algorithm to perform only fine gate element sub-channel analysis and calculation, solving the control volume interface flow velocity, and not performing thermal hydraulic calculation based on the selected data assimilation algorithm; if yes, performing thermal hydraulic calculation based on the selected data assimilation algorithm, solving the control volume interface flow velocity, and not performing the numerical calculation process of the selected CFD algorithm;

[0113] S46, assembling and solving the mass conservation equation using the interface flow velocity to obtain a pressure correction value;

[0114] S47, using the pressure correction value to correct the pressure and velocity, and using the corrected pressure field and velocity field to update the flow velocity at the interface of the control volume using Rhie-Chow interpolation;

[0115] S5, iteratively updating the core thermal hydraulic values ​​in the solution area and judging whether the iteration meets the convergence requirement, if not, repeating step S4 until the convergence requirement is met;

[0116] S6, if CFD simulation data and / or experimental data in the current time layer exist, then updating the prior covariance matrix of temperature and velocity to obtain a posterior covariance matrix;

[0117] Take the calculation of the posterior covariance matrix of Kalman filtering as an example to illustrate:

[0118] The velocity posterior covariance matrix:

[0119]

[0120] Temperature posterior covariance matrix:

[0121] {P Tk,k =(IK Tk Π Tk ) Tk,k-1

[0122] Where: P xk,k , P yk,k , Pzk,k , P Tk,k They represent the posterior covariance matrix of the three velocity components in the x, y, and z directions at the k time layer and the posterior covariance matrix of the temperature at the k time layer respectively;

[0123] S7, based on the set conditions, determine whether the numerical solution process is completed, and if so, output the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field, wherein the set conditions are the set numerical simulation time.

[0124] Specifically, in S45, the numerical calculation process of the selected CFD algorithm includes:

[0125] The velocity prediction value is used to solve the control volume interface flow velocity through Rhie-Chow interpolation.

[0126] Specifically, in S45, the thermal hydraulic calculation based on the selected data assimilation algorithm includes:

[0127] S4501, calculating the velocity Kalman gain and the temperature Kalman gain in the current time layer taking into account the measurement error according to the velocity prior covariance matrix and the temperature prior covariance matrix, the velocity transfer matrix and the temperature transfer matrix in the current time layer;

[0128] Take the Kalman gain of Kalman filtering as an example to illustrate:

[0129] Velocity Kalman gain calculation:

[0130]

[0131] Temperature Kalman gain calculation:

[0132]

[0133] Where: K xk , K yk , K zk , K Tk Respectively represent the Kalman gain of the three velocity components in the x, y, and z directions at the k time layer and the Kalman gain of the temperature at the k time layer; Π xk ,Π yk ,Π zk , Π Tk They represent the transformation matrix of the three velocity components in the x, y, and z directions in the k time layer and the transformation matrix of the temperature in the k time layer respectively; R xk , R yk , R zk , R Tk They represent the uncertainty of the three observed velocity components in the x, y, and z directions at the k time layer, and the uncertainty of the observed temperature at the k time layer;

[0134] S4502, based on the calculated Kalman gain, velocity prediction value and temperature prediction value, the velocity field and temperature field are updated to obtain a gain velocity prediction value and a gain temperature prediction value; although this step involves solving the momentum equation, it is worth noting that the solution in this step is to use the velocity prediction value to assemble and update the momentum equation for explicit solution;

[0135] Taking the solution of the energy conservation equation and momentum conservation in the fine grid element sub-channel analysis method of a pressurized water reactor and the use of Kalman filtering as an example, the following is explained:

[0136] Gain speed prediction value solution:

[0137]

[0138] Gain temperature prediction solution:

[0139]

[0140] in: They represent the predicted gain values ​​of the three velocity components in the x, y, and z directions at the k time layer and the predicted gain value of the temperature at the k time layer respectively; ξ xk , yk , zk They represent the product of the Kalman gain and the new information of the three velocity components in the x, y, and z directions at the k time layer, respectively. They are only for the convenience of writing and have no actual physical meaning.

[0141] S4503, using the gain velocity prediction value, solve the control volume interface flow velocity through Rhie-Chow interpolation.

[0142] Furthermore, the step S5 iteratively updates the core thermal hydraulic values ​​in the solution area and determines whether the iteration meets the convergence requirement. If not, repeat step S4 until the convergence requirement is met. Specifically, the step S5 includes:

[0143] Iterate and update the obtained gain temperature prediction value and gain speed prediction value and judge whether the iteration meets the convergence requirement; and update the physical parameters such as density and viscosity coefficient according to the temperature field at the time of convergence;

[0144] If the convergence requirements are met, exit the loop and proceed to step S6 to update the time layer t=t+Δt. If the convergence requirements are not met, assign the gain speed prediction value and the gain speed prediction value to the speed prediction value and the temperature prediction value, and return to step S4502 for a new round of loop until the convergence requirements are met.

[0145] Specifically, the step S7, based on the set conditions, determines whether the numerical solution process is finished, specifically includes:

[0146] It is determined whether the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, the converged velocity field, velocity field and pressure field obtained in the current time layer are assigned as the initial field to the next time layer, and the process returns to step S43 to start a new time layer cycle.

[0147] Otherwise, the numerical solution process is terminated, and the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field are output.

[0148] The present invention also provides a core thermal hydraulic numerical solution system based on data assimilation, which is used to execute the above-mentioned core thermal hydraulic numerical solution method based on data assimilation, comprising:

[0149] A control equation group construction module is used to establish a control equation group according to the thermal hydraulic problem to be analyzed, close and discretize the control equation group, and form a complete linear control equation group for numerical solution, wherein the complete linear control equation group includes a mass conservation equation, an energy conservation equation, and a momentum conservation equation;

[0150] A solution region determination module is used to determine the solution region according to the geometric structure of the object to be analyzed and the thermal hydraulic problem;

[0151] The data transfer equation establishment module is used to establish data transfer methods of thermal hydraulic methods of different scales according to the type of observation data and the thermal hydraulic calculation method used;

[0152] An algorithm selection module is used to select a data assimilation algorithm and a CFD algorithm according to the thermal hydraulic problem to be analyzed, and perform joint calculations to obtain the core thermal hydraulic values ​​of the solution area, wherein the data assimilation algorithm is a data assimilation algorithm with a prediction-correction two-step structure, and the CFD algorithm is a CFD algorithm with a solution-correction two-step structure;

[0153] A convergence judgment module is used to iteratively update the core thermal hydraulic values ​​in the solution area and judge whether the iteration meets the convergence requirements;

[0154] The observation data judgment module is used to judge whether there is CFD simulation data and / or experimental data in the current time layer. If so, the prior covariance matrix of temperature and velocity is updated to obtain the posterior covariance matrix;

[0155] The solution end judgment module is used to judge whether the numerical solution process is completed based on the set conditions. If so, it outputs the core thermal hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

[0156] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0157] Those skilled in the art can understand that the modules in the system in the embodiment can be distributed in the system of the embodiment according to the description of the embodiment, or can be changed accordingly and located in one or more systems or devices different from the embodiment. The modules in the above embodiment can be combined into one module, or can be further divided into multiple sub-modules.

[0158] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for numerical solution of core thermal hydraulics based on data assimilation, characterized in that: The following steps are involved: S1, according to the thermal hydraulic problem to be analyzed, a control equation group is established, and the control equation group is closed and discretized to form a complete linear control equation group for numerical solution, wherein the complete linear control equation group includes a mass conservation equation, an energy conservation equation, and a momentum conservation equation; S2, determine the solution area according to the geometric structure of the object to be analyzed and the thermal hydraulic problem; S3, establish data transfer methods for thermal-hydraulic methods of different scales according to the type of observation data and the thermal-hydraulic calculation method used; S4, according to the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected, and joint calculations are performed to obtain the core thermal-hydraulic values ​​of the solution area, wherein the data assimilation algorithm is a data assimilation algorithm with a prediction-correction two-step structure, and the CFD algorithm is a CFD algorithm with a solution-correction two-step structure; S5, iteratively updating the core thermal hydraulic values ​​in the solution area and judging whether the iteration meets the convergence requirement, if not, repeating step S4 until the convergence requirement is met; S6, if CFD simulation data and / or experimental data in the current time layer exist, then updating the prior covariance matrix of temperature and velocity to obtain a posterior covariance matrix; S7, based on the set conditions, determine whether the numerical solution process is completed. If so, output the core thermal hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

2. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 1 is characterized in that: S1, according to the thermal hydraulic problem to be analyzed, establishes a control equation group, closes and discretizes the control equation group, and forms a complete linear control equation group for numerical solution, which specifically includes: According to the boundary conditions and initial conditions of the thermal-hydraulic problem to be analyzed, a group of control equations describing the thermal-hydraulic phenomena is established. The coolant flow and heat transfer model is used to close the group of control equations. The group of control equations is discretized using space and time discrete formats to obtain a complete linear group of control equations for numerical solution.

3. The core thermal hydraulic numerical solution method based on data assimilation according to claim 1 is characterized in that: S2, according to the geometric structure of the object to be analyzed and the thermal hydraulic problem, determines the area to be solved, specifically including: According to the thermal-hydraulic problem to be analyzed, the solution area to be calculated using the data assimilation algorithm is divided, and the divided solution area is the overall solution domain or a partial area of ​​the thermal-hydraulic problem to be analyzed.

4. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 1 is characterized in that: S3, according to the observed data type and the thermal hydraulic calculation method used, establishes data transmission methods of thermal hydraulic methods of different scales, specifically including: For the data obtained by CFD simulation, experimental measurement data or actual operation data of the unit, which have different data sizes, data sources and data resolutions, data transmission methods of thermal-hydraulic methods at different scales are established to realize data transmission in time and space.

5. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 1 is characterized in that: S4, according to the thermal hydraulic problem to be analyzed, selects a data assimilation algorithm and a CFD algorithm, and performs joint calculations to obtain the core thermal hydraulic values ​​of the solution area, specifically including: S41, according to the boundary conditions and initial conditions of the thermal hydraulic problem to be analyzed, setting the initial values ​​of various physical field parameters in the physical field of the solution area under steady-state conditions or transient conditions of the reactor system; S42, using the time marching method to solve the transient physical field of the outer layer, updating the solution on each time layer and judging whether the numerical solution time has ended; S43, in each time layer, solving the energy conservation equation to obtain a predicted value of the temperature of the coolant, assembling and solving the linearized momentum conservation equation to obtain a predicted value of the speed of the coolant; S44, calculating a velocity priori covariance matrix and a temperature priori covariance matrix of the current time layer according to the velocity transfer matrix and the temperature transfer matrix in the current time layer; S45, determining whether there is observation data in the solution area, wherein the observation data includes at least one of CFD simulation data and experimental measurement data; if not, performing the numerical calculation process of the selected CFD algorithm to solve the interface flow velocity of the control body without performing the thermal hydraulic calculation based on the selected data assimilation algorithm; if yes, performing the thermal hydraulic calculation based on the selected data assimilation algorithm to solve the interface flow velocity of the control body without performing the numerical calculation process of the selected CFD algorithm; S46, assembling and solving the mass conservation equation using the interface flow rate to obtain a pressure correction value; S47, using the pressure correction value to correct the pressure and velocity, and using the corrected pressure field and velocity field to update the flow velocity at the interface of the control volume using Rhie-Chow interpolation.

6. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 5 is characterized in that: In S45, the numerical calculation process of the selected CFD algorithm includes: The velocity prediction value is used to solve the control volume interface flow velocity through Rhie-Chow interpolation.

7. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 5 is characterized in that: In S45, the thermal hydraulic calculation based on the selected data assimilation algorithm includes: S4501, calculating the velocity Kalman gain and the temperature Kalman gain in the current time layer taking into account the measurement error according to the velocity prior covariance matrix and the temperature prior covariance matrix, the velocity transfer matrix and the temperature transfer matrix in the current time layer; S4502, updating the velocity field and the temperature field according to the calculated Kalman gain, the velocity prediction value and the temperature prediction value, and obtaining a gain velocity prediction value and a gain temperature prediction value; S4503, using the gain velocity prediction value, solve the control volume interface flow velocity through Rhie-Chow interpolation.

8. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 7 is characterized in that: The step S5, iteratively updating the core thermal hydraulic values ​​in the solution area and determining whether the iteration meets the convergence requirement, if not, repeating step S4 until the convergence requirement is met, specifically includes: Iteratively update the obtained gain temperature prediction value and gain speed prediction value and determine whether the iteration meets the convergence requirement; If the convergence requirements are met, exit the loop and proceed to step S6 to update the time layer. If the convergence requirements are not met, assign the gain speed prediction value and the gain speed prediction value to the speed prediction value and the temperature prediction value, and return to step S4502 for a new round of loop until the convergence requirements are met.

9. The method for numerically solving core thermal hydraulics based on data assimilation according to claim 5, characterized in that: The step S7, based on the set conditions, determines whether the numerical solution process is finished, specifically includes: It is determined whether the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, the converged velocity field, velocity field and pressure field obtained in the current time layer are assigned as the initial field to the next time layer, and the process returns to step S43 to start a new time layer cycle. Otherwise, the numerical solution process is terminated, and the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field are output.

10. A core thermal hydraulic numerical solution system based on data assimilation, used to execute the core thermal hydraulic numerical solution method based on data assimilation according to any one of claims 1 to 9, characterized in that: include: A control equation group construction module is used to establish a control equation group according to the thermal hydraulic problem to be analyzed, close and discretize the control equation group, and form a complete linear control equation group for numerical solution, wherein the complete linear control equation group includes a mass conservation equation, an energy conservation equation, and a momentum conservation equation; A solution region determination module is used to determine the solution region according to the geometric structure of the object to be analyzed and the thermal hydraulic problem; The data transfer equation establishment module is used to establish data transfer methods of thermal hydraulic methods of different scales according to the type of observation data and the thermal hydraulic calculation method used; An algorithm selection module is used to select a data assimilation algorithm and a CFD algorithm according to the thermal hydraulic problem to be analyzed, and perform joint calculations to obtain the core thermal hydraulic values ​​of the solution area, wherein the data assimilation algorithm is a data assimilation algorithm with a prediction-correction two-step structure, and the CFD algorithm is a CFD algorithm with a solution-correction two-step structure; A convergence judgment module is used to iteratively update the core thermal hydraulic values ​​in the solution area and judge whether the iteration meets the convergence requirements; The observation data judgment module is used to judge whether there is CFD simulation data and / or experimental data in the current time layer. If so, the prior covariance matrix of temperature and velocity is updated to obtain the posterior covariance matrix; The solution completion judgment module is used to judge whether the numerical solution process is completed based on the set conditions. If so, it outputs the core thermal hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

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