Supercritical water reactor fuel rod bundle circumferential heat exchange coefficient analysis method and system
By incorporating dimensionless weights trained by BPNN into subchannel programs, the accuracy of the circumferential heat transfer coefficient distribution of fuel rod bundles in supercritical water reactors was solved, achieving a more precise three-dimensional temperature distribution and improving the safety and economy of supercritical water reactors.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2025-12-23
- Publication Date
- 2026-05-08
AI Technical Summary
In the existing technology, the circumferential heat transfer coefficient distribution analysis method of supercritical water reactor fuel rod bundles cannot accurately reflect the three-dimensional temperature distribution within the fuel rod bundle. Especially when operating near the quasi-critical line, the traditional two-dimensional model has a large calculation error, which affects the estimation accuracy of fuel cladding temperature and thus affects the safety and economy of the reactor core.
By using backpropagation neural networks (BPNN) in conjunction with experimental data, we trained and verified the empirical relationship of the circumferential heat transfer coefficient, extracted the dimensionless weights, and incorporated them into the sub-channel program to achieve more accurate three-dimensional temperature distribution analysis.
By leveraging the nonlinear prediction performance of BPNN, the specific influencing factors of circumferential heat transfer nonuniformity in fuel rod bundles were clarified, improving the accuracy and safety of temperature distribution within the fuel rod bundles of supercritical water reactors. This provides a reference for the optimized design of core grid structures and enhances the economy and safety of the system.
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Figure CN121997709A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of temperature distribution technology for supercritical water reactors, and more specifically, to a method and system for analyzing the circumferential heat transfer coefficient of fuel rod bundles in supercritical water reactors. Background Technology
[0002] Supercritical water reactors (SCWRs), as a promising fourth-generation nuclear energy system, present a series of technical challenges in their high-temperature, high-pressure operation, which, while offering high efficiency, also urgently require solutions. Among these challenges, the predictive analysis of heat transfer in the close-grid structure of the SCWR is closely related to the overall system's safety and economics, and is one of the key technical difficulties for further improving SCWR design. In the conceptual design of SCWRs, the close-grid structure materials used in traditional light water reactors are inherited. While close-grid fuel elements offer advantages such as improved fuel conversion ratios, they also result in significant circumferential temperature inhomogeneity within the close-grid rod bundle. When the SCWR operates near the quasi-critical line, the physical properties of water change drastically, directly affecting the circumferential heat transfer coefficient distribution of the fuel rods, thus influencing the temperature distribution of the fuel cladding and ultimately impacting the overall safety of the reactor core.
[0003] In existing technologies, the heat transfer coefficient distribution within a tightly packed fuel bar bundle is often estimated using a two-dimensional simple subchannel model, which cannot generate the circumferential heat transfer coefficient distribution of the fuel bar bundle, making it difficult to achieve accurate three-dimensional temperature distribution estimation within the bundle.
[0004] Existing reactor thermal-hydraulic programs typically employ two-dimensional models to handle fuel rod cladding temperatures, neglecting the circumferential variation in fuel rod temperature distribution. However, in reality, the circumferential heat transfer coefficient of the cladding exhibits non-uniformity. Ignoring this non-uniformity when the grid diameter ratio is greater than 1.3 can lead to significant calculation errors, making it impossible to accurately estimate the maximum cladding temperature. This is especially true for supercritical water reactors operating near the quasi-critical line, where traditional calculation and analysis methods are no longer applicable. Summary of the Invention
[0005] To address the aforementioned problems, this invention provides a method for analyzing the circumferential heat transfer coefficient of a supercritical water reactor fuel rod bundle, comprising: acquiring experimental data on the circumferential temperature distribution of a supercritical water reactor fuel rod bundle and an empirical formula for the circumferential heat transfer coefficient; incorporating the empirical formula into a subchannel program; performing a thermo-hydraulic analysis on the tightly packed structure fuel rod bundle according to the subchannel program, and extracting dimensionless numbers affecting the local heat transfer coefficient from the empirical formula for the circumferential heat transfer coefficient; constructing a backpropagation neural network and training the backpropagation neural network based on the experimental data; verifying the trained backpropagation neural network, and if it meets the requirements, obtaining the weights of the dimensionless numbers based on the trained backpropagation neural network; substituting the weights of the dimensionless numbers into the empirical formula for the circumferential heat transfer coefficient to obtain a new empirical formula and incorporating it into the subchannel program; and determining the circumferential temperature distribution of the supercritical water reactor fuel rod bundle based on the subchannel program.
[0006] The method for analyzing the circumferential heat transfer coefficient of supercritical water reactor fuel rod bundles provided in this invention utilizes the excellent predictive performance of BPNN for nonlinear relationships. It can clearly identify the specific influence weights of nonlinear factors affecting the circumferential heat transfer inhomogeneity of fuel rod bundles in the compact grid structure under operating conditions near the quasi-critical line where physical properties change drastically. The weight results obtained by BPNN can be written into known empirical formulas for heat transfer coefficients, and the new empirical formulas can be incorporated into sub-channel programs to achieve more accurate and detailed three-dimensional circumferential temperature distribution results within the fuel rod bundles. This can provide a reference for the optimized design of SCWR core grid structures, improving the economy and safety of SCWRs.
[0007] Optionally, the dimensionless number includes the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity.
[0008] The embodiments of the present invention use a backpropagation neural network to quantitatively analyze the weights of the gate diameter ratio, Prandtl number, and the ratio of the cladding to the fluid thermal conductivity.
[0009] Optionally, the step of incorporating the empirical formula for the circumferential heat transfer coefficient into a sub-channel program includes: establishing a calling relationship between the sub-channel program and the sub-program for solving the three-dimensional temperature field; the sub-program includes the empirical formula for the circumferential heat transfer coefficient.
[0010] In this embodiment of the invention, the empirical formula for the circumferential heat transfer coefficient is incorporated into a sub-channel program, which can use the empirical formula for the circumferential heat transfer coefficient by calling the sub-program.
[0011] Optionally, the construction of the backpropagation neural network and the training of the backpropagation neural network based on the experimental data include: initializing the dimensionless weights, performing forward propagation, calculating the network output; calculating the loss function to measure the difference between the predicted value and the actual value, and updating the network weights and biases through the backpropagation algorithm.
[0012] The embodiments of the present invention train a backpropagation neural network based on experimental data, and use a nonlinear activation function to learn and simulate the three dimensionless numbers of nonlinear influences mentioned above, and have good interpretability.
[0013] Optionally, the verification of the trained backpropagation neural network includes: evaluating the performance of the trained backpropagation neural network using the experimental data; adjusting the model parameters and structure based on the evaluation results; and using regularization techniques to prevent overfitting.
[0014] The embodiments of the present invention validate the new model with specific influence weights obtained through training based on experimental data, thereby optimizing the model and avoiding overfitting.
[0015] Optionally, the empirical formula for the circumferential heat transfer coefficient is as follows: .
[0016] in, Where Pr is the local heat transfer coefficient and Pr is the Prandtl number. The grid diameter ratio, It is the ratio of the thermal conductivity of the cladding to that of the fluid.
[0017] This invention provides an empirical formula for the circumferential heat transfer coefficient. Based on this formula, dimensionless numbers that affect the local heat transfer coefficient can be extracted.
[0018] Optionally, the variable transfer between the subchannel program and the subprogram includes: the subprogram obtaining the heat transfer coefficient of the subchannel it faces and the temperature and physical properties of the fluid from the subchannel program; the subprogram returning the calorific value of the fuel rod to the subchannel program; assuming that in the three-dimensional fuel model: the portion of fuel rod J facing subchannel N is divided into K grids along the circumference, then the grid height in a certain axial direction is... The heat obtained by subchannel N from fuel rod J at the axial position is:
[0019]
[0020] in, Let be the circumferential length of the k-th grid on the shell surface; When the subchannel program needs to call the cladding surface temperature, the wall temperature of the fuel rod J facing the subchannel N is: .
[0021] Optionally, the subchannel program is the COBRA-IV subchannel model program.
[0022] This invention provides a system for analyzing the circumferential heat transfer coefficient of a supercritical water reactor fuel rod bundle, comprising: a preparation module for acquiring experimental data on the circumferential temperature distribution of the supercritical water reactor fuel rod bundle and an empirical formula for the circumferential heat transfer coefficient, and programming the empirical formula into a sub-channel program; an analysis module for performing thermo-hydraulic analysis on the tightly packed structure fuel rod bundle according to the sub-channel program, and extracting dimensionless numbers affecting the local heat transfer coefficient in the empirical formula for the circumferential heat transfer coefficient; a model training module for constructing a backpropagation neural network and training the backpropagation neural network according to the experimental data; a verification module for verifying the trained backpropagation neural network, and if it meets the requirements, obtaining the weights of the dimensionless numbers based on the trained backpropagation neural network; a programming module for substituting the weights of the dimensionless numbers into the empirical formula for the circumferential heat transfer coefficient to obtain a new empirical formula and programming it into the sub-channel program; and a temperature distribution determination module for determining the circumferential temperature distribution of the supercritical water reactor fuel rod bundle based on the sub-channel program.
[0023] Optionally, the dimensionless number includes the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity.
[0024] The supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis system of this invention can achieve the same technical effect as the supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis method described above. Attached Figure Description
[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0026] Figure 1 A schematic flowchart illustrating the method for analyzing the circumferential heat transfer coefficient of a supercritical water reactor fuel rod bundle provided in an embodiment of the present invention; Figure 2 This is a typical diagram of subchannel partitioning; Figure 3 This is a simplified flowchart illustrating the transient calculation of the sub-channel program in an embodiment of the present invention; Figure 4 This is a specific program principle roadmap in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of the supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis system provided in an embodiment of the present invention. Detailed Implementation
[0027] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
[0028] Backpropagation Neural Network (BPNN) is a multi-layer feedforward neural network that trains network weights using the backpropagation algorithm. A BPNN consists of an input layer, hidden layers, and an output layer, with the hidden layers potentially having multiple layers. This network structure enables BPNNs to learn and simulate complex nonlinear relationships.
[0029] This invention provides a method for analyzing the non-uniformity of the circumferential heat transfer coefficient of fuel rod bundles in supercritical water reactors by incorporating a backpropagation neural network. By utilizing the excellent predictive performance of the backpropagation neural network for nonlinear relationships, it is possible to clarify the specific influence weights of nonlinear factors affecting the non-uniformity of the circumferential heat transfer of fuel rod bundles in the compact grid structure under operating conditions near the quasi-critical line where physical properties change drastically.
[0030] Figure 1 A schematic flowchart of the method for analyzing the circumferential heat transfer coefficient of supercritical water reactor fuel rod bundles provided in an embodiment of the present invention is shown. The method includes: S102: Obtain experimental data on the circumferential temperature distribution of the fuel rod bundle in a supercritical water reactor and the empirical formula for the circumferential heat transfer coefficient, and then incorporate the empirical formula for the circumferential heat transfer coefficient into the subchannel program.
[0031] The experimental data can be divided into a test set, a validation set, and a training set. The empirical formula for the circumferential heat transfer coefficient can include dimensionless numbers such as the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity.
[0032] For example, based on experimental data from the Supercritical Water-Cooled Reactor Fuel Performance Verification Test (SCWR-FQT) test rig (0.6m in total length), circumferential distribution experimental data of the fuel rod surface and side coolant fluid temperature at axial height z = 0.2~0.4m were randomly selected, and the data were divided into test set, verification set, and training set in a ratio of 0.2:0.1:0.7. For example, the above sub-channel program is the COBRA-IV program.
[0033] By incorporating the aforementioned empirical formula for the circumferential heat transfer coefficient into a sub-channel program, a calling relationship can be established between the sub-channel program and the sub-program for solving the three-dimensional temperature field. This sub-program includes the aforementioned empirical formula for the circumferential heat transfer coefficient. Taking the sub-program FUEL3D.f as an example, the sub-program FUEL3D.f is called during the "Solve Fuel Rod Model" step in the COBRA-IV program to solve the three-dimensional temperature field of the fuel rod.
[0034] S104. Perform thermal-hydraulic analysis on the tightly packed grid structure rod bundle according to the above sub-channel program, and extract the dimensionless number affecting the local heat transfer coefficient in the empirical formula of the circumferential heat transfer coefficient.
[0035] A subchannel program was used to perform thermo-hydraulic analysis on a tightly packed grid structure of rod bundles, extracting dimensionless numbers affecting the local heat transfer coefficient from empirical formulas. For non-uniform fuel heat conduction models, mesh generation can be performed.
[0036] Specifically, the aforementioned dimensionless numbers include the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity. The main factors affecting the circumferential heat transfer non-uniformity within the rod bundle are the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity. However, the specific influence weights are currently only qualitatively determined, without quantitatively available conclusions. BPNN, on the other hand, can learn and simulate these three nonlinearly influential dimensionless numbers through a nonlinear activation function, and it has good interpretability.
[0037] S106, Construct a backpropagation neural network and train the backpropagation neural network based on the experimental data above.
[0038] A BPNN network structure is constructed and the network weights and biases are initialized. The network is then trained using the aforementioned training set. Specifically, dimensionless weights are first initialized, followed by forward propagation to calculate the network output. A loss function is calculated to measure the difference between the predicted and actual values, and the network weights and biases are updated using the backpropagation algorithm.
[0039] S108, verify the trained backpropagation neural network. If it meets the requirements, obtain the dimensionless weights based on the trained backpropagation neural network.
[0040] The performance of the trained backpropagation neural network is evaluated using experimental data. For example, the overall model performance is evaluated using the validation set described above. Then, the model parameters and structure are adjusted based on the evaluation results, and regularization techniques are used to prevent overfitting.
[0041] S110, based on the dimensionless number of weights, is substituted into the empirical relationship of the circumferential heat transfer coefficient to obtain a new empirical relationship, which is then incorporated into the sub-channel program.
[0042] The finalized dimensionless weights of the influence are incorporated into the sub-channel program to form a new model capable of analyzing the non-uniformity of the circumferential heat transfer coefficient of the tightly packed bar bundle when the SCWR is running near the quasi-critical line.
[0043] The weighting results obtained through BPNN can be written into the known empirical formula for heat transfer coefficient, and the new empirical formula can be incorporated into the sub-channel program to achieve more accurate and detailed three-dimensional circumferential temperature distribution results within the rod bundle.
[0044] S112, Based on the above sub-channel program, determine the circumferential temperature distribution of the supercritical water reactor fuel rod bundle.
[0045] The method for analyzing the circumferential heat transfer coefficient of supercritical water reactor fuel rod bundles provided in this invention utilizes the excellent predictive performance of BPNN for nonlinear relationships. It can clearly identify the specific influence weights of nonlinear factors affecting the circumferential heat transfer inhomogeneity of fuel rod bundles in the compact grid structure under operating conditions near the quasi-critical line where physical properties change drastically. The weight results obtained by BPNN can be written into known empirical formulas for heat transfer coefficients, and the new empirical formulas can be incorporated into sub-channel programs to achieve more accurate and detailed three-dimensional circumferential temperature distribution results within the fuel rod bundles. This can provide a reference for the optimized design of SCWR core grid structures, improving the economy and safety of SCWRs.
[0046] The following embodiments detail the above-described method for analyzing the circumferential heat transfer coefficient inhomogeneity of supercritical water reactor fuel rod bundles using a fused backpropagation neural network. Specifically, it includes the following steps: Step 1: Data Preparation For example, the COBRA-IV subchannel model program is used in this embodiment.
[0047] The sub-channel model assumes that there is a lateral exchange of mass, momentum and heat between coolants in adjacent channels during the flow process, so the mass flow rate of coolant in the channel will change continuously along the axial direction. Figure 2 A typical sub-channel partitioning diagram is shown. Figure 2 The diagram shows multiple vertical fuel rods, as well as sub-channels i and j.
[0048] by Figure 2 Taking subchannel i as an example, the common forms of mass, energy, and momentum conservation in the single-fluid model are as follows.
[0049] (1) Continuity equation (1) (2) Energy equation (2) (3) Axial momentum equation (3) (4) Transverse momentum equation (4) In the formula, The density of subchannel i is expressed in kg / m³. For time; The axial mass increment within subchannel i; The transverse mass mixing rate between subchannel i and subchannel j, in kg / sm; Enthalpy of cross-flow mixed transport, unit: J / kg; Enthalpy is the specific enthalpy of the fluid within subchannel i, expressed in J / kg; is the specific enthalpy of the fluid within subchannel j, expressed in J / kg; The mass flow rate within subchannel i is expressed in kg / s. Let i be the cross-sectional area of sub-channel i, in m2; The transverse energy mixing rate. The transverse momentum mixing rate is expressed in kg / sm. The speed of cross-flow mixing and transmission, in m / s; ρ represents the mass force, in N / kg; z represents the height along the flow direction. {} represents the average mass flow density over the transverse direction. The average material derivative of the fluid pressure within subchannel i reflects the rate of change of pressure with time and flow. The axial velocity of the fluid within subchannel i is expressed in m / s. is the axial velocity of the fluid in subchannel j, in m / s; J is the total number of adjacent subchannels in subchannel i where mixing occurs; Let be the heat flux density per unit length of subchannel i, in W / m. It is the acceleration due to gravity; The axial pressure gradient within subchannel i; The total frictional force, including axial viscous friction and form resistance, within subchannel i is expressed in N.
[0050] Based on the above fundamental conservation equations, taking the implicit time algorithm of the COBRA-IV program as an example, Figure 3 A simplified flowchart illustrating the transient calculation of the subchannel program is shown. Figure 3 The flowchart shown mainly includes: initializing boundary conditions; iteratively solving for the fuel rod temperature in the fuel rod model. T R Fuel cladding temperature T C Solve the nodal enthalpy of the energy equation h j Calculate the surface heat transfer coefficient HTC i Fluid temperature T f ; Calculate nodal pressure p j .
[0051] Specifically, the COBRA-IV program obtains the temperature values at up to five points radially from the center of the fuel rod to the cladding surface by solving the following equation.
[0052] (5) In the formula, It is the dimensionless temperature at radial node i at the current time step (n+1 steps); This is the dimensionless temperature at radial node i at the previous time step (n steps); For fluid density, For fluid isobaric specific heat, Reference temperature thermal conductivity at the bottom For temperature difference, For volumetric heat release rate, Height along the flow direction; Is with The corresponding actual temperature; The geometric coefficient matrix or coupling coefficient describes the contribution of the temperature of radial node l to the heat flow of radial node i; It is the dimensionless temperature at radial node l at the current time step (n+1 steps); N is the number of other radial nodes besides i; Let be the fuel thermal conductivity at node i; Let J be the thermal conductivity at the axial node j-1, which is at the same radial position as node i. Let J be the thermal conductivity at the axial node j+1, which is at the same radial position as node i. The temperature at the axial node j-1, which is at the same radial position as node i; Let J be the temperature at the axial node j+1, which is at the same radial position as node i.
[0053] (6) In the formula, For the air gap equivalent heat transfer coefficient, For the surface temperature of fuel pellets, For the outer surface temperature of the fuel cladding, The boundary flux coefficient vector obtained by discretizing the boundary conditions; This is the current time step.
[0054] (7) In the formula, Let i be the dimensionless temperature at time step n+1, at the radial node i of the shell. Let i be the dimensionless temperature at time step n and the radial node i of the shell. This represents the actual temperature of the outer surface of the fuel rod at time step n+1. This represents the actual temperature of the outer surface of the fuel cladding at time step n+1. For fuel cladding density, For fuel cladding, constant pressure specific heat capacity, For fuel rod radius, For fuel cladding radius, For fuel cladding thickness, The heat transfer coefficient of the cladding surface; This is the mainstream temperature of the coolant; Let i be the shell temperature at the same radial position i and axial position j+1 at time step n+1; The cladding temperature at the same radial position i and axial position j-1 at time step n+1; Let be the thermal conductivity of the cladding material at radial node i of the cladding.
[0055] Derivation of empirical formulas for dimensionless factor and circumferential heat transfer coefficient distribution, and CFD (Computational Fluid Dynamics) solution for undetermined coefficients.
[0056] The following normalized heat transfer coefficient distribution relationship can be obtained through theoretical derivation: (8) In the formula, The normalized local heat transfer coefficient; For Reynolds number, For Prandtl numbers, For the thermal conductivity of the shell, For the thermal conductivity of the coolant, For the thermal conductivity of fuel, For grid diameter ratio, The angle is dimensionless; , , , , This corresponds to the experience index; , is a constant coefficient.
[0057] The coefficients and dimensions of each term are undetermined coefficients, which are determined by computational fluid dynamics (CFD).
[0058] For the square rod bundle: (9) For the triangular rod bundle: (10) In the formula Angle (unit: radians).
[0059] For supercritical water, combining existing derivations with Bishop's formula, the final formula for calculating the heat transfer coefficient is as follows: (11) in, The local heat transfer coefficient; The average heat transfer coefficient is calculated based on the Bishop formula; For density, The specific heat at constant pressure at the local wall temperature; The average isobaric specific heat at the wall surface; Density at the local wall temperature; The density is at the average wall temperature; The thermal conductivity of the coolant at the main fluid temperature; The thermal conductivity of the cladding at the average temperature.
[0060] In the subchannel program, the formula for calculating the fuel rod temperature field distribution is as follows: (12) in, For time, For temperature, radial coordinates For thermal conductivity, For angle, Height along the flow direction, To determine the volumetric heat release rate, a third type of heat transfer method is applied to the surface of the fuel cladding. Boundary conditions, For wall temperature, The mainstream temperature. The heat transfer coefficient, taking into account the circumferential heat transfer coefficient distribution, is calculated by the following formula: (13) Average heat transfer coefficient Take the heat transfer coefficient of the sub-channel facing at that circumferential position; is a constant coefficient.
[0061] Experimental data was used as the basis for the dataset, which was divided into training, validation, and test sets. Sub-channel program boundary conditions were set, and the grid diameter ratio was included. Prandtl number Pr, ratio of cladding thermal conductivity to fluid thermal conductivity The empirical formula for the dimensionless circumferential heat transfer coefficient is incorporated into the subchannel program.
[0062] The sub-channel program is compiled using a subroutine call method. In the "Solve Fuel Rod Model" step of the COBRA-IV program, the subroutine FUEL3D.f is called to solve the three-dimensional temperature field of the fuel rod.
[0063] The variable transfer between the main program and the subroutine is as follows: (1) The subroutine obtains the heat transfer coefficient of the subchannel it faces and the temperature and physical properties of the fluid from the main program; (2) The subroutine returns the calorific value of the fuel rod to the main program. Assume that in the three-dimensional fuel model, the portion of fuel rod J facing subchannel N is divided into K grids along the circumference, then the grid height along a certain axis is... The heat obtained by channel N from fuel rod J at the axial position It is expressed as follows: (14) in Calculated by equation (13). The circumferential length of the k-th grid on the shell surface, The wall temperature of the k-th grid on the shell surface, This represents the mainstream fluid temperature of the Nth sub-channel. When the main program needs to call the cladding surface temperature, the wall temperature of the fuel rod J facing the Nth sub-channel is: (15) Step 2: Subchannel program analysis The thermal-hydraulic analysis of the tightly packed grid structure rod bundle was performed using a subchannel program, and the dimensionless numbers affecting the local heat transfer coefficient in the empirical formula were extracted.
[0064] Considering the variation of coolant properties along the circumferential direction, the relationship of the local heat transfer coefficient can be obtained as follows: (16) Step 3: Construct the BPNN network and its coupling with the subchannel program Construct the BPNN network structure and initialize the network weights and biases.
[0065] The BPNN network is coupled into the sub-channel program, the relevant dimensionless weights are initialized, and the BPNN model is trained. Forward propagation is performed, the network output is calculated, and the loss function is calculated to measure the difference between the predicted and actual values. The network weights and biases are updated through the backpropagation algorithm. Finally, the dimensionless weights that have been trained are incorporated into the sub-channel program.
[0066] Step 4: Verify the new model obtained in Step 3, which includes specific influence weights. Use a validation set to evaluate the overall model performance, adjust model parameters and structure, and use regularization techniques to prevent overfitting.
[0067] Step 5: Model Establishment The finalized dimensionless weights of the influence are incorporated into the sub-channel program to form a new model capable of analyzing the non-uniformity of the circumferential heat transfer coefficient of the tightly packed bar bundle when the SCWR is running near the quasi-critical line.
[0068] The specific program principle roadmap is as follows: Figure 4 As shown. In Figure 4 The diagram shows four parts: data preparation, BPNN network construction, sub-channel 3D fuel rod model subroutine, and sub-channel program analysis.
[0069] The data preparation included dividing the SCWR rod bundle circumferential temperature distribution experimental dataset into training, validation, and test sets, and then performing training and validation based on these sets respectively. The sub-channel 3D fuel rod model subroutine was used to calculate the calorific value of the fuel rods. The BPNN network construction included initializing dimensionless numbers, model training, and outputting the weights of each dimensionless number after training. The sub-channel program analysis... Figure 3 The subchannel program calculation flow is shown. The subchannel program includes extended three-dimensional calculation capabilities to achieve calculations of circumferential heat transfer non-uniformity.
[0070] Compared to existing methods, the method proposed in this invention utilizes the excellent predictive performance of BPNN for nonlinear relationships to clearly define the specific influence weights of nonlinear factors affecting the circumferential heat transfer inhomogeneity of fuel rod bundles in a compact grid structure under operating conditions near the quasi-critical line where physical properties change drastically. Currently, the main factors influencing circumferential heat transfer inhomogeneity within the fuel rod bundle are identified as the grid diameter ratio, Prandtl number, and the ratio of cladding thermal conductivity to fluid thermal conductivity. However, only qualitative conclusions regarding the specific influence weights are available; quantitative conclusions are not yet available. BPNN, on the other hand, can learn and simulate the dimensionless numbers of these three nonlinear influences through a nonlinear activation function, and it possesses good interpretability. The weight results obtained through BPNN can be incorporated into known empirical formulas for heat transfer coefficients, and these new empirical formulas can be programmed into sub-channel programs to achieve more accurate and detailed results of the three-dimensional circumferential temperature distribution within the fuel rod bundle. This can provide a reference for the optimized design of SCWR core grid structures, improving the economy and safety of SCWRs.
[0071] Figure 5 This diagram illustrates the structure of a supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis system provided in an embodiment of the present invention. The system includes: Preparation module 501 is used to obtain experimental data on the circumferential temperature distribution of fuel rod bundles in supercritical water reactors and empirical formulas for the circumferential heat transfer coefficient, and to incorporate the empirical formulas for the circumferential heat transfer coefficient into the sub-channel program. Analysis module 502 is used to perform thermal-hydraulic analysis on the tightly packed grid structure rod bundle according to the sub-channel program, and extract the dimensionless number affecting the local heat transfer coefficient in the empirical formula of the circumferential heat transfer coefficient. Model training module 503 is used to construct the backpropagation neural network and train the backpropagation neural network based on experimental data. The verification module 504 is used to verify the trained backpropagation neural network. If the requirements are met, the dimensionless weights are obtained based on the trained backpropagation neural network. Module 505 is used to substitute the dimensionless weights into the empirical formula for the circumferential heat transfer coefficient to obtain a new empirical formula, which is then incorporated into the sub-channel program. Temperature distribution determination module 506 is used to determine the circumferential temperature distribution of supercritical water reactor fuel rod bundles based on subchannel programs.
[0072] Optionally, dimensionless numbers include grid diameter ratio, Prandtl number, and the ratio of cladding thermal conductivity to fluid thermal conductivity.
[0073] The supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis system provided in this embodiment of the invention can achieve the same technical effect as the supercritical water reactor fuel rod bundle circumferential heat transfer coefficient analysis method described above.
[0074] This invention also provides a computer-readable storage medium storing a computer program. When the computer program is read and executed by a processor, it implements the method provided in the above embodiments and achieves the same technical effect. To avoid repetition, further details are omitted here. The computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.
[0075] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by computer-controlled devices. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. The storage medium can be a memory, a disk, an optical disk, etc.
[0076] While the present invention has been disclosed above, it is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.
[0077] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0078] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for analyzing the circumferential heat transfer coefficient of fuel rod bundles in a supercritical water reactor, characterized in that, include: Experimental data on the circumferential temperature distribution of fuel rod bundles in supercritical water reactors and empirical formulas for circumferential heat transfer coefficients are obtained, and the empirical formulas for circumferential heat transfer coefficients are incorporated into the sub-channel program. The thermal-hydraulic analysis of the tightly packed grid structure rod bundle is performed according to the sub-channel program, and the dimensionless number affecting the local heat transfer coefficient in the empirical formula of the circumferential heat transfer coefficient is extracted. Construct a backpropagation neural network and train the backpropagation neural network based on the experimental data; Verify the trained backpropagation neural network; if it meets the requirements, obtain the weights of the dimensionless number based on the trained backpropagation neural network. Substituting the weights of the dimensionless numbers into the empirical formula for the circumferential heat transfer coefficient, a new empirical formula is obtained and incorporated into the subchannel program. The circumferential temperature distribution of the supercritical water reactor fuel rod bundle is determined based on the subchannel program.
2. The method according to claim 1, characterized in that, The dimensionless numbers include the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity.
3. The method according to claim 1, characterized in that, The step of incorporating the empirical formula for the circumferential heat transfer coefficient into the sub-channel program includes: Establish the calling relationship between the sub-channel program and the sub-program for solving the three-dimensional temperature field; the sub-program includes the empirical formula for the circumferential heat transfer coefficient.
4. The method according to claim 1, characterized in that, The construction of the backpropagation neural network and the training of the backpropagation neural network based on the experimental data include: Initialize the dimensionless weights, perform forward propagation, and calculate the network output; The loss function is calculated to measure the difference between the predicted and actual values, and the weights and biases of the network are updated through the backpropagation algorithm.
5. The method according to claim 1, characterized in that, The verification of the trained backpropagation neural network includes: The performance of the trained backpropagation neural network was evaluated using the experimental data. The model parameters and structure are adjusted based on the evaluation results, and regularization techniques are used to prevent overfitting.
6. The method according to claim 1, characterized in that, The empirical formula for the circumferential heat transfer coefficient is as follows: 。 in, Where Pr is the local heat transfer coefficient and Pr is the Prandtl number. The grid diameter ratio, It is the ratio of the thermal conductivity of the cladding to that of the fluid.
7. The method according to claim 1, characterized in that, The variable passing between the subchannel program and the subprogram includes: The subroutine obtains the heat transfer coefficient and fluid temperature and properties of the sub-channel it is facing from the sub-channel program; The subroutine returns the heat output of the fuel rod to the subchannel program; assuming that in the three-dimensional fuel model: the portion of fuel rod J facing subchannel N is divided into K grids along the circumference, then the grid height along a certain axis is... The heat obtained by subchannel N from fuel rod J at the axial position is: in, Let be the circumferential length of the k-th grid on the shell surface; When the subchannel program needs to call the cladding surface temperature, the wall temperature of the fuel rod J facing the subchannel N is: 。 8. The method according to claim 1, characterized in that, The subchannel program is the COBRA-IV subchannel model program.
9. A system for analyzing the circumferential heat transfer coefficient of a supercritical water reactor fuel rod bundle, characterized in that, include: The preparation module is used to obtain experimental data on the circumferential temperature distribution of the fuel rod bundle in a supercritical water reactor and the empirical formula for the circumferential heat transfer coefficient, and to incorporate the empirical formula for the circumferential heat transfer coefficient into the sub-channel program. The analysis module is used to perform thermal-hydraulic analysis on the tightly packed grid structure rod bundle according to the sub-channel program, and extract the dimensionless numbers that affect the local heat transfer coefficient in the empirical formula of the circumferential heat transfer coefficient. The model training module is used to construct a backpropagation neural network and train the backpropagation neural network based on the experimental data. The verification module is used to verify the trained backpropagation neural network. If the requirements are met, the weights of the dimensionless number are obtained based on the trained backpropagation neural network. The module is used to substitute the dimensionless number into the empirical formula of the circumferential heat transfer coefficient based on its weight, obtain a new empirical formula, and then program it into the sub-channel program. The temperature distribution determination module is used to determine the circumferential temperature distribution of the supercritical water reactor fuel rod bundle based on the sub-channel program.
10. The system according to claim 9, characterized in that, The dimensionless numbers include the grid diameter ratio, Prandtl number, and the ratio of the cladding thermal conductivity to the fluid thermal conductivity.