A deep learning method for predicting thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger

Abstract

The application provides a deep learning method for predicting thermal hydraulic characteristics of a sodium-cooled fast reactor heat exchanger, and belongs to the technical field of a sodium-cooled fast reactor passive residual heat removal system; the method comprises the following steps: a first DNN is used to approximate low-fidelity flow and temperature distribution; a second DNN is used to build a nonlinear relationship between low-fidelity and high-fidelity data; and a physical information partial differential equation and a boundary condition are used as constraints to inject a third DNN, so as to optimize a prediction result; by combining the advantages of a fluid heat transfer partial differential equation and data driving, the method can realize high-fidelity prediction of flow velocity and temperature in a sodium-cooled fast reactor PCHE by using only low-fidelity data, solves the problem that physical information in a heat exchanger is difficult to measure, and has important significance for improving the inherent safety of a sodium-cooled fast reactor and the safety of a reactor core.

Description

TECHNICAL FIELD

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

[0002] The sodium-cooled fast reactor is an advanced nuclear reactor technology, and its passive residual heat removal system continuously removes the heat of the reactor 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 micro-channel structure of the sodium-cooled fast reactor heat exchanger, the local flow parameters are difficult to measure directly, and liquid sodium as the working fluid has high activity, making experimental research face great challenges.

[0003] In order to overcome these difficulties, 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 the heat exchanger. Although these methods provide solutions to a certain extent, the need for high-precision grids, large amount of calculation 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), a new idea is provided for the prediction of thermal-hydraulic characteristics. PINN can realize accurate prediction of 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 actual engineering applications, because most numerical simulations can only provide low-fidelity data. PINN models trained using low-fidelity data are prone to bias, affecting the accuracy and robustness of the prediction results.

[0005] Therefore, how to effectively use low-fidelity data to improve the prediction accuracy and efficiency of the thermal-hydraulic characteristics of the sodium-cooled fast reactor heat exchanger through deep learning methods has become a problem to be solved. The present application proposes an innovative deep learning method by serially fusing three deep neural networks (DNNs) and combining physical information partial differential equations and boundary conditions as constraints, which realizes accurate prediction of high-fidelity flow velocity and temperature distribution of the sodium-cooled fast reactor printed circuit board heat exchanger (PCHE) based on low-fidelity data. SUMMARY

[0006] In view of the above problems, the application provides an innovative method using a deep learning method, in particular a physical information neural network (PINN) technology, aiming to efficiently and accurately predict high-fidelity flow rate and temperature distribution of a sodium-cooled fast reactor printed circuit board heat exchanger (PCHE) from low-fidelity data, so as to optimize the design, safety analysis and operation performance of the sodium-cooled fast reactor.

[0007] In order to achieve the above-mentioned purpose, the application adopts the following technical scheme: a deep learning method for predicting 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 rate and temperature distribution, and high-fidelity input coordinates;

[0009] S2: Approximate the low-fidelity flow rate and temperature distribution by a first deep neural network (DNN); S3: Construct a nonlinear relationship between the low-fidelity data and the high-fidelity data by a second DNN;

[0010] S4: Inject the physical information partial differential equation and boundary conditions into a 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] wherein is used to represent the coordinates of the low-fidelity grid, is the flow rate, temperature and pressure solution output by the low-fidelity grid and low-precision CFD solver; the training process of the first DNN is described by the function G1, 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 the hidden layer, the outputs of all neurons in the upstream layer are taken as the input.

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

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

[0016]

[0017] wherein represents an activation function;

[0018] A loss function L1(θ) based on mean squared error is introduced, and gradient descent 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 velocity and temperature distribution corresponding to the high-fidelity input coordinates; the flow velocity and temperature distribution results in this step are still low-fidelity, and the output is as follows:

[0021]

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

[0023] The third DNN in S4 has 5-dimensional input and 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.

[0024] The expression for the total loss function is:

[0025] L3(θ3)=λ D L D +λ Phy L Phy +λ B L B

[0026]

[0027] The total loss function L3(θ3) comes from the data loss L D Physical loss L Phy and boundary loss L B ;

[0028] Where λ D , λ Phy and λ B These are the corresponding weight constants of the loss function. These 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:

[0029] Data loss:

[0030]

[0031] Physical loss - continuity equation:

[0032]

[0033] Physical loss-momentum equation:

[0034]

[0035] Physical loss-energy equation:

[0036]

[0037] Boundary loss:

[0038]

[0039] The final result of the axial velocity (u) and temperature (T) distribution can be written as:

[0040]

[0041] The third DNN focuses primarily on the axial velocity and temperature distribution in the printed circuit board heat exchanger (PCHE) of the sodium-cooled fast reactor.

[0042] The deep learning method also includes using a trained model to quickly and efficiently predict the high-fidelity flow velocity and temperature distribution within PCHE channels with different fin shapes in a sodium-cooled fast reactor, based on arbitrary low-fidelity data input.

[0043] The deep learning method described above can significantly improve prediction accuracy and computational efficiency, and is suitable for the prediction and analysis of the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

[0044] Compared with existing technologies, this invention has the following advantages: The deep learning method proposed in this invention effectively constructs the nonlinear relationship between low-fidelity and high-fidelity data by cascading and fusing three deep neural networks (DNNs), significantly improving the prediction accuracy of the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers. Simultaneously, this method utilizes deep learning to replace the traditional numerical simulation process, greatly shortening the computation time and improving prediction efficiency, providing strong support for the design, optimization, and safe operation of sodium-cooled fast reactors.

[0045] This invention embeds physical conservation laws into a deep learning model, using partial differential equations of physical information and boundary conditions as constraints to improve and optimize the model's prediction results. This innovative design not only ensures the accuracy of the prediction results but also significantly enhances the model's robustness and generalization ability, enabling it to maintain stable prediction performance under different operating conditions.

[0046] Compared to traditional methods that require a large amount of high-fidelity data for model training, this invention can achieve high-accuracy predictions with only low-fidelity data. This not only reduces the dependence on the amount of initial sampled data but also significantly reduces computational costs and resource consumption, providing a new approach for the efficient prediction of the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

[0047] The deep learning method proposed in this invention can quickly and accurately predict the high-fidelity flow rate and temperature distribution of printed circuit board heat exchangers (PCHEs) in sodium-cooled fast reactors, providing important basis for the design, optimization, and operation control of sodium-cooled fast reactors. The application of this method will accelerate the engineering process of sodium-cooled fast reactor technology and promote its widespread use in the nuclear energy field.

[0048] The successful implementation of this invention demonstrates the enormous potential of combining deep learning with physical modeling in predicting complex engineering problems. By integrating physical information into deep learning models, not only are prediction accuracy and efficiency improved, but solutions that can be learned from for similar problems in other fields are also provided, promoting the integrated development of deep learning and physical modeling. Attached Figure Description

[0049] Figure 1 This is a flowchart of the deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger, as described in this invention.

[0050] Figure 2 This is a schematic diagram of the configuration of the first DNN model of the deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention.

[0051] Figure 3 This is a schematic diagram of the configuration of the second DNN model in the deep learning method of the present invention for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger.

[0052] Figure 4 This is a schematic diagram of the third DNN training process of the deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to the present invention.

[0053] Figure 5 A schematic diagram comparing the low-fidelity flow field results, reference results, and prediction results provided by this invention;

[0054] Figure 6 A schematic diagram comparing the low-fidelity temperature field results, reference results, and predicted results provided by this invention. Detailed Implementation

[0055] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings:

[0056] Example 1

[0057] like Figures 1-6The diagram illustrates in detail the deep learning method proposed in this invention for predicting the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

[0058] This embodiment uses three deep neural networks (DNNs) to construct the prediction model, denoted as DNN1, DNN2, and DNN3. These networks will be used to process low-fidelity data, construct the nonlinear relationship between low-fidelity and high-fidelity data, and optimize the prediction results through physical constraints.

[0059] S1: Data Preparation

[0060] 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 typically comes from lower-precision CFD simulations, while high-fidelity data comes from higher-precision simulation or experimental data.

[0061] Data preprocessing: The input data is normalized to ensure stable convergence during training. Simultaneously, to enhance the model's generalization ability, Gaussian noise (mean = 0, standard deviation = 0.05) is added to the low-fidelity data.

[0062] S2: Construct the first DNN (DNN1)

[0063] Network Structure: DNN1 employs a multilayer perceptron architecture, comprising 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 velocity and temperature distributions. The number of hidden layers and neurons is determined based on the complexity of the specific task.

[0064] Training process: The mean squared error (MSE) is used as the loss function, and the network parameters are optimized using the gradient descent algorithm. During training, the network weights and biases are continuously adjusted until the loss function converges to a predetermined threshold.

[0065] Output results: For a given high-fidelity input coordinate, DNN1 can output the corresponding low-fidelity flow rate and temperature distribution, although these results are still low-fidelity.

[0066] S3: Construct the second DNN (DNN2)

[0067] Network Structure: DNN2 also uses a multilayer perceptron structure, but the input layer contains 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.

[0068] Training process: The model is trained using an augmented dataset containing Gaussian noise to enhance its generalization ability. The loss function is also MSE, and the network parameters are optimized using gradient descent.

[0069] 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.

[0070] S4: Construct a third DNN (DNN3) and introduce physical constraints

[0071] Network structure: The structure of DNN3 is similar to that of DNN2, but the input layer contains 5-dimensional data (including predictions from DNN2 and additional physical parameters). The output layer outputs optimized high-fidelity flow rate and temperature distributions.

[0072] Physical constraints: The Navier-Stokes equations, energy equations, and boundary conditions of the computational domain 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).

[0073] Training process: The total loss function consists of data loss and physical loss, and their importance is balanced by adjusting the weight constants. The network parameters are optimized using gradient descent until the total loss function converges to a predetermined threshold.

[0074] Output results: The trained DNN3 can output optimized high-fidelity flow rate and temperature distribution. These results are not only related to low-fidelity data, but are also strictly limited by physical constraints, thus making them more accurate and reliable.

[0075] Results Validation: The prediction accuracy and efficiency of this method are validated by comparing the prediction results output by DNN3 with real high-fidelity data (or higher-precision simulated data). Figure 5 and Figure 6As shown, the flow field and temperature field information predicted by this method are basically consistent with the actual flow field information, indicating that this method can effectively predict the thermal-hydraulic characteristics in the heat exchanger of a sodium-cooled fast reactor (PCHE). This embodiment achieves accurate prediction of high-fidelity flow velocity and temperature distribution in a PCHE based on low-fidelity data by cascading and fusing three deep neural networks and combining physical information partial differential equations and boundary conditions as constraints. This method not only improves prediction accuracy and efficiency but also reduces dependence on the amount of initial sampled data, providing strong support for the design, optimization, and safe operation of sodium-cooled fast reactors. The method of this invention mainly includes three deep neural networks (DNNs). The first DNN is purely data-driven and responsible for establishing the relationship between input coordinates and low-fidelity output. The second DNN uses a purely data-driven method to construct the nonlinear correlation between low-fidelity and high-fidelity data. The third DNN considers the Navier-Stokes equations, energy functions, and corresponding boundary conditions with respect to the computational domain 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 distribution in the PCHE channel of a sodium-cooled fast reactor.

[0076] Example 2

[0077] like Figure 1 As shown, a deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger includes the following steps:

[0078] S1: Given low-fidelity input coordinates, corresponding low-fidelity flow rate and temperature distributions, and high-fidelity input coordinates.

[0079] S2: Approximates low-fidelity flow and temperature distributions using a first DNN. A typical configuration for the first DNN model is as follows: Figure 2 As shown. The first DNN formula can be expressed as:

[0080]

[0081] in Coordinates used to represent low-fidelity grids It is a low-fidelity output of flow, temperature, and pressure solutions from a low-fidelity mesh and a low-precision CFD solver.

[0082] The training process of the first DNN is described by the function G1, where the internal variables of the neurons are θ1, representing all trainable hyperparameters, weights (w) and biases (b), and t represents the training step. For each neuron in the output and hidden layers, the outputs of all neurons in the upstream layers are used as inputs. Therefore, the neurons in each layer l can be computed using the following function:

[0083]

[0084] in This represents the activation function.

[0085] A loss function L1(θ) based on mean squared error (MSE) is introduced, and the gradient descent (GD) algorithm guides the optimization direction of the hyperparameters until the error L1(θ) reaches the convergence error. L1(θ) is...

[0086]

[0087] For high-fidelity input coordinates For example, with finer grid elements, the first DNN can immediately output the flow rate and temperature distribution corresponding to the high-fidelity input coordinates. It's worth noting that the flow rate and temperature distribution results at this step are still low-fidelity, and the output is as follows:

[0088]

[0089] S3: Construct a non-linear relationship between low-fidelity and high-fidelity data using a second DNN. The second DNN is key to in-depth research into 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 second network has an 8-dimensional input. Discrete low-fidelity data from the first DNN Coordinates of high-fidelity grid information Composition. To achieve better generalization performance, Gaussian noise data (mean = 0, standard deviation = 0.05) was added to construct the training dataset for the second neural network. The output is relatively high-fidelity data. Obtaining prediction results using a purely data-driven approach:

[0090]

[0091] S4: Partial differential equations and boundary conditions are injected 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 first two purely 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 .

[0092] L3(θ3)=λ D L D +λ Phy L Phy +λB L B

[0093]

[0094] Where λ D , λ Phy and λ B These are the corresponding weight constants of the loss function. These 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 the PCHE; therefore, the data loss function consists only of the axial velocity (u) and temperature (T) distribution terms to save computational costs. The detailed form of a single loss function can be written as follows:

[0095] Data loss:

[0096]

[0097] Physical loss - continuity equation:

[0098]

[0099] Physical loss-momentum equation:

[0100]

[0101] Physical loss-energy equation:

[0102]

[0103] Boundary loss:

[0104]

[0105] This embodiment mainly focuses on the axial flow velocity (u) and temperature (T) distribution. The final result can be written as:

[0106]

[0107] This embodiment uses three well-trained deep neural networks (DNNs) to ultimately obtain high-fidelity flow and temperature distribution in the PCHE channel of a sodium-cooled fast reactor.

[0108] pass Figure 5 and Figure 6 A comparison of the flow field information and temperature information reveals that the flow field information and temperature field information predicted by the method in this embodiment are basically consistent with the actual flow field information, thus indicating that the method in this embodiment can effectively predict the flow field and temperature field information.

[0109] Of course, the above description is only a preferred embodiment of this embodiment. This embodiment is not limited to the above-listed embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by this embodiment.

Claims

1. A deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger, characterized in that: Includes the following steps: S1: Given low-fidelity input coordinates, corresponding low-fidelity flow rate and temperature distribution, and high-fidelity input coordinates; S2: Approximates low-fidelity flow and temperature distributions using a first deep neural network (DNN); S3: Construct a non-linear relationship between low-fidelity and high-fidelity data using a second DNN; S4: Physical information partial differential equations and boundary conditions are injected as physical constraints into the third DNN to improve and optimize the results of the second DNN; the third DNN in S4 has 5-dimensional input and 5-dimensional output, and its total loss function includes data loss, physical loss, and boundary loss, used to optimize the results of the second DNN; 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 These are the corresponding weight constants of the loss function. These represent the continuity, momentum, and energy loss terms, respectively.

2. The deep learning method for predicting the 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 grids The flow rate, temperature, and pressure solutions are output by a low-fidelity grid and a low-precision CFD solver; the training process of the first DNN is described by the function G1, with the neuron of the internal variable being θ1, which represents all trainable hyperparameter weights (w) and biases (b), and t representing the training step; for each neuron in the output layer and hidden layer, the outputs of all neurons in the upstream layer are used as inputs.

3. The deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 2, characterized in that: The S2 further includes training the first DNN using a mean squared error loss function and a gradient descent algorithm until the error converges, in order to obtain approximate values ​​for low-fidelity flow and temperature distributions.

4. A deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 2 or 3, characterized in that: The neurons in each layer l can be calculated using the following function: Where F(·) represents the activation function; A loss function L1(θ) based on mean squared error is introduced, and gradient descent 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 rate and temperature distribution corresponding to the high-fidelity input coordinates; the flow rate and temperature distribution results in this step are still low-fidelity, and the output is as follows:

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

6. The deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to claim 1, characterized in that: The data loss function consists only of 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 loss-energy equation: Boundary loss: The final result of the axial velocity (u) and temperature (T) distribution can be written as:

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

8. The deep learning method for predicting the 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 the high-fidelity flow velocity and temperature distribution within PCHE channels with different fin shapes in a sodium-cooled fast reactor, based on arbitrary low-fidelity data input.

9. A deep learning method for predicting the thermal-hydraulic characteristics of a sodium-cooled fast reactor heat exchanger according to any one of claims 1 to 8, characterized in that: The deep learning method described above can significantly improve prediction accuracy and computational efficiency, and is suitable for the prediction and analysis of the thermal-hydraulic characteristics of sodium-cooled fast reactor heat exchangers.

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