A numerical solution method and system for reactor core thermal-hydraulic systems based on data assimilation

Abstract

This invention provides a numerical solution method and system for reactor core thermal-hydraulic problems based on data assimilation. The method includes: establishing a set of governing equations based on the thermal-hydraulic problem to be analyzed, and performing closure and discretization processing to form a complete linear set of governing equations; determining the solution domain; establishing data transfer methods for thermal-hydraulic methods at different scales; selecting a data assimilation algorithm and a CFD algorithm based on the thermal-hydraulic problem to be analyzed, and performing joint calculations; determining whether the iteration has reached the convergence requirement; if CFD simulation data and / or experimental data exist in the current time layer, updating the prior covariance matrices of temperature and velocity to obtain the posterior covariance matrix; and determining whether the numerical solution process has ended. This invention can integrate observation information from different sources and at different resolutions to perform rapid thermal-hydraulic calculations on the reactor core, improving the predictive capabilities of coolant flow and heat transfer models, and enhancing the accuracy of fine-grid sub-channel calculation methods.

Description

Technical Field

[0001] This invention relates to the field of reactor thermal-hydraulic design technology, and in particular to a numerical solution method and system for reactor core thermal-hydraulic processes based on data assimilation. Background Technology

[0002] The purpose of reactor thermal-hydraulic design is to determine the core's heat transfer capacity and coolant flow characteristics, ensuring that the heat generated in the reactor core can be safely and reliably removed through the coolant. To guarantee reactor safety and economic efficiency, it is necessary to understand the variations in its thermal-hydraulic parameters and ensure that these parameters do not exceed the design limits set by thermal design criteria. Currently, the main methods for core thermal-hydraulic calculation and analysis include single-channel analysis, sub-channel analysis, and computational fluid dynamics (CFD) analysis.

[0003] Low-resolution, medium-resolution thermal-hydraulic analysis methods, exemplified by subchannel analysis, are currently the reference tools for rapid core thermal-hydraulic analysis and safety reviews. However, using these methods requires numerous coolant flow and heat transfer models to describe the flow and heat transfer behavior of the coolant in the core, ensuring the governing equations are closed-form and solvable. Most of these coolant flow and heat transfer models are empirical correlations derived from experiments, and their applicability to thermal-hydraulic calculations varies under different boundary conditions and operating conditions, resulting in significant uncertainties and errors in the numerical calculations of local thermal-hydraulic parameters. On the other hand, computational fluid dynamics (CFD) methods, capable of simulating complex thermal-hydraulic phenomena at high resolution, have become tools for refined thermal-hydraulic calculation analysis and design of reactor cores. However, their main limitation is that even with sufficient computational resources, CFD calculations for large core flow areas require a long computation time, making it difficult to meet the requirements of engineering applications.

[0004] To comprehensively utilize the advantages of two different analytical methods, scholars both domestically and internationally have proposed various multi-scale coupled computational methods for thermal-hydraulic systems, such as the domain decomposition method and the domain overlap method. However, these methods suffer from problems such as high data transfer complexity, low computational stability, high difficulty in algorithm convergence, and low computational time efficiency.

[0005] Given the characteristics of the two different thermal-hydraulic analysis methods mentioned above and the shortcomings of existing multi-scale coupling methods for thermal-hydraulic analysis, there is an urgent need to provide a more complete numerical solution method for core thermal-hydraulic analysis in order to overcome at least one technical problem existing in the prior art. Summary of the Invention

[0006] The purpose of this invention is to provide a numerical solution method and system for reactor core thermal-hydraulic analysis based on data assimilation. Considering the errors of the simulated field obtained by low-to-medium resolution thermal-hydraulic analysis methods and the simulated field or / and experimental measurement field obtained by high-precision CFD methods, this invention integrates observation information from different sources and at different resolutions to perform rapid thermal-hydraulic calculations on the reactor core, thereby improving the predictive ability of coolant flow and heat transfer models and enhancing the accuracy of fine-grid sub-channel calculation methods.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A numerical solution method for reactor core thermal-hydraulic processes based on data assimilation includes the following steps:

[0009] S1. Based on the thermal-hydraulic problem to be analyzed, establish a set of governing equations, and perform closed-loop and discretized processing on the set of governing equations to form a complete linear set of governing equations for numerical solution. The complete linear set of governing equations includes the mass conservation equation, the energy conservation equation, and the momentum conservation equation.

[0010] S2, Determine the solution domain based on the geometry and thermal-hydraulic problems of the object to be analyzed;

[0011] S3. Based on the data types of the observed data and the thermal hydraulic calculation methods used, establish the data transfer methods for thermal hydraulic methods at different scales.

[0012] S4. Based on the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected and jointly calculated to obtain the core thermal-hydraulic values ​​of the solution region. 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 update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement. If not, repeat step S4 until the convergence requirement is reached.

[0014] S6. If CFD simulation data and / or experimental data exist in the current time layer, update the prior covariance matrices of temperature and velocity to obtain the posterior covariance matrix.

[0015] S7, based on the set conditions, determines whether the numerical solution process has ended. If so, it outputs the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

[0016] Further, in step S1, based on the thermal-hydraulic problem to be analyzed, a set of governing equations is established. This set of governing equations is then closed-looped and discretized to form a complete linear set of governing equations for numerical solution, specifically including:

[0017] Based on the boundary and initial conditions of the thermal-hydraulic problem to be analyzed, a set of governing equations describing the thermal-hydraulic phenomenon is established. The governing equations are closed using a coolant flow and heat transfer model. The governing equations are discretized using spatial and temporal discretization schemes to obtain a complete set of linear governing equations for numerical solution.

[0018] Furthermore, step S2, based on the geometry and thermo-hydraulic problem of the object to be analyzed, determines the region to be solved, specifically including:

[0019] Based on the thermal-hydraulic problem to be analyzed, the solution domain that needs to be calculated using the data assimilation algorithm is defined. The defined solution domain is either the overall solution domain or a part of the thermal-hydraulic problem to be analyzed.

[0020] Furthermore, S3 establishes data transfer methods for different scales of thermal hydraulic methods based on the observed data type and the thermal hydraulic calculation method used, specifically including:

[0021] For data obtained from CFD simulations, experimental measurements, or actual unit operation data, which vary in size, source, and resolution, different data transfer methods for thermal hydraulic methods of different scales should be established to achieve data transfer in both time and space.

[0022] Further, in step S4, based on the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected and jointly calculated to obtain the core thermal-hydraulic values ​​of the solution domain, specifically including:

[0023] S41, Based on the boundary conditions and initial conditions of the thermal-hydraulic problem to be analyzed, set the initial values ​​of each physical field parameter in the solution domain under the steady-state or transient conditions of the reactor system.

[0024] S42 uses the time-progression method to solve the transient physical field of the outer layer, updates the solution at each time level, and determines whether the numerical solution time has ended.

[0025] S43, within each time layer, solve the energy conservation equation to obtain the predicted temperature of the coolant, assemble and solve the linearized momentum conservation equation to obtain the predicted velocity of the coolant.

[0026] S44, Calculate the velocity prior covariance matrix and temperature prior covariance matrix of the current time layer based on the velocity transition matrix and temperature transition matrix of the current time layer;

[0027] S45, determine whether there is observation data in the solution area. The observation data includes at least one of CFD simulation data and experimental measurement data. If not, perform the numerical calculation process of the selected CFD algorithm to solve the flow velocity at the control volume interface, but do not perform the thermo-hydraulic calculation based on the selected data assimilation algorithm. If yes, perform the thermo-hydraulic calculation based on the selected data assimilation algorithm to solve the flow velocity at the control volume interface, but do not perform the numerical calculation process of the selected CFD algorithm.

[0028] S46, use the interface flow velocity to assemble and solve the mass conservation equation to obtain the pressure correction value;

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

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

[0031] The velocity at the control volume interface is solved using the predicted velocity values ​​and Rhie-Chow interpolation.

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

[0033] S4501, based on the velocity prior covariance matrix and temperature prior covariance matrix, velocity transfer matrix and temperature transfer matrix in the current time layer, calculate the velocity Kalman gain and temperature Kalman gain in the current time layer considering measurement error.

[0034] S4502 updates the velocity field and temperature field based on the calculated Kalman gain, velocity prediction value and temperature prediction value to obtain the gain-velocity prediction value and gain-temperature prediction value.

[0035] S4503 uses the gain velocity prediction value and Rhie-Chow interpolation to solve for the flow velocity at the control volume interface.

[0036] Further, in step S5, the core thermal-hydraulic values ​​of the solution domain are iteratively updated and it is determined whether the iteration has reached the convergence requirement. If not, step S4 is repeated until the convergence requirement is met. Specifically, this includes:

[0037] The obtained gain temperature prediction value and gain rate prediction value are iteratively updated, and it is determined whether the iteration has reached the convergence requirement.

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

[0039] Furthermore, step S7, based on set conditions, determines whether the numerical solution process has ended, specifically including:

[0040] Determine if the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, assign the converged velocity field, velocity field and pressure field obtained in this time layer as the initial field to the next time layer, and return to step S43 to start a new time layer loop.

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

[0042] This invention also provides a core thermal-hydraulic numerical solution system based on data assimilation, used to execute the above-described core thermal-hydraulic numerical solution method based on data assimilation, comprising:

[0043] The control equations construction module is used to establish a control equations set based on the thermal-hydraulic problem to be analyzed, and to perform closed and discretized processing on the control equations set to form a complete linear control equations set for numerical solution. The complete linear control equations set includes mass conservation equations, energy conservation equations, and momentum conservation equations.

[0044] The solution domain determination module is used to determine the solution domain based on the geometry and thermal-hydraulic problems of the object to be analyzed.

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

[0046] The 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 region. 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] The convergence judgment module is used to iteratively update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement.

[0048] The observation data judgment module is used to determine 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 determine whether the numerical solution process has ended based on 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 specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0051] (1) This invention uses a data assimilation method to enable data exchange and fusion between two different scale thermal hydraulic calculation methods, namely high-resolution CFD calculation method and medium- and low-resolution thermal hydraulic calculation method, during the solution process. Compared with the traditional coupling method, this method has a simpler calculation process, lower data transfer complexity, higher calculation stability, lower algorithm convergence difficulty, and higher computational time economy. It supports thermal hydraulic calculation analysis based on data assimilation algorithm for reactor types containing open fuel assemblies. This invention supports 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 computational time economy of existing multi-scale thermal hydraulic coupling methods.

[0052] (2) This invention integrates data from different sources and at different resolutions into the numerical solution process, reducing the errors and uncertainties introduced by directly modeling complex thermal-hydraulic phenomena (such as turbulent mixing and directional crossflow). Compared with solving thermal-hydraulic phenomena using low-to-medium resolution methods alone, this method can improve the accuracy of numerical calculation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating the numerical solution method for core thermal-hydraulic problems based on data assimilation, as described in an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram of the solution domain division for applying the data assimilation algorithm in an embodiment of the present invention, wherein (a) is the global solution domain and (b) is the local region of interest. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] As stated in the background technology, subchannel analysis methods have the characteristics of low fidelity and rapid thermal-hydraulic calculation and analysis. CFD methods can provide a detailed description of complex flow and heat transfer phenomena in the reactor core, but require a long computation time. Existing multi-scale coupling methods have problems such as high data transfer complexity, low computational stability, high algorithm convergence difficulty, and low computational time economy.

[0058] In view of the characteristics of the two different scale thermal-hydraulic analysis methods mentioned above and the shortcomings of existing multi-scale coupling methods for thermal-hydraulic analysis, this invention, based on considering the errors of the simulated field obtained by the low-to-medium resolution thermal-hydraulic analysis method and the simulated field or / and experimental measurement field obtained by the high-precision CFD method, integrates observation information from different sources and at different resolutions to use a multi-scale thermal-hydraulic calculation method to perform rapid thermal-hydraulic calculations on the reactor core, thereby improving the predictive ability of coolant flow and heat transfer models and enhancing the accuracy of low-to-medium resolution thermal-hydraulic analysis methods.

[0059] This invention provides a numerical solution method for reactor core thermal-hydraulic problems based on data assimilation, in order to solve the technical problems in the prior art.

[0060] This invention, taking into account the errors of the simulated field obtained by low-to-medium resolution thermal-hydraulic analysis methods and the simulated field or / and experimental measurement field obtained by high-precision CFD methods, integrates observation information from different sources and at different resolutions to perform rapid thermal-hydraulic calculations on the reactor core using a data assimilation-based thermal-hydraulic calculation method. This improves the predictive ability of coolant flow and heat transfer models and enhances the accuracy of the fine-grid sub-channel calculation method.

[0061] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

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

[0063] S1. Analyze the core type and solution scale. Based on the boundary and initial conditions of the thermal-hydraulic problem to be analyzed, establish a set of governing equations describing the thermal-hydraulic phenomena. Use a coolant flow and heat transfer model to close the set of governing equations. Discretize the set of governing equations using spatial and temporal discretization schemes to obtain a complete linear set of governing equations for numerical solution. Specifically, this may include:

[0064] Step S11: Based on the core type, boundary conditions, and initial conditions, establish the governing equations describing the thermal-hydraulic phenomena. This method can be used for numerical simulation of open-channel core types without wall-mounted components, such as pressurized water reactors, sodium-cooled fast reactors, and lead-bismuth fast reactors.

[0065] Taking the analysis of fine-grid subchannels in a pressurized water reactor core as an example, and establishing a set of three-dimensional governing equations for fine-grid subchannels, this will be explained:

[0066] mass conservation equation:

[0067]

[0068] Momentum conservation equation:

[0069]

[0070] Energy conservation equation:

[0071]

[0072] Where ρ represents the density of the coolant, in kg / m³. 3 The symbols u, v, and w represent the velocities of the coolant in the x, y, and z directions, respectively, with units of m / s; the symbol p represents pressure, with units of Pa; the symbol g... x g y g z These represent the gravitational accelerations in the x, y, and z directions, respectively, in m / s². 2 The symbol T represents the temperature of the coolant, in K; the symbol k represents the thermal conductivity, in W / (m·K); the symbol M... Mx M My M Mz M represents the turbulent mixing of momentum in the x, y, and z directions, respectively, in kg / (m·s); symbol M E For turbulent mixing of energy, unit: J / (m 2 ·s); symbol S Mx S My S Mz These are the momentum sources in the x, y, and z directions, formed by frictional and form drag pressure drops introduced by structures such as fuel rod bundles, assembly box walls, and positioning grids, respectively, in kg / (m²). 2 ·s 2); symbol S E Energy source term, unit: J / (m 3 ·s).

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

[0074] S in the governing equation M S E M M M E All of these require flow and heat transfer models for description, and a closed set of control equations. Discretizing the closed set of control equations yields a complete set of linear control equations that can be solved numerically.

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

[0076] The lateral flow resistance coefficient f in the rod bundle region can be calculated using the Gaddis-Gnielinski correlation, and its expression is as follows:

[0077]

[0078] Among them, f l f is a dimensionless factor influencing laminar flow resistance. t This is a dimensionless factor representing the influence of turbulence on flow resistance.

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

[0080]

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

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

[0083]

[0084] Where the superscript "0" represents the value at the previous time step; it is dimensionless; a represents the coefficient of the coefficient matrix, which is also dimensionless; φ represents the flux, which can represent temperature T in K. When representing temperature, the above equation ▽p 0=0; can represent the three components of velocity u, v, w, in m / s; f represents the time layer weighting factor, taking values ​​in the interval [0,1]. When f = 0, it represents the explicit time format; when f = 1, it represents the implicit time format. It is dimensionless; ΔV represents the volume of the control volume, in m³. 3 S C S represents the constant part of the source term; P The constant part of the source term is represented; Δt represents the time step, in seconds; F e F w F n F s F t F b These represent the mass flow rates at the east, west, north, south, upper, and lower interfaces of the control volume, respectively, in kg / s.

[0085] S2. Based on the thermal-hydraulic analysis problem to be analyzed, the solution domain for which the data assimilation algorithm needs to be used for calculation is defined. The defined solution domain can be the overall solution domain of the thermal-hydraulic problem to be analyzed, or it can be a region of interest, such as the downstream area of ​​a mixing vane where turbulence is intense.

[0086] The following explanation uses a typical fuel assembly from a pressurized water reactor as an example:

[0087] like Figure 2 As shown, the solution domain is divided according to the mesh. If numerical calculations using the solution method described in this invention are only performed in the region of interest, the mesh index is marked, and the discrete equations for this part of the mesh are calculated using the computational method of this invention. If the computational method of this invention is used for the entire solution domain, it is not necessary to mark the mesh index.

[0088] S3. Establish data transfer methods for different scales of thermal hydraulic methods. Data obtained from CFD simulations, experimental measurements, or actual unit operation data vary in size, source, and resolution. Therefore, an efficient and accurate data transfer method needs to be established based on the control coordinates to achieve accurate data transfer in both time and space.

[0089] The following example illustrates the data transfer between the fine grid subchannel analysis method and the CFD method in pressurized water reactors:

[0090] Take the coordinate values ​​of the center node of the fine grid sub-channel control volume, find the grid containing these coordinate values ​​in the CFD grid as the mapping grid, and use the physical field values ​​of the grid as the observation data for data assimilation.

[0091] S4. Based on 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 domain.

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

[0093] Specifically, in step S4, based on the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected and jointly calculated to obtain the core thermal-hydraulic values ​​of the solution domain, specifically including:

[0094] S41. Based on the boundary conditions and initial conditions of the thermal-hydraulic problem to be analyzed, set the initial values ​​of each physical field parameter in the solution domain under the steady-state or transient conditions of the reactor system. In order to enable iterative solution, an initial field needs to be given. For the initial iteration, the temperature field, velocity field, and pressure field can be set to zero field. For non-initial times, the temperature field, velocity field, and pressure field in the current time layer are initialized to the field values ​​obtained by the iteration convergence in the previous time layer.

[0095] S42, for transient thermal hydraulic problems, the time step method is used to solve the transient physical field, and the solution is updated at each time level, the Kalman gain is updated (if data assimilation is performed), and a judgment is made on whether the numerical calculation time has ended.

[0096] S43, within each time layer, solve the energy conservation equation to obtain the predicted temperature of the coolant, assemble and solve the linearized momentum conservation equation to obtain the predicted velocity of the coolant.

[0097] The solution of the energy conservation equation and momentum conservation equation in the analysis method of fine grid sub-channels in pressurized water reactors, and the application of Kalman filtering, are used as examples for illustration:

[0098] Using the physical fields (temperature field, velocity field, pressure field) obtained from the previous time layer k-1 or the previous iteration k-1, the predicted values ​​of the physical fields (predicted values ​​of temperature field, velocity field, pressure field) for 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 Here are the predicted velocity values ​​in the x, y, and z directions, in m / s, and the predicted temperature value, in K; H x , H y , H z , H T Let represent the state transition matrices for velocity u in the x-direction, velocity v in the y-direction, velocity w in the z-direction, and temperature T, respectively, and they are dimensionless. and p k-1,k-1 These represent 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, Calculate the velocity prior covariance matrix and temperature prior covariance matrix of the current time layer based on the velocity transition matrix and temperature transition matrix of the current time layer;

[0105] The calculation of the prior covariance matrix of Kalman filtering will be used as an example for illustration:

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

[0107] Velocity covariance prediction matrix:

[0108]

[0109] Temperature covariance prediction matrix:

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

[0111] Among them, P xk,k-1 P yk,k-1 P zk,k-1 P Tk,k-1 Let P represent the prior covariance matrices of the three velocity components in the x, y, and z directions at time level k, and the prior covariance matrix of the temperature at time level k, respectively; xk-1,k-1 P yk-1,k-1 P zk-1,k-1 P Tk-1,k-1Let Q represent the posterior covariance matrices of the three velocity components in the x, y, and z directions at time level k-1, and the posterior covariance matrix of the temperature at time level k-1, respectively; the superscript "T" indicates the matrix transpose operation; Q xk Q yk Q zk Q Tk Let represent the prior covariance matrices of the three momentum conservation equation components in the x, y, and z directions at time level k, and the prior covariance matrix of the energy conservation equation at time level k, respectively.

[0112] S45, determine whether there is observation data in the solution area. The observation data includes at least one of CFD simulation data and experimental measurement data. If not, perform the numerical calculation process of the selected CFD algorithm. For example, use a SIMPLE-type algorithm to perform fine-grained sub-channel analysis calculations and solve the flow velocity at the control volume interface, without performing thermal-hydraulic calculations based on the selected data assimilation algorithm. If yes, perform thermal-hydraulic calculations based on the selected data assimilation algorithm to solve the flow velocity at the control volume interface, without performing the numerical calculation process of the selected CFD algorithm.

[0113] S46, use the interface flow velocity to assemble and solve the mass conservation equation to obtain the pressure correction value;

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

[0115] S5. Iteratively update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement. If not, repeat step S4 until the convergence requirement is reached.

[0116] S6. If CFD simulation data and / or experimental data exist in the current time layer, update the prior covariance matrices of temperature and velocity to obtain the posterior covariance matrix.

[0117] The following explanation uses the calculation of the posterior covariance matrix of Kalman filtering as an example:

[0118] Posterior velocity covariance matrix:

[0119]

[0120] Temperature posterior covariance matrix:

[0121] {P Tk,k =(IK Tk Π Tk )P Tk,k-1

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

[0123] S7. Based on the set conditions, determine whether the numerical solution process has ended. If so, output the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field. The set conditions are the set numerical simulation time.

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

[0125] The velocity at the control volume interface is solved using the predicted velocity values ​​and Rhie-Chow interpolation.

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

[0127] S4501, based on the velocity prior covariance matrix and temperature prior covariance matrix, velocity transfer matrix and temperature transfer matrix in the current time layer, calculate the velocity Kalman gain and temperature Kalman gain in the current time layer considering measurement error.

[0128] Let's take the Kalman gain of Kalman filtering as an example for explanation:

[0129] Speed ​​Kalman gain calculation:

[0130]

[0131] Temperature Kalman gain calculation:

[0132]

[0133] Where: K xk K yk K zk K Tk These represent the Kalman gains of the three velocity components in the x, y, and z directions at time level k, and the Kalman gain of the temperature at time level k, respectively; Π xk Π yk Π zk Π Tk Let R represent the transformation matrices of the three velocity components in the x, y, and z directions at time level k, and the transformation matrix of the temperature at time level k, respectively; xk R yk R zk R Tk These represent the uncertainties of the three observed velocity components in the x, y, and z directions at time level k, and the uncertainties of the observed temperature at time level k, respectively.

[0134] S4502, based on the calculated Kalman gain, velocity prediction, and temperature prediction, update the velocity field and temperature field to obtain the gain-velocity prediction and gain-temperature prediction. Although this step involves solving the momentum equation, it is worth noting that the solution in this step is an explicit solution using the velocity prediction to assemble and update the momentum equation.

[0135] The solution of the energy conservation equation and momentum conservation equation in the analysis method of fine grid sub-channels in pressurized water reactors, and the application of Kalman filtering, are used as examples for illustration:

[0136] Determining the gain velocity prediction:

[0137]

[0138] Determining the predicted gain temperature:

[0139]

[0140] in: ξ represents the predicted gain values ​​of the three velocity components in the x, y, and z directions at time level k, and the predicted gain value of the temperature at time level k, respectively; xk ξ yk ξ zk These represent the products of the Kalman gain and the innovation in the x, y, and z velocity components at time k, respectively. They are for ease of writing and have no actual physical meaning.

[0141] S4503 uses the gain velocity prediction value and Rhie-Chow interpolation to solve for the flow velocity at the control volume interface.

[0142] Further, in step S5, the core thermal-hydraulic values ​​of the solution domain are iteratively updated and it is determined whether the iteration has reached the convergence requirement. If not, step S4 is repeated until the convergence requirement is met. Specifically, this includes:

[0143] The obtained gain temperature prediction value and gain rate prediction value are iteratively updated and it is determined whether the iteration has reached the convergence requirement; and the physical property parameters such as density and viscosity coefficient are updated according to the temperature field at the convergence point.

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

[0145] Specifically, S7, based on set conditions, determines whether the numerical solution process has ended, including:

[0146] Determine if the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, assign the converged velocity field, velocity field and pressure field obtained in this time layer as the initial field to the next time layer, and return to step S43 to start a new time layer loop.

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

[0148] This invention also provides a core thermal-hydraulic numerical solution system based on data assimilation, used to execute the above-described core thermal-hydraulic numerical solution method based on data assimilation, comprising:

[0149] The control equations construction module is used to establish a control equations set based on the thermal-hydraulic problem to be analyzed, and to perform closed and discretized processing on the control equations set to form a complete linear control equations set for numerical solution. The complete linear control equations set includes mass conservation equations, energy conservation equations, and momentum conservation equations.

[0150] The solution domain determination module is used to determine the solution domain based on the geometry and thermal-hydraulic problems of the object to be analyzed.

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

[0152] The 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 region. 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] The convergence judgment module is used to iteratively update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement.

[0154] The observation data judgment module is used to determine 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 completion judgment module is used to determine whether the numerical solution process has ended based on 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 will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0157] Those skilled in the art will understand that the modules in the system of the embodiments can be distributed in the system of the embodiments as described in the embodiments, or they can be located in one or more systems or devices different from this embodiment with corresponding changes. The modules of the above embodiments can be combined into one module, or they can be further divided into multiple sub-modules.

[0158] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A numerical solution method for reactor core thermal-hydraulic processes based on data assimilation, characterized in that, Includes the following steps: S1. Based on the thermal-hydraulic problem to be analyzed, establish a set of governing equations, and perform closed-loop and discretized processing on the set of governing equations to form a complete linear set of governing equations for numerical solution. The complete linear set of governing equations includes the mass conservation equation, the energy conservation equation, and the momentum conservation equation. S2, Determine the solution domain based on the geometry and thermal-hydraulic problems of the object to be analyzed; S3. Based on the data types of the observed data and the thermal hydraulic calculation methods used, establish the data transfer methods for thermal hydraulic methods at different scales. S4. Based on the thermal-hydraulic problem to be analyzed, a data assimilation algorithm and a CFD algorithm are selected and jointly calculated to obtain the core thermal-hydraulic values ​​of the solution region. 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 update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement. If not, repeat step S4 until the convergence requirement is reached. S6. If CFD simulation data and / or experimental data exist in the current time layer, update the prior covariance matrices of temperature and velocity to obtain the posterior covariance matrix. S7, based on the set conditions, determines whether the numerical solution process has ended. If so, it outputs the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

2. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 1, characterized in that, S1 involves establishing a set of governing equations based on the thermal-hydraulic problem to be analyzed. This set of equations is then closed and discretized to form a complete linear set of governing equations for numerical solution. Specifically, this includes: Based on the boundary and initial conditions of the thermal-hydraulic problem to be analyzed, a set of governing equations describing the thermal-hydraulic phenomenon is established. The governing equations are closed using a coolant flow and heat transfer model. The governing equations are discretized using spatial and temporal discretization schemes to obtain a complete set of linear governing equations for numerical solution.

3. The numerical solution method for core thermal-hydraulic problems based on data assimilation according to claim 1, characterized in that, S2, based on the geometry and thermal-hydraulic problems of the object to be analyzed, determines the region to be solved, specifically including: Based on the thermal-hydraulic problem to be analyzed, the solution domain that needs to be calculated using the data assimilation algorithm is defined. The defined solution domain is either the overall solution domain or a part of the thermal-hydraulic problem to be analyzed.

4. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 1, characterized in that, S3 establishes data transfer methods for different scales of thermal hydraulic methods based on the data type of the observation and the thermal hydraulic calculation method used, specifically including: For data obtained from CFD simulations, experimental measurements, or actual unit operation data, which vary in size, source, and resolution, different data transfer methods for thermal hydraulic methods of different scales should be established to achieve data transfer in both time and space.

5. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 1, characterized in that, S4 involves selecting a data assimilation algorithm and a CFD algorithm based on the thermal-hydraulic problem to be analyzed, and performing joint calculations to obtain the core thermal-hydraulic values ​​for the solution domain. Specifically, this includes: S41, Based on the boundary conditions and initial conditions of the thermal-hydraulic problem to be analyzed, set the initial values ​​of each physical field parameter in the solution domain under the steady-state or transient conditions of the reactor system. S42 uses the time-progression method to solve the transient physical field of the outer layer, updates the solution at each time level, and determines whether the numerical solution time has ended. S43, within each time layer, solve the energy conservation equation to obtain the predicted temperature of the coolant, assemble and solve the linearized momentum conservation equation to obtain the predicted velocity of the coolant. S44, Calculate the velocity prior covariance matrix and temperature prior covariance matrix of the current time layer based on the velocity transition matrix and temperature transition matrix of the current time layer; S45, determine whether there is observation data in the solution area. The observation data includes at least one of CFD simulation data and experimental measurement data. If not, perform the numerical calculation process of the selected CFD algorithm to solve the flow velocity at the control volume interface, but do not perform the thermo-hydraulic calculation based on the selected data assimilation algorithm. If yes, perform the thermo-hydraulic calculation based on the selected data assimilation algorithm to solve the flow velocity at the control volume interface, but do not perform the numerical calculation process of the selected CFD algorithm. S46, use the interface flow velocity to assemble and solve the mass conservation equation to obtain the pressure correction value; S47, use pressure correction values ​​to correct pressure and velocity, and use the corrected pressure field and velocity field to update the flow velocity at the control volume interface using Rhie-Chow interpolation.

6. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 5, characterized in that, In S45, the numerical computation process of the selected CFD algorithm includes: The velocity at the control volume interface is solved using the predicted velocity values ​​and Rhie-Chow interpolation.

7. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 5, characterized in that, In step S45, the thermal-hydraulic calculation based on the selected data assimilation algorithm includes: S4501, based on the velocity prior covariance matrix and temperature prior covariance matrix, velocity transfer matrix and temperature transfer matrix in the current time layer, calculate the velocity Kalman gain and temperature Kalman gain in the current time layer considering measurement error. S4502 updates the velocity field and temperature field based on the calculated Kalman gain, velocity prediction value and temperature prediction value to obtain the gain-velocity prediction value and gain-temperature prediction value. S4503 uses the gain velocity prediction value and Rhie-Chow interpolation to solve for the flow velocity at the control volume interface.

8. The numerical solution method for core thermal-hydraulic systems based on data assimilation according to claim 7, characterized in that, Step S5 involves iteratively updating the core thermal-hydraulic values ​​in the solution domain and determining whether the iteration has reached convergence. If not, step S4 is repeated until convergence is achieved. Specifically, this includes: The obtained gain temperature prediction value and gain rate prediction value are iteratively updated, and it is determined whether the iteration has reached the convergence requirement. If the convergence requirement is met, exit the loop and proceed to step S6 to update the time layer. If the convergence requirement is not met, assign the gain speed prediction value and the gain speed prediction value to the speed prediction value and the temperature prediction value, return to step S4502 to start a new round of looping, until the convergence requirement is met.

9. The numerical solution method for core thermal-hydraulic processes based on data assimilation according to claim 5, characterized in that, S7, based on set conditions, determines whether the numerical solution process has ended, specifically including: Determine if the time exceeds the set numerical simulation time. If it does not exceed the set numerical simulation time, assign the converged velocity field, velocity field and pressure field obtained in this time layer as the initial field to the next time layer, and return to step S43 to start a new time layer loop. Otherwise, the numerical solution process ends, and the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field are output.

10. A numerical solution system for core thermal-hydraulic systems based on data assimilation, used to execute the numerical solution method for core thermal-hydraulic systems based on data assimilation as described in any one of claims 1-9, characterized in that, include: The control equations construction module is used to establish a control equations set based on the thermal-hydraulic problem to be analyzed, and to perform closed and discretized processing on the control equations set to form a complete linear control equations set for numerical solution. The complete linear control equations set includes mass conservation equations, energy conservation equations, and momentum conservation equations. The solution domain determination module is used to determine the solution domain based on the geometry and thermal-hydraulic problems of the object to be analyzed. The data transfer equation establishment module is used to establish data transfer methods for different scales of thermal hydraulic methods based on the type of observation data and the thermal hydraulic calculation method used. The 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 region. 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. The convergence judgment module is used to iteratively update the core thermal-hydraulic values ​​of the solution domain and determine whether the iteration has reached the convergence requirement. The observation data judgment module is used to determine 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 determine whether the numerical solution process has ended based on set conditions. If so, it outputs the core thermal-hydraulic values ​​corresponding to the solved velocity field, pressure field, and temperature field.

Images