Deep learning method for predicting thermal hydraulic characteristics of sodium-cooled fast reactor heat exchanger

Abstract

The invention provides a deep learning method for predicting thermal hydraulic characteristics of a heat exchanger of a sodium-cooled fast reactor, and belongs to the technical field of passive residual heat removal systems of sodium-cooled fast reactors. The method comprises the following steps of: approximating low-fidelity flow and temperature distribution by using a first DNN; constructing a nonlinear relationship between the low-fidelity data and the high-fidelity data through the second DNN; the physical information partial differential equation and the boundary condition are used as constraints to be injected into the third DNN, and a prediction result is optimized; according to the method, the fluid heat transfer partial differential equation and the data driving advantages are combined, high-fidelity prediction of the flow velocity and the temperature in the sodium-cooled fast reactor PCHE can be achieved only through low-fidelity data, the problem that physical information in a heat exchanger is difficult to measure is solved, and the method has great significance in improving the inherent safety of the sodium-cooled fast reactor and the safety of a reactor core.

Description

Technical Field

[0001] The present invention relates to the fields of nuclear energy engineering and advanced computing technology, and in particular to a deep learning method for predicting thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger. Background Art

[0002] The sodium-cooled fast reactor is an advanced nuclear reactor technology. Its passive residual heat removal system continuously removes the heat from the core by utilizing thermal-hydraulic characteristics to ensure the safe operation of the reactor. In the residual heat removal system, the heat exchanger is a key component, and the accurate estimation of its thermal-hydraulic characteristics is crucial for the design and safety analysis of the reactor. However, due to the complex microchannel structure of the sodium-cooled fast reactor heat exchanger, the local flow parameters are difficult to measure directly, and the liquid sodium as a working fluid is highly active, which makes experimental research face great challenges.

[0003] In order to overcome these problems, numerical simulation methods such as finite volume method, finite element method, boundary element method and meshless method are widely used to predict and analyze the flow and heat transfer process in heat exchangers. Although these methods provide solutions to a certain extent, the need for high-precision grids, huge computational workload and complex implementation process limit their application efficiency.

[0004] In recent years, with the rapid development of deep neural network technology, especially the research progress of physical information neural network (PINN), new ideas have been provided for the prediction of thermal hydraulic characteristics. PINN can accurately predict complex physical systems by combining deep learning with traditional physical models. However, the traditional PINN method relies on a large amount of high-fidelity data for model training, which is often difficult to achieve in practical engineering applications because most numerical simulations can only provide low-fidelity data. PINN models trained with low-fidelity data are prone to deviations, affecting the accuracy and robustness of the prediction results.

[0005] Therefore, how to effectively use low-fidelity data and improve the prediction accuracy and efficiency of the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers through deep learning methods has become a problem that needs to be solved urgently. In response to this problem, the present invention proposes an innovative deep learning method, which achieves accurate prediction of high-fidelity flow rate and temperature distribution of sodium-cooled fast reactor printed circuit board heat exchangers (PCHE) based on low-fidelity data by fusing three deep neural networks (DNNs) in series and combining physical information partial differential equations and boundary conditions as constraints. Summary of the invention

[0006] In view of the above problems, the present invention provides an innovative method using deep learning methods, especially combining physical information neural network (PINN) technology, aiming to efficiently and accurately predict the high-fidelity flow rate and temperature distribution of a printed circuit board heat exchanger (PCHE) of a sodium-cooled fast reactor through low-fidelity data, thereby optimizing the design, safety analysis and operating performance of the sodium-cooled fast reactor.

[0007] In order to achieve the above object, the present invention adopts the following technical solution: a deep learning method for predicting the thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger, comprising the following steps:

[0008] S1: Given low-fidelity input coordinates, corresponding low-fidelity flow velocity and temperature distributions, and high-fidelity input coordinates;

[0009] S2: Approximate low-fidelity flow and temperature distributions through the first deep neural network (DNN); S3: Construct nonlinear relationships between low-fidelity data and high-fidelity data through the second DNN;

[0010] S4: Inject physics-informed partial differential equations and boundary conditions into the third DNN as physical constraints to improve and optimize the results of the second DNN.

[0011] The first DNN expression in S2 is:

[0012]

[0013] in Coordinates used to represent the low-fidelity mesh, are the flow rate, temperature and pressure solutions output by the low-precision CFD solver on a low-fidelity grid; the training process of the first DNN is described by the function G1, the neuron of the internal variable is θ1, which represents all trainable hyperparameter weights (w) and biases (b), and t represents the training step; for each neuron in the output layer and hidden layer, the output of all neurons in the upstream layer is used as input.

[0014] The S2 also includes training the first DNN through a mean square error loss function and a gradient descent algorithm until the error converges to obtain an approximation of the low-fidelity flow and temperature distribution.

[0015] The number of neurons in each layer l can be calculated by the following function:

[0016]

[0017] Where F() represents the activation function;

[0018] The loss function L1(θ) of the mean square error is introduced, and the gradient descent algorithm is used to guide the optimization direction of the hyperparameters until the error L1(θ) reaches the convergence error; L1(θ) is

[0019]

[0020] For high-fidelity input coordinates The first DNN can immediately output the flow rate and temperature distribution corresponding to the high-fidelity input coordinates; the flow rate and temperature distribution results of this step are still low-fidelity, and the output results are:

[0021]

[0022] The input of the second DNN in S3 includes the coordinates of the discrete low-fidelity data and high-fidelity grid information from the first DNN, and Gaussian noise data is added to construct a training data set, and the output is relatively high-fidelity data.

[0023] The third DNN in S4 has a 5-dimensional input and a 5-dimensional output, and its total loss function includes data loss, physical loss and boundary loss, which is used to optimize the result of the second DNN. 7. A deep learning method for predicting the thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 6, characterized in that: the expression of the total loss function is:

[0024] L3(θ3)=λ D L D +λ Phy L Phy +λ B L B

[0025]

[0026] The total loss function L3(θ3) comes from the data loss L D , physical loss L Phy and boundary loss L B ;

[0027] where λ D ,λ Phy and λ B is the corresponding weight constant of the loss function, They represent continuity, momentum and energy loss terms respectively; the data loss function consists only of the axial velocity (u) and temperature (T) distribution terms. The detailed form of a single loss function can be written as follows:

[0028] Data loss:

[0029]

[0030] Physical loss-continuity equation:

[0031]

[0032] Physical loss-momentum equation:

[0033]

[0034] Physical losses - energy equation:

[0035]

[0036] Boundary loss:

[0037]

[0038] The final result of the axial velocity (u) and temperature (T) distribution can be written as:

[0039]

[0040] The third DNN focuses on the axial flow velocity and temperature distribution in the printed circuit heat exchanger (PCHE) in a sodium-cooled fast reactor.

[0041] The deep learning method also includes using a trained model to quickly and efficiently predict high-fidelity flow rate and temperature distribution in a PCHE flow channel with fins of different shapes in a sodium-cooled fast reactor based on any low-fidelity data input.

[0042] The deep learning method can significantly improve prediction accuracy and computational efficiency, and is suitable for the prediction and analysis of thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

[0043] Compared with the prior art, the present invention has the following advantages: the deep learning method proposed in the present invention effectively constructs a nonlinear relationship between low-fidelity data and high-fidelity data by tandemly fusing three deep neural networks (DNNs), significantly improving the prediction accuracy of the thermal-hydraulic characteristics of the sodium-cooled fast reactor heat exchanger. At the same time, the method uses deep learning to replace the traditional numerical simulation process, greatly shortens the calculation time, improves the prediction efficiency, and provides strong support for the design, optimization and safe operation of sodium-cooled fast reactors.

[0044] The present invention embeds physical conservation laws in the deep learning model, and uses physical information partial differential equations and boundary conditions as constraints to improve and optimize the model prediction results. This innovative design not only ensures the accuracy of the prediction results, but also significantly enhances the robustness and generalization ability of the model, enabling it to maintain stable prediction performance under different working conditions.

[0045] Compared with traditional methods that require a large amount of high-fidelity data for model training, the present invention only requires low-fidelity data to achieve high-precision prediction. This not only reduces the dependence on the number of initial sampled data, but also significantly reduces the computing cost and resource consumption, providing a new way to efficiently predict the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

[0046] The deep learning method proposed in this paper can quickly and accurately predict the high-fidelity flow rate and temperature distribution of the sodium-cooled fast reactor printed circuit board heat exchanger (PCHE), providing an important basis for the design, optimization and operation control of the sodium-cooled fast reactor. The application of this method will promote the engineering process of sodium-cooled fast reactor technology and promote its widespread application in the nuclear energy field.

[0047] The successful practice of this invention demonstrates the great potential of combining deep learning with physical modeling in the prediction of complex engineering problems. By integrating physical information into the deep learning model, it not only improves the prediction accuracy and efficiency, but also provides a reference solution for similar problems in other fields, promoting the integrated development of deep learning and physical modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The overall flow chart of the deep learning method for predicting the thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention;

[0049] Figure 2 A schematic diagram of the configuration of a first DNN model of a deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention;

[0050] Figure 3 A schematic diagram of the configuration of a second DNN model of the deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention;

[0051] Figure 4 A schematic diagram of a third DNN training process of the deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention;

[0052] Figure 5 A schematic diagram comparing the low-fidelity flow field results, reference results and predicted results provided by the present invention;

[0053] Figure 6 This is a schematic diagram comparing the low-fidelity results, reference results and predicted results of the temperature field provided by the present invention. DETAILED DESCRIPTION

[0054] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings:

[0055] Example 1

[0056] like Figure 1-6As shown, it is used to explain in detail the deep learning method proposed by the present invention for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger.

[0057] This embodiment uses three deep neural networks (DNNs) to build a prediction model, which are denoted as DNN1, DNN2 and DNN3. These networks will be used to process low-fidelity data, build nonlinear relationships between low-fidelity and high-fidelity data, and optimize prediction results through physical constraints.

[0058] S1: Data Preparation

[0059] Input data: Prepare low-fidelity input coordinates, corresponding low-fidelity flow velocity and temperature distribution data, and high-fidelity input coordinates. These data can be obtained through numerical simulation or experiments, where low-fidelity data usually comes from lower-precision CFD simulations, while high-fidelity data comes from higher-precision simulation or experimental data.

[0060] Data preprocessing: Normalize the input data to ensure that the data can converge stably during the training process. At the same time, in order to enhance the generalization ability of the model, add Gaussian noise (mean = 0, standard deviation = 0.05) to the low-fidelity data.

[0061] S2: Build the first DNN (DNN1)

[0062] Network structure: DNN1 adopts a multi-layer perceptron structure, which includes an input layer, several hidden layers, and an output layer. The input layer receives low-fidelity input coordinates, and the output layer outputs the corresponding low-fidelity flow rate and temperature distribution. The number of hidden layers and neurons is determined according to the complexity of the specific task.

[0063] Training process: Use mean square error (MSE) as the loss function and optimize the network parameters through the gradient descent algorithm. During the training process, the network weights and biases are continuously adjusted until the loss function converges to the predetermined threshold.

[0064] Output results: For given high-fidelity input coordinates, DNN1 is able to output corresponding low-fidelity flow rate and temperature distributions, although these results are still low-fidelity.

[0065] S3: Build the second DNN (DNN2)

[0066] Network structure: DNN2 also uses a multi-layer perceptron structure, but the input layer contains the coordinates of discrete low-fidelity data and high-fidelity grid information from DNN1. The output layer outputs relatively high-fidelity flow velocity and temperature distribution prediction results.

[0067] Training process: Use an augmented dataset containing Gaussian noise for training to enhance the generalization ability of the model. The loss function also uses MSE, and the network parameters are optimized through the gradient descent algorithm.

[0068] Output results: DNN2 can output relatively high-fidelity flow velocity and temperature distribution prediction results based on low-fidelity data and high-fidelity grid information.

[0069] S4: Build the third DNN (DNN3) and introduce physical constraints

[0070] Network structure: The structure of DNN3 is similar to that of DNN2, but the input layer contains 5-dimensional data (including the prediction results from DNN2 and additional physical parameters). The output layer outputs the optimized high-fidelity flow rate and temperature distribution.

[0071] Physical constraints: The Navier-Stokes equations, energy equations, and boundary conditions of the computational area are embedded into DNN3 as physical constraints. These constraints are transformed into optimizable mathematical expressions by defining physical loss functions (including continuity loss, momentum loss, energy loss, and boundary loss).

[0072] Training process: The total loss function consists of data loss and physical loss, and the importance of the two is balanced by adjusting the weight constants and. The gradient descent algorithm is used to optimize the network parameters until the total loss function converges to a predetermined threshold.

[0073] Output results: The trained DNN3 is able to output optimized high-fidelity flow rate and temperature distributions, which are not only related to low-fidelity data but also strictly limited by physical constraints, making them more accurate and reliable.

[0074] Results verification: By comparing the prediction results output by DNN3 with real high-fidelity data (or higher-precision simulated data), the prediction accuracy and efficiency of this method are verified. Figure 5 and Figure 6As shown, the flow field information and temperature field information predicted by this method are basically consistent with the real flow field information, indicating that this method can effectively predict the thermal hydraulic characteristics in the sodium-cooled fast reactor heat exchanger. This embodiment realizes the accurate prediction of the high-fidelity flow rate and temperature distribution of the sodium-cooled fast reactor PCHE based on low-fidelity data by connecting three deep neural networks in series and combining physical information partial differential equations and boundary conditions as constraints. This method not only improves the prediction accuracy and efficiency, but also reduces the dependence on the number of initial sampling data, providing strong support for the design, optimization and safe operation of sodium-cooled fast reactors. The method of the present invention mainly includes three deep neural networks (DNNs). The first DNN is purely data-driven and is responsible for establishing the relationship between the input coordinates and the low-fidelity output. The second DNN adopts a purely data-driven method to construct the nonlinear correlation between low-fidelity data and high-fidelity data. The third DNN considers the Navier-Stokes equations, energy functions and corresponding boundary conditions on the calculation area as additional physical constraints to optimize and refine the results of the second DNN. A well-trained model can eventually obtain high-fidelity flow and temperature distributions of the PCHE flow channel in a sodium-cooled fast reactor.

[0075] Example 2

[0076] like Figure 1 As shown, a deep learning method for predicting the thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger comprises the following steps:

[0077] S1: Given low-fidelity input coordinates, the corresponding low-fidelity flow velocity and temperature distributions, and the high-fidelity input coordinates.

[0078] S2: Approximate low-fidelity flow and temperature distributions through the first DNN. The typical configuration of the first DNN model is as follows Figure 2 As shown. The first DNN formula can be expressed as

[0079]

[0080] in Coordinates used to represent the low-fidelity mesh, The output of flow, temperature and pressure solutions is a result of a low fidelity mesh and a low accuracy CFD solver.

[0081] The training process of the first DNN is described by the function G1, where the internal variable neuron is θ1, which represents all trainable hyperparameter weights (w) and biases (b), and t represents the training step. For each neuron in the output layer and hidden layer, the output of all neurons in the upstream layer is taken as input. Therefore, the neurons in each layer l can be calculated by the following function:

[0082]

[0083] Where F() represents the activation function.

[0084] The loss function L1(θ) of mean square error (MSE) is introduced, and the gradient descent (GD) algorithm is used to guide the optimization direction of the hyperparameters until the error L1(θ) reaches the convergence error. L1(θ) is

[0085]

[0086] For high-fidelity input coordinates For example, with finer mesh elements, the first DNN can immediately output the flow and temperature distribution corresponding to the high-fidelity input coordinates. It is worth noting that the flow and temperature distribution results at this step are still low-fidelity, and the output results are:

[0087]

[0088] S3: Construct the nonlinear relationship between low-fidelity data and high-fidelity data through the second DNN. The second DNN is the key point to deeply study the relationship between low-fidelity and high-fidelity data. Its configuration is as follows Figure 3 As shown, it is similar to the first DNN. The 8-dimensional input of the second network Discrete low-fidelity data from the first DNN and high-fidelity mesh information In order to obtain better generalization performance, Gaussian noise data (mean = 0, standard deviation = 0.05) was added to construct the training data set for the second neural network. The output is relatively high-fidelity data Obtain prediction results through a purely data-driven approach:

[0089]

[0090] S4: Inject partial differential equations and boundary conditions as physical constraints into the last DNN to improve and optimize the results of the second DNN. The last DNN has a 5-dimensional input 5-dimensional output The configuration of the hidden layer network is similar to the previous two pure data-driven networks, such as Figure 4 As shown. The total loss function L3(θ3) comes from the data loss L D , physical loss L Phy and boundary loss L B .

[0091] L3(θ3)=λ D L D +λ Phy L Phy +λ B LB

[0092]

[0093] where λ D ,λ Phy and λ B is the corresponding weight constant of the loss function, Represent the continuity, momentum and energy loss terms respectively. It is worth noting that this embodiment only focuses on the axial velocity and temperature distribution in PCHE, so the data loss function only consists of the axial velocity (u) and temperature (T) distribution terms to save computational cost. The detailed form of a single loss function can be written as follows:

[0094] Data loss:

[0095]

[0096] Physical loss-continuity equation:

[0097]

[0098] Physical loss-momentum equation:

[0099]

[0100] Physical losses - energy equation:

[0101]

[0102] Boundary loss:

[0103]

[0104] This example mainly focuses on the final results of the axial flow velocity (u) and temperature (T) distribution, which can be written as:

[0105]

[0106] In this embodiment, a well-trained model using three deep neural networks (DNNs) can ultimately obtain high-fidelity flow and temperature distribution of the PCHE flow channel in a sodium-cooled fast reactor.

[0107] pass Figure 5 and Figure 6 By comparing the flow field information and temperature information, it can be found that the flow field information and temperature field information predicted by the method of this embodiment are basically consistent with the actual flow field information results, which shows that the method of this embodiment can well predict the flow field and temperature field information.

[0108] Of course, the above description is only a preferred embodiment of this embodiment, and this embodiment is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technical personnel familiar with the field under the guidance of this specification fall within the substantive scope of this specification and should be protected by this embodiment.

Claims

1. A deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger, characterized in that: The following steps are involved: S1: Given low-fidelity input coordinates, corresponding low-fidelity flow velocity and temperature distributions, and high-fidelity input coordinates; S2: Approximating low-fidelity flow and temperature distributions through the first deep neural network (DNN); S3: Constructing a nonlinear relationship between low-fidelity data and high-fidelity data through a second DNN; S4: Inject physics-informed partial differential equations and boundary conditions into the third DNN as physical constraints to improve and optimize the results of the second DNN.

2. The deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1, characterized in that: The first DNN expression in S2 is: in Coordinates used to represent low-fidelity meshes, are the flow rate, temperature and pressure solutions output by the low-precision CFD solver on a low-fidelity grid; the training process of the first DNN is described by the function G1, the neuron of the internal variable is θ1, which represents all trainable hyperparameter weights (w) and biases (b), and t represents the training step; for each neuron in the output layer and hidden layer, the output of all neurons in the upstream layer is used as input.

3. The deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 2, characterized in that: The S2 also includes training the first DNN through a mean square error loss function and a gradient descent algorithm until the error converges to obtain an approximation of the low-fidelity flow and temperature distribution.

4. A deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 2 or 3, characterized in that: The number of neurons in each layer l can be calculated by the following function: Where F() represents the activation function; The loss function L1(θ) of the mean square error is introduced, and the gradient descent algorithm is used to guide the optimization direction of the hyperparameters until the error L1(θ) reaches the convergence error; L1(θ) is For high-fidelity input coordinates The first DNN can immediately output the flow and temperature distribution corresponding to the high-fidelity input coordinates; the flow rate and temperature distribution results at this step are still low-fidelity, and the output results are:

5. The deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1, characterized in that: The input of the second DNN in S3 includes the coordinates of the discrete low-fidelity data and high-fidelity grid information from the first DNN, and Gaussian noise data is added to construct a training data set, and the output is relatively high-fidelity data.

6. The deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1, characterized in that: The third DNN in S4 has a 5-dimensional input and a 5-dimensional output, and its total loss function includes data loss, physical loss and boundary loss, which is used to optimize the result of the second DNN.

7. A deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 6, characterized in that: The expression of the total loss function is: L3(θ3)=λ D L D +λ Phy L Phy +λ B L B The total loss function L3(θ3) comes from the data loss L D , physical loss L Phy and boundary loss L B ; where λ D ,λ Phy and λ B is the corresponding weight constant of the loss function, Represent the continuity, momentum and energy loss terms respectively; the data loss function consists only of the axial velocity (u) and temperature (T) distribution terms. The detailed form of a single loss function can be written as follows: Data loss: Physical loss-continuity equation: Physical loss-momentum equation: Physical losses - energy equation: Boundary loss: The final result of the axial velocity (u) and temperature (T) distribution can be written as:

8. A deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1 or 6, characterized in that: The third DNN focuses on the axial flow velocity and temperature distribution in the printed circuit heat exchanger (PCHE) in a sodium-cooled fast reactor.

9. The deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1, characterized in that: The deep learning method also includes using a trained model to quickly and efficiently predict high-fidelity flow rate and temperature distribution in a PCHE flow channel with fins of different shapes in a sodium-cooled fast reactor based on any low-fidelity data input.

10. A deep learning method for predicting thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to any one of claims 1 to 9, characterized in that: The deep learning method can significantly improve prediction accuracy and computational efficiency, and is suitable for the prediction and analysis of thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

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