A method for rapid prediction of flow and heat transfer characteristics of supercritical carbon dioxide in a micro-channel heat exchanger

Abstract

This invention relates to the field of thermal hydraulics, specifically to a rapid prediction method for the flow and heat transfer characteristics of supercritical carbon dioxide in microchannel heat exchangers. The method includes: dividing a training set and a test set according to a preset operating condition parameter space, and generating a full-order flow field database under multiple operating conditions through numerical simulation; performing intrinsic orthogonal decomposition on the full-order flow field database to extract key modes of the dominant flow and heat transfer characteristics to construct a reduced-order solution space; training an optimized neural network model using the training set to establish a mapping relationship between the operating conditions and the reduced-order solution space; reconstructing the flow field and temperature field information based on the mapping relationship, and calculating and outputting the predicted flow and heat transfer characteristics. The aim is to solve the technical problem of low computational efficiency in predicting the flow and heat transfer characteristics of supercritical carbon dioxide in microchannel heat exchangers.

Description

Technical Field

[0001] This invention relates to the field of thermal hydraulics, specifically to a method for rapid prediction of the heat transfer characteristics of supercritical carbon dioxide flow in a microchannel heat exchanger. Background Technology

[0002] Supercritical carbon dioxide (S-CO2) exhibits abrupt property changes near its critical point, significantly reducing compression work and improving energy conversion efficiency. The supercritical carbon dioxide Brayton cycle is well-suited for small modular reactors (SMRs), fourth-generation reactors, and fusion reactors.

[0003] In compact nuclear power systems, microchannel compact heat exchangers (MCDs) are key thermal devices that must meet the design requirements of high heat load, large temperature difference, and small volume. MCDs include various flow channel configurations such as straight-through channels, broken-line channels, airfoil channels, and S-shaped channels. The flow channel configuration and structural parameters directly affect the heat transfer performance of the MCD, but its multivariate and multi-objective design optimization process is highly complex, requiring high-precision flow heat transfer characteristic analysis to find the optimal flow channel configuration and optimal structural parameters of the MCD under specific operating conditions. Currently, numerical simulation of S-CO2 flow heat transfer in microchannels mainly relies on refined computational fluid dynamics (CFD) methods. The governing equations of this method exhibit highly nonlinear characteristics, requiring the use of ultra-dense grids to ensure solution accuracy, resulting in an exponential increase in computational resource consumption. Secondly, the optimization of multi-channel configuration parameters requires traversing a massive number of operating condition combinations, and a single full-order CFD simulation takes a long time, thus limiting the efficiency of design iteration. Summary of the Invention

[0004] To address the technical problem of low computational efficiency in predicting the heat transfer characteristics of supercritical carbon dioxide flow in microchannel heat exchangers, this invention provides a rapid prediction method for the heat transfer characteristics of supercritical carbon dioxide flow in microchannel heat exchangers. The specific technical solution adopted is as follows:

[0005] The present invention provides a method for rapid prediction of the heat transfer characteristics of supercritical carbon dioxide flow in microchannel heat exchangers, the method comprising:

[0006] The training set and test set are divided according to the preset working condition parameter space, and a full-order flow field database under multiple working conditions is generated through numerical simulation.

[0007] The full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes of the dominant flow heat transfer characteristics in order to construct a reduced-order solution space;

[0008] An optimized neural network model is trained using the training set to establish a mapping relationship between operating parameters and the reduced-order solution space;

[0009] Based on the mapping relationship, the flow field and temperature field information are reconstructed, and the predicted results of flow heat transfer characteristics are calculated and output.

[0010] Furthermore, a full-order flow field database under multiple operating conditions is generated through numerical simulation, including:

[0011] Three-dimensional geometric modeling was performed based on the microchannel flow configuration, and mesh independence analysis was conducted.

[0012] We call upon the variable physical property parameter data of supercritical carbon dioxide and combine it with a turbulence model to perform batch numerical simulation calculations for multiple operating conditions.

[0013] Extract flow field, temperature field and pressure field data under various working conditions to generate a multi-dimensional physical field information snapshot set.

[0014] Furthermore, the full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes of the dominant flow heat transfer characteristics to construct a reduced-order solution space, including:

[0015] The mean value of the full-order flow field data is removed.

[0016] The mode set characterizing the flow heat transfer features is extracted using the orthogonal matrix decomposition method;

[0017] Based on a preset energy cutoff threshold, key modes are selected from the mode set to construct a low-dimensional reduced-order solution space.

[0018] Furthermore, based on a preset energy cutoff threshold, key modes are selected from the mode set to construct a low-dimensional reduced-order solution space, including:

[0019] Calculate the energy contribution rate of each mode and sum them up in descending order of energy contribution rate;

[0020] The minimum number of modes to be retained is determined by comparing the cumulative contribution rate with the preset energy cutoff threshold.

[0021] The preserved modes are used as key modes for constructing the reduced-order solution space.

[0022] Furthermore, an optimized neural network model is trained using the training set to establish a mapping relationship between operating parameters and the reduced-order solution space, including:

[0023] The candidate range for the number of hidden layer nodes is generated based on the empirical relationship between the number of nodes in the input layer and the output layer.

[0024] The optimal network structure is determined by comparing all node number configurations within the candidate range and comparing training errors.

[0025] A global search algorithm is used to optimize the initial weights and thresholds of the neural network;

[0026] The network parameters are iteratively updated based on the training set data, and the model accuracy is verified through the test set.

[0027] Furthermore, a global search algorithm is used to optimize the initial weights and thresholds of the neural network, including:

[0028] The input and output data are normalized, and multiple sets of random weight and threshold combinations are initialized.

[0029] The prediction error of each weight threshold is calculated as the fitness value, and individuals with high fitness are selected for parameter cross-pollination and perturbation.

[0030] The optimal weight threshold is output by iteratively updating the weight threshold combination until the preset termination condition is met.

[0031] Furthermore, the iterative update of the network parameters includes:

[0032] The network is initialized based on the optimal weight threshold, and the network parameters are iteratively updated using training set data.

[0033] An adaptive step-size optimization algorithm is used to dynamically adjust the learning rate in order to minimize the prediction error function;

[0034] Training is terminated based on the error convergence condition or the maximum number of iterations, and a mapping model between the operating parameters and the reduced-order solution space is obtained.

[0035] Furthermore, the flow field and temperature field information are reconstructed based on the mapping relationship, including:

[0036] Based on the key modes in the reduced-order solution space, obtain the corresponding mode coefficients;

[0037] The modal coefficients are linearly combined with the key modes, and the mean field is superimposed to generate the reconstructed flow field and temperature field;

[0038] Spatial interpolation is performed on the reconstructed field information to restore the full-order physical field distribution.

[0039] Furthermore, based on the mapping relationship, the flow field and temperature field information are reconstructed, and the predicted results of the flow heat transfer characteristics are calculated and output, including:

[0040] Based on the reconstructed flow field information, multiple calculation sections are divided along the microchannel axis, and the flow channel is divided into several continuous segments.

[0041] Extract the average temperature, velocity, and pressure parameters of the fluid mass flow rate within each segment;

[0042] The heat flux density and energy transfer characteristics are calculated based on the relationship between enthalpy change and pressure drop of adjacent segments.

[0043] Furthermore, the heat flux density and energy transfer characteristics are calculated, including:

[0044] The local heat transfer coefficient is calculated piecewise based on the ratio of heat flux density to the temperature difference at the fluid-solid interface.

[0045] The friction factor is calculated based on the relationship between pressure drop and flow kinetic energy, combined with the flow channel geometric parameters.

[0046] The calculation results of each segment are weighted and integrated to output the overall heat transfer coefficient and friction factor of the microchannel.

[0047] The present invention has the following beneficial effects:

[0048] This invention provides a rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers. It constructs a reduced-order solution space by extracting key modes through intrinsic orthogonal decomposition, reducing model complexity while preserving the main features of the flow and temperature fields, ensuring high-precision reconstruction of the physical fields. Furthermore, it utilizes an optimized neural network to establish a mapping relationship between operating parameters and the reduced-order solution space, transforming traditional time-consuming CFD simulations into efficient predictions and improving computational efficiency. Finally, it calculates and outputs the predicted flow heat transfer characteristics through field information reconstruction and piecewise integration, balancing the rapid acquisition of global and local parameters. This method achieves rapid and high-precision prediction under multiple configurations and wide parameter scenarios without the need to construct complex reduced-order control equations. Attached Figure Description

[0049] To more clearly illustrate the technical solutions and advantages 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 A flowchart of a method for rapid prediction of supercritical carbon dioxide flow heat transfer characteristics in a microchannel heat exchanger, provided in an embodiment of the present invention.

[0051] Figure 2 The flowchart shows the algorithm for a rapid prediction method of supercritical carbon dioxide flow heat transfer characteristics in a microchannel heat exchanger, as provided in an embodiment of the present invention.

[0052] Figure 3 This is a schematic diagram of the geometric model of a polygonal microchannel provided in one embodiment of the present invention;

[0053] Figure 4 This is a schematic diagram of mesh division provided in one embodiment of the present invention;

[0054] Figure 5 A cold fluid friction factor distribution diagram provided in one embodiment of the present invention;

[0055] Figure 6 A thermal fluid friction factor distribution diagram provided in one embodiment of the present invention;

[0056] Figure 7 A cold fluid heat transfer coefficient distribution diagram provided in one embodiment of the present invention;

[0057] Figure 8 A heat transfer coefficient distribution diagram of a thermal fluid provided in one embodiment of the present invention. Detailed Implementation

[0058] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in a microchannel heat exchanger proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0060] The following description, in conjunction with the accompanying drawings, details the specific scheme of the rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers provided by this invention.

[0061] The interior of a microchannel heat exchanger comprises a flow field, a temperature field, and a pressure field. The flow field describes the fluid flow state within the microchannel heat exchanger, including the fluid velocity, direction, and flow trajectory. The temperature field represents the temperature distribution at various locations within the microchannel heat exchanger; different regions exhibit temperature differences due to varying degrees of heat exchange. By studying the temperature field, the heat transfer effect between hot and cold fluids can be clarified, and whether there are areas of localized overheating or undercooling within the heat exchanger can be identified. The pressure field reflects the pressure distribution throughout the microchannel heat exchanger. As the fluid flows within the microchannels, the pressure changes due to variations in the channel's shape and size, as well as friction between the fluid and the channel walls. Therefore, the flow field, temperature field, and pressure field are crucial for optimizing the design of microchannel heat exchangers and improving their heat exchange efficiency and operational performance.

[0062] While the Proper Orthogonal Decomposition (POD) method has applications in the field of flow heat transfer, its traditional approach combines POD with the Galerkin projection method to project high-dimensional problems into a low-dimensional space for solution, thereby reducing computational costs. However, this method relies on the complex construction of reduced-order governing equations, limiting its applicability to highly nonlinear systems. Furthermore, existing neural network-based prediction techniques often focus on global parameters such as heat transfer coefficients, making it difficult to efficiently predict high-dimensional physical quantities such as local temperature and velocity fields. Directly training neural networks on large-scale grid data is also not feasible. Therefore, this invention provides an innovative method that balances computational efficiency and prediction accuracy to overcome the technical bottleneck of rapid analysis of S-CO2 flow heat transfer in microchannels.

[0063] Please see Figure 1 and Figure 2 This document illustrates a method flowchart and algorithm flowchart for a rapid prediction method of supercritical carbon dioxide flow heat transfer characteristics in a microchannel heat exchanger, provided by an embodiment of the present invention. The method includes:

[0064] Step S100: Divide the training set and test set according to the preset working condition parameter space, and generate a full-order flow field database under multiple working conditions through numerical simulation; specifically, the preset working condition parameter space refers to the sampling range of working condition parameters, as shown in Table 1:

[0065]

[0066] Table 1 Sampling range of operating parameters

[0067] In Table 1, Indicates the inlet temperature of the cold fluid. Hot fluid inlet temperature, Cold fluid outlet pressure, Indicates the outlet pressure of the hot fluid, The inlet mass flow rate is represented by the sampling range of operating parameters recorded in Table 1. The Latin hypercube sampling method is used to sample the operating parameters, construct a five-dimensional parameter space, and add one sample point at the minimum and maximum values ​​of each dimension parameter to ensure coverage of extreme operating conditions. 332 sets of samples are generated by the above method, and then the samples are randomly divided into training set and test set at a ratio of 5:1, with 282 sets of training set and 50 sets of test set.

[0068] Step S100 specifically includes:

[0069] Step S110: Perform 3D geometric modeling based on the microchannel flow configuration and conduct mesh independence analysis; specifically, use ICEM software to construct a 3D geometric model based on the microchannel flow configuration, see [link to relevant documentation]. Figure 3 As shown, Figure 3 This is a schematic diagram of the three-dimensional geometric model of a polygonal flow channel. Figure 3 The red areas represent hot runners, and the blue areas represent cold runners; then, meshing is performed on the 3D geometric model, which can be found in [reference needed]. Figure 4 The example demonstrates a hybrid mesh partitioning strategy, employing different mesh types for different regions. Mesh independence analysis specifically examines the impact of mesh partitioning on the computational results. This embodiment uses meshes of varying densities and types for calculations. If the computational results do not significantly change with mesh variations within a certain error range, the results demonstrate mesh independence. For instance, in fluid dynamics simulations, coarse, medium, and fine meshes are used to simulate fluid flow within microchannels. If the calculated values ​​of key parameters such as velocity and pressure are similar across different meshes, the simulation results demonstrate mesh independence. This means the selected mesh effectively and accurately reflects the physical phenomena, and subsequent calculations can be based on this mesh without further mesh refinement, thus reducing computational costs.

[0070] Step S120: Call up the variable physical property parameter data of supercritical carbon dioxide and perform batch numerical simulation calculations for multiple operating conditions in combination with the turbulence model; specifically, the variable physical property parameter data of supercritical carbon dioxide can be called up from the NIST REFRPROP database. The NIST REFRPROP database refers to the REFPROP database developed by the National Institute of Standards and Technology (NIST). REFPROP is a software tool and related database used to calculate the thermophysical properties of fluids. Through the NIST REFRPROP database, the density, viscosity, thermal conductivity, specific heat capacity at constant pressure and other parameter data of S-CO2 in the supercritical state can be obtained;

[0071] The turbulence model adopts the k-ω SST model, where k is the turbulent kinetic energy, ω is the specific dissipation rate, and SST is the shear stress transport. By writing Fluent Journal script files, the batch calculation of load parameters, boundary conditions, solver iteration, and result output, as well as the batch extraction of full-order field information, can be completed automatically.

[0072] Step S130: Extract flow field, temperature field, and pressure field data for each operating condition to generate a multi-dimensional physical field information snapshot set; specifically, extract the three-dimensional flow field physical data of each operating condition parameter, namely velocity, temperature, and pressure, from the Fluent result file, organize them into one-dimensional column vectors according to the grid node coordinates, and concatenate the column vectors of all operating conditions column by column to form a snapshot matrix. , The total number of operating conditions is 332. The physical field dimension, i.e., the total number of grids, is the snapshot matrix. It can be represented as:

[0073]

[0074] In the formula, It is a snapshot matrix that stores the physical field data for all working conditions, with each column corresponding to the full field information for one working condition; Represents the first in the snapshot matrix Column vectors, representing combinations of operating parameters. The physical field distribution under the given conditions can be temperature, velocity, or pressure. For the first The combination of operating parameters, including the cold fluid inlet temperature. Inlet temperature of hot fluid Cold fluid outlet pressure Hot fluid outlet pressure and inbound quality flow For each working condition , Its physical field column vector is used as the first column of the snapshot matrix. Columns; Each column of the snapshot matrix corresponds to the distribution of physical quantities across the entire field for a given operating condition; This is the set of grid node coordinates; taking the temperature field snapshot matrix as an example. Each column Indicates working conditions The temperature distribution of all grid nodes is shown below, with row indices corresponding to grid node positions and column indices corresponding to operating condition numbers. This embodiment can provide a standard input format for intrinsic orthogonal decomposition (POD). By performing singular value decomposition (SVD) on the snapshot matrix, the main flow field modes across operating conditions can be extracted, thereby compressing the high-dimensional physical field into a low-dimensional space composed of a few key modes.

[0075] This embodiment ensures coverage of multiple parameter ranges and extreme conditions through Latin hypercube sampling and boundary point supplementation. It achieves a balance between computational accuracy and efficiency by combining hybrid mesh generation and mesh independence analysis. The REFPROP database, coupled with Fluent scripts, enables automated batch simulation of variable-property S-CO2 flow heat transfer. Finally, high-dimensional physical field data is organized using a snapshot matrix structure. This workflow not only provides a high-quality, fully covered full-order solution dataset for subsequent POD order reduction but also significantly reduces the manual intervention cost and computation time of traditional CFD simulations through mesh optimization and batch computation, while ensuring the physical realism and reliability of the full-order solutions.

[0076] Step S200: Perform intrinsic orthogonal decomposition on the full-order flow field database to extract key modes of the dominant flow heat transfer characteristics in order to construct a reduced-order solution space;

[0077] Step S200 specifically includes:

[0078] Step S210: Perform mean-removal processing on the full-order flow field data; perform snapshot matrix... The average physical quantity of each grid node under all operating conditions is calculated row by row to obtain the mean field vector. ; Create a snapshot column vector for each operating condition Subtract the mean field vector element by element This yields the mean-free fluctuation field matrix. , wave field vector It can be represented as:

[0079]

[0080] Among them, the mean-removed fluctuation field matrix It only includes fluctuation information of each working condition relative to the mean field, eliminating the interference of the global mean on subsequent mode decomposition;

[0081] Step S220: Extract the mode set characterizing the flow heat transfer features using the orthogonal matrix decomposition method; specifically, for the wave field matrix... Singular value decomposition can be represented as:

[0082]

[0083] In the formula, It is a left singular vector matrix, whose column vectors are spatial modes, used to characterize the distribution pattern of physical fields in space; It is a diagonal matrix, and the diagonal elements are singular values. The magnitude of the singular values ​​reflects the energy proportion or variance contribution of the corresponding mode. It is a right singular vector matrix, and the column vectors are the parametric modes, representing the weight distribution of each mode in the working condition parameter space; This is the transpose. SVD achieves orthogonal decomposition of complex flow fields by decomposing high-dimensional physical fields into linear combinations of spatial modes and parameter weights, allowing subsequent reconstruction of the flow field distribution containing the main features using only a small number of POD bases.

[0084] Step S230: Based on a preset energy cutoff threshold, key modes are selected from the mode set to construct a low-dimensional reduced-order solution space; wherein, the reduced-order solution space specifically refers to the low-dimensional feature subspace extracted from the full-order flow field database through intrinsic orthogonal decomposition (POD), which is used to reduce the dimension of the full-order physical field of millions of grids to tens of dimensions; and then, as the output target of the neural network, a mapping relationship between the operating parameters and the modal coefficients is established to achieve efficient flow field reconstruction.

[0085] Step S231: Calculate the energy contribution rate of each mode and accumulate them in descending order of energy contribution rate; specifically, in the singular value decomposition (SVD) of step S220, the diagonal elements of the singular value matrix are sorted from largest to smallest; the square of the singular value corresponds to the modal energy, and the modes are sorted from highest to lowest energy contribution rate to calculate the cumulative energy contribution rate of multiple modes:

[0086] Step S232: Determine the minimum number of modes to be retained based on the comparison between the cumulative contribution rate and the preset energy cutoff threshold; specifically, according to the formula:

[0087]

[0088] In the formula, For the first Each eigenvalue is a modal energy. A preset energy cutoff threshold is set; based on this formula, a binary search method can be used to search for the minimum number of modes to be retained. ;

[0089] Step S233: The preserved mode is used as the key mode for constructing the reduced-order solution space; specifically, the preceding mode is extracted from the left singular vector matrix. Left singular eigenvectors This constitutes the POD basis matrix. ,Right now:

[0090]

[0091] Wherein, each POD basis vector , i.e., key mode, which corresponds to a heat transfer mode;

[0092] In this embodiment, mean removal eliminates the global offset of the flow field, ensuring that subsequent mode decomposition focuses on the differences between operating conditions. Furthermore, singular value decomposition and truncation extract key POD bases from the full-order flow field of millions of grid cells, reducing the order of magnitude of the physical field dimension. Simultaneously, a cumulative energy threshold preserves the principal features. This method does not rely on heat transfer differential equations or turbulence model assumptions; it constructs a reduced-order solution space solely through statistical data characteristics, making it suitable for general modeling of complex microchannel configurations and varying physical properties. This step, as a link between full-order simulation and rapid prediction, provides low-dimensional and efficient input for the subsequent neural network to establish the mapping relationship between operating parameters and the reduced-order solution space. Ultimately, the construction of the reduced-order solution space achieves a balance between computational efficiency and physical realism.

[0093] Step S300: Train the optimized neural network model using the training set and establish the mapping relationship between the operating parameters and the reduced-order solution space;

[0094] Step S300 specifically includes:

[0095] Step S310: Generate a candidate range for the number of hidden layer nodes based on the empirical relationship between the number of nodes in the input layer and the output layer; specifically, the number of input layer nodes corresponds to the dimension of operating condition parameters, i.e., the 5 nodes recorded in Table 1; the number of output layer nodes corresponds to the dimension of the reduced-order solution space. This refers to the number of POD bases; the candidate range for the number of hidden layer nodes can be determined using the following empirical formula:

[0096]

[0097] In the formula, This represents the candidate range for the number of hidden layer nodes; Input the number of nodes in the layer; This represents the number of nodes in the output layer. The adjustment factor is an integer between 1 and 10;

[0098] Step S320: Traverse all node configurations within the candidate range and determine the optimal network structure by comparing training errors; specifically, for the candidate node count determined in step S310, construct a BP neural network one by one, traverse all hidden layer nodes within the determined candidate range, calculate the network error, and select the neural network configuration with the smallest error; the number of hidden layer nodes in the neural network established for the five variables in this embodiment is shown in Table 2:

[0099] Table 2 Number of Hidden Layer Nodes in Neural Networks

[0100]

[0101] in, For pressure field; For temperature field; , , The velocity field has three components, and the number of nodes in its hidden layer was calculated for each component.

[0102] Step S330: Optimize the initial weights and thresholds of the neural network using a global search algorithm, including:

[0103] Step S331: Normalize the input and output data and initialize multiple sets of random weight and threshold combinations; specifically, perform max-min normalization on the input working condition parameters and output POD coefficients to ensure that all data are mapped to the [0,1] interval, avoiding gradient update imbalance due to differences in units; then use a genetic algorithm to randomly generate initial weight and threshold combinations as the initial population.

[0104] Step S332: Calculate the prediction error of each weight threshold as the fitness value, and select individuals with high fitness for parameter crossover and perturbation; specifically, the roulette wheel selection method can be used to select the top 50% of individuals as parents according to the fitness ratio; then, the parents are crossovered at a single point to generate offspring individuals; finally, the weight threshold of individuals is randomly perturbed with a preset low probability to maintain population diversity.

[0105] Step S333: Iteratively update the weight threshold combination until a preset termination condition is met, and output the optimal weight threshold; for example, set the maximum number of iterations to 50, and calculate the optimal fitness of the population after each iteration. If the fitness does not significantly improve for 10 consecutive generations, terminate the iteration early. Output the weight threshold of the optimal individual as the initial parameters of the BP neural network for subsequent training.

[0106] In this embodiment, the search range of hidden layer nodes is narrowed based on empirical formulas for input and output dimensions, and cross-validation is used to avoid overfitting, which can ensure that the network structure matches the spatial dimension of the reduced-order solution. The network structure is optimized for velocity, temperature and pressure fields respectively, allowing different physical quantities to adopt independent hidden layer configurations as shown in Table 4, which can be adapted to their respective modal energy distribution characteristics.

[0107] Step S340: Iteratively update the network parameters based on the training set data, and verify the model accuracy through the test set;

[0108] The iterative update of the network parameters includes:

[0109] Step S341: Initialize the network based on the optimal weights and thresholds, and iteratively update the network parameters using training set data. Specifically, the optimal weights and thresholds obtained through genetic algorithm optimization are used as the initial parameters of the neural network. The predicted values ​​are calculated using forward propagation with training set data, and the gradient of the error with respect to the parameters is calculated using backpropagation algorithm. Then, the network parameters are iteratively updated using the Levenberg-Marquardt (LM) algorithm. The LM algorithm effectively combines the stability of gradient descent and the fast convergence of Newton's method. By adaptively adjusting the damping factor to balance the parameter update step size, it can avoid getting trapped in local optima.

[0110] Step S342: The learning rate is dynamically adjusted using an adaptive step size optimization algorithm to minimize the prediction error function. The adaptive step size mechanism can avoid oscillations caused by an excessively high learning rate or slow convergence caused by an excessively low learning rate, ensuring that the model decreases rapidly in the early stages of training and is finely adjusted in the later stages, thereby accelerating convergence and improving the final accuracy.

[0111] Step S343: Terminate training based on the error convergence condition or the maximum number of iterations to obtain the mapping relationship model between the working condition parameters and the reduced-order solution space; the error convergence condition can be configured to be that when the loss function of the training set or validation set decreases by less than a preset threshold for multiple consecutive iterations, the model is considered to have converged; the error convergence condition can also be configured to forcibly terminate training if it has not converged after reaching the preset maximum number of training rounds; the finally generated model establishes a nonlinear mapping relationship between the working condition parameters (input layer) and the coefficients of the reduced-order solution space (output layer), which can be used to quickly predict the POD coefficient under new working conditions.

[0112] The model accuracy verification includes:

[0113] The full-field prediction error norm is calculated based on the test set data, and the relative error distribution of local spatial points is statistically analyzed. Error evaluation criteria include the full-field L2 error. and the local relative error of each spatial point For each operating condition in the test set, the trained neural network is used to predict the POD coefficients. The physical field is reconstructed based on the POD basis matrix from step S200 to obtain the predicted physical field matrix. The predicted physical field matrix is ​​compared with the true physical field matrix obtained from the full-order CFD simulation, and the L2 error between the two is calculated to measure the global prediction accuracy. This error reflects the overall similarity between the predicted and true fields; a smaller value indicates a higher global matching degree. On the other hand, for each grid node, the relative error between the predicted and true values ​​for that node under all operating conditions in the test set is calculated, and the average value is taken. By analyzing the local error distribution, prediction defects in specific regions of the microchannel can be located, such as velocity field errors or wall heat flux density errors in the flow separation zone.

[0114] The expressions for the L2 norm error and the local relative error are:

[0115]

[0116]

[0117] In the formula, The predicted physical field matrix; Results are from full-order numerical simulations; L2 norm error. It can measure the overall similarity between the predicted field and the real field; the smaller the value, the higher the global matching degree. Represents the test set; Indicates the first Predicted values ​​for each working condition; Indicates the first Numerical simulation results for each working condition; according to the formula, if the evaluation results of the second norm error and the local relative error do not meet the accuracy requirements, the model parameters or structure should be adjusted: for example, increasing the number of hidden layer nodes to improve the network's expressive power, expanding the training set sample size, supplementing the working condition data corresponding to the high error region, adjusting the number of POD bases, and retaining more flow field details by increasing key modes.

[0118] The L2 norm errors of the five field quantities predicted in this example are shown in Table 3:

[0119] Table 3. Norm error of each field quantity

[0120]

[0121] Table 3 lists the five field quantities predicted in the rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers: For pressure, For temperature, , , The L2 error represents the velocity component. The L2 error measures the overall similarity between the predicted and actual fields; a smaller value indicates a higher global match. Table 3 shows that the L2 errors for each field are relatively small. The L2 error for the pressure field is 0.039%, and for the temperature field, it is 0.28%, indicating high accuracy in predicting pressure and temperature, reflecting the actual physical field well. While the velocity field prediction error is slightly higher than the pressure and temperature field errors, it remains relatively low in practical applications, indicating that the model's velocity field prediction also possesses a certain degree of reliability, capturing the main characteristics and trends of the velocity field. This meets the accuracy requirements of practical engineering applications and can be used in engineering scenarios such as the design and optimization of microchannel heat exchangers.

[0122] In summary, this embodiment utilizes the LM algorithm and adaptive learning rate to accelerate the training process, improving convergence speed compared to the traditional BP algorithm. The trained model can predict new operating conditions in milliseconds, transforming traditional CFD simulations into real-time responses and significantly improving efficiency. Based on error feedback, the network structure and training strategy are dynamically adjusted, enabling the model to automatically adapt to complex scenarios such as variable properties of supercritical carbon dioxide and multi-channel configurations, avoiding overfitting or underfitting and enhancing the model's generalization ability over a wide parameter range. Variable properties refer to the drastic changes in the density, specific heat capacity, and thermal conductivity of supercritical carbon dioxide with temperature or pressure, rendering traditional constant property assumptions inapplicable. Property correction coefficients need to be introduced, or a coupled correlation model between the property field and the flow heat transfer field needs to be established to quantify the impact of property changes on momentum or energy transfer and incorporate it into the constitutive relation.

[0123] Step S400: Reconstruct the flow field and temperature field information based on the mapping relationship, calculate and output the predicted results of flow heat transfer characteristics;

[0124] Among them, the reconstructing of flow field and temperature field information based on mapping relationships includes:

[0125] Step S410: Obtain the corresponding modal coefficients based on the key modes in the reduced-order solution space; input the operating parameters into the trained neural network model. This neural network establishes a mapping relationship between the operating parameters and the reduced-order solution space through step S300. Its structure includes an input layer, a hidden layer, and an output layer. The neural network calculates through forward propagation and outputs the modal coefficient vector of the reduced-order solution space. For each physical quantity, the output modal coefficient vector contains... One element;

[0126] Step S411: Linearly combine the modal coefficients with the key modes, and superimpose the mean field to generate the reconstructed flow field and temperature field; perform spatial interpolation on the reconstructed field information to recover the full-order physical field distribution; specifically, by using the mean field... With each key mode By linearly superimposing the corresponding POD coefficients, the physical field can be reconstructed. Utilizing key information in the low-dimensional reduced-order solution space, the reconstructed physical field can be quickly obtained from the operating parameters, which can be expressed as:

[0127]

[0128] In the formula, Indicates the location and working conditions The reconstructed physical field A set of grid node coordinates; The mean field is the average value of the physical fields such as the flow field or temperature field obtained by the mean removal process in step S200. The POD coefficient, obtained through neural network output, reflects the operating conditions. Next The contribution weights of each key mode to the physical field will vary depending on the operating conditions. The values ​​are different; This represents the POD basis vectors, i.e., the key modes determined in step S230. Each key mode corresponds to a heat transfer or flow mode, describing the physical field in space. Distribution characteristics on;

[0129] In this embodiment, reduced-order models were established for three-dimensional velocity, temperature, and pressure. The dimensions of the reduced-order physical fields and the errors in the reduction process are shown in Table 4.

[0130] Table 4. Dimensions of the reduced physical fields and errors in the reduction process.

[0131]

[0132] Table 4 records relevant information after establishing a reduced-order model for three-dimensional velocity, temperature, and pressure in the study of supercritical carbon dioxide flow heat transfer characteristics in a microchannel heat exchanger. The reduced-order physical field dimensions show the dimensions of different physical quantities in the space after the reduction process. The reduced-order dimension for pressure is 3, for temperature it is 23, and for velocity components it is 10, 12, and 21, respectively. These dimensions represent the low-dimensional spatial dimensions required to describe the corresponding physical quantities after extracting key modes using methods such as intrinsic orthogonal decomposition (POD). The reduction process error is given as a percentage for each physical quantity in the reduced-order model, reflecting the degree of deviation of the reduced-order model from the original high-dimensional physical field information.

[0133] As can be seen from Table 4, from the perspective of the reduced physical field dimension, each physical quantity is compressed from a high-dimensional space to a relatively low-dimensional space. This indicates that the POD reduction method effectively reduces the dimensionality required to describe the physical field, lowers computational complexity, and improves the efficiency of subsequent computational analysis. On the other hand, the errors of the reduced model vary for different physical quantities, with the pressure field showing the smallest error, indicating that the reduced model approximates the pressure field to the highest degree and can well preserve the original characteristics of the pressure field. Although the accuracy of the reduced model varies for different physical quantities, it can generally guarantee an approximate restoration of the original physical field and can be used for subsequent flow and heat transfer characteristic analysis. Therefore, this reduced model can significantly reduce the computational dimensionality while keeping the error within a reasonable range, which is of great value for the research and engineering application of supercritical carbon dioxide flow and heat transfer characteristics in microchannel heat exchangers. It can provide an efficient computational model for rapidly predicting flow and heat transfer characteristics without significantly sacrificing accuracy.

[0134] In summary, this embodiment, based on a well-trained neural network that establishes a mapping relationship between operating parameters and the reduced-order solution space, can quickly obtain modal coefficients from the input operating parameters without performing complex and time-consuming full-order numerical simulations. This significantly shortens computation time and enables rapid conversion from operating parameters to key physical field information, meeting the real-time requirements in engineering. Furthermore, based on the constructed low-dimensional reduced-order solution space, the modal coefficients output by the neural network describe the key features of the physical field in a low-dimensional space. This approach avoids processing high-dimensional and complex original flow field data, reducing computational complexity while preserving the main variation patterns of the physical field. This improves computational efficiency while maintaining a certain level of accuracy.

[0135] The calculation and output of the predicted flow heat transfer characteristics include:

[0136] Step S420: Based on the reconstructed flow field information, multiple calculation sections are divided along the microchannel axis, dividing the flow channel into several continuous segments; to more accurately analyze the flow and heat transfer characteristics within the microchannel and avoid the influence of complex boundary conditions at the inlet and outlet, sections perpendicular to the channel axis and far from the inlet and outlet are selected. Four cross-sections are used in this embodiment, dividing the middle flow channel into three segments. The location of the cross-sections can be determined based on factors such as the length of the microchannel and the extent of flow development, and is generally required to be in areas where the flow is stable and less affected by inlet and outlet disturbances.

[0137] Step S421: Extract the average temperature, velocity, and pressure parameters of the fluid mass flow rate within each segment. For each flow channel segment, determine the cross-sectional area of ​​the channel based on the flow field information reconstructed in step S410. The inlet mass flow rate is obtained by measurement or calculation. Due to mass conservation within the flow channel, the mass flow rate within each segment can be considered approximately equal to the inlet mass flow rate. Within each flow channel segment, based on the reconstructed temperature field information, the temperature at different locations within that segment is statistically averaged to obtain the average temperature of the fluid in that segment. Specifically, the temperature values ​​of all grid nodes within that segment can be arithmetically averaged, or a weighted average can be performed based on the weights of different locations. The extraction of velocity and pressure parameters is also based on the reconstructed flow field information, extracting the velocity and pressure parameters of the fluid within each flow channel segment.

[0138] Step S422: Calculate heat flux density and energy transfer characteristics based on the enthalpy change and pressure drop relationship of adjacent segments; including: calculating the local heat transfer coefficient segment by segment according to the ratio of heat flux density to fluid-solid interface temperature difference; calculating the friction factor based on the relationship between pressure drop and flow kinetic energy, combined with the flow channel geometric parameters; weighting and integrating the calculation results of each segment to output the overall heat transfer coefficient and friction factor of the microchannel; wherein, for the first segment... hot runner section, based on extraction pressure and average temperature By consulting the property table of supercritical carbon dioxide, the corresponding specific enthalpy was obtained. The heat flux enthalpy calculation can be expressed as:

[0139]

[0140] In the formula, For the first Enthalpy of heat flow in a hot runner section; The cross-sectional area of ​​the flow channel; For inlet quality flow rate;

[0141] The heat flux density can be calculated using the difference in enthalpy between two adjacent segments, and can be expressed as:

[0142]

[0143] In the formula, Indicates the first Heat flux density of the hot runner section; Indicates the first The heat flux enthalpy of a heat flow channel segment; that is, by subtracting the heat flux enthalpy of the current segment from the heat flux enthalpy of the next segment, the heat flux density of that segment per unit time is obtained, which reflects the heat transfer rate within that segment of the channel.

[0144] The local heat transfer coefficient can be calculated as follows:

[0145]

[0146] Among them, subscript This represents the average value. Indicates hot runner, Indicates a solid region; express No. part The average temperature of the solid wall surface; Indicates the first The average temperature of the fluid in a section; the formula uses the ratio of heat flux density to the temperature difference at the fluid-solid interface to obtain the local heat transfer coefficient, which reflects the heat transfer capacity between the fluid and the solid wall in that section of the flow channel.

[0147] Finally, the friction factor is calculated based on the relationship between pressure drop and flow kinetic energy, combined with the flow channel geometry parameters. For example, by measuring or calculating the pressure drop between two adjacent sections, and combining parameters such as fluid velocity and density, the friction factor is calculated using the Darcy-Weisbach formula. The principle is to determine the friction factor through the relationship between pressure drop and flow-related parameters, reflecting the resistance characteristics of fluid flow within the flow channel. The heat transfer coefficients and friction factors calculated for each section are weighted and integrated to finally output the overall heat transfer coefficient and friction factor of the microchannel, thus obtaining the heat transfer and flow performance indicators of the entire microchannel heat exchanger.

[0148] See Figures 5 to 8The scatter plot shown illustrates the comparison between predicted and actual values, with the horizontal axis representing the actual value and the vertical axis representing the predicted value. Each subplot has three lines: the middle dashed line represents the ideal case where the predicted and actual values ​​are equal; the upper and lower solid lines represent the boundaries of +10% and -10% relative errors, respectively; the blue scatter points represent the correspondence between predicted and actual values ​​for different calculation examples, with each scatter point indicating the coordinate position of the predicted and actual values ​​for a given example. Therefore, it can be understood that the relative error of the convective heat transfer coefficient for 99% of the examples in the test set is within 10%, with a maximum error of 12.7%; the relative error of the friction factor for 97% of the examples is within 10%, with a maximum error of 16.6%. In terms of computational efficiency, traditional CFD numerical simulations require tens of minutes to calculate a single example, while the simulation method of this invention only requires 3 seconds, increasing the calculation speed by hundreds of times and reducing the model dimensionality by approximately [missing information]. The method of this invention significantly improves computational efficiency, providing rapid results and meeting the speed requirements of practical engineering. In summary, the non-invasive order reduction method based on POD proposed in this invention, in the S-CO2 flow heat transfer problem within microchannels, not only meets accuracy requirements (with fundamental field norm errors all below 3%), but also greatly reduces the dimensionality of the physical field and improves computational speed, enabling better prediction of the field distribution patterns of S-CO2 flow heat transfer within microchannels.

[0149] In summary, the rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers provided by this invention solves the problem of the large amount of computational resources and time required by traditional full-order CFD solutions. Utilizing the reconstructed flow and temperature field information, it rapidly performs flow channel segmentation and parameter calculations, reducing the reconstruction and parameter calculation time from several hours to seconds, significantly improving computational efficiency and meeting the engineering requirements for rapid calculations. The calculations can accurately obtain key parameters such as the overall heat transfer coefficient and friction factor of the microchannel, meeting engineering accuracy requirements.

[0150] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0151] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A rapid prediction method for the heat transfer characteristics of supercritical carbon dioxide flow in a microchannel heat exchanger, characterized in that, The method includes: The training set and test set are divided according to the preset working condition parameter space, and a full-order flow field database under multiple working conditions is generated through numerical simulation. The full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes of the dominant flow heat transfer characteristics in order to construct a reduced-order solution space; An optimized neural network model is trained using the training set to establish a mapping relationship between operating parameters and the reduced-order solution space, including: The candidate range for the number of hidden layer nodes is generated based on the empirical relationship between the number of nodes in the input layer and the output layer. The optimal network structure is determined by comparing all node number configurations within the candidate range and comparing training errors. A global search algorithm is used to optimize the initial weights and thresholds of the neural network, including: The input and output data are normalized, and multiple sets of random weight and threshold combinations are initialized. The prediction error of each weight threshold is calculated as the fitness value, and individuals with high fitness are selected for parameter cross-pollination and perturbation. The optimal weight threshold is output by iteratively updating the weight threshold combination until the preset termination condition is met. The network parameters are iteratively updated based on the training set data, and the model accuracy is verified through the test set. Based on the mapping relationship, the flow field and temperature field information are reconstructed, and the predicted results of flow heat transfer characteristics are calculated and output, including: Based on the key modes in the reduced-order solution space, obtain the corresponding mode coefficients; The modal coefficients are linearly combined with the key modes, and the mean field is superimposed to generate the reconstructed flow field and temperature field; Spatial interpolation is performed on the reconstructed field information to restore the full-order physical field distribution; Based on the reconstructed flow field information, multiple calculation sections are divided along the microchannel axis, and the flow channel is divided into several continuous segments. Extract the average temperature, velocity, and pressure parameters of the fluid mass flow rate within each segment; The heat flux density and energy transfer characteristics are calculated based on the relationship between enthalpy change and pressure drop of adjacent segments.

2. The rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers as described in claim 1, characterized in that, A full-order flow field database under multiple operating conditions is generated through numerical simulation, including: Three-dimensional geometric modeling was performed based on the microchannel flow configuration, and mesh independence analysis was conducted. We call upon the variable physical property parameter data of supercritical carbon dioxide and combine it with a turbulence model to perform batch numerical simulation calculations for multiple operating conditions. Extract flow field, temperature field and pressure field data under various working conditions to generate a multi-dimensional physical field information snapshot set.

3. The rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers as described in claim 1, characterized in that, The full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes of the dominant flow heat transfer characteristics in order to construct a reduced-order solution space, including: The mean value of the full-order flow field data is removed. The mode set characterizing the flow heat transfer features is extracted using the orthogonal matrix decomposition method; Based on a preset energy cutoff threshold, key modes are selected from the mode set to construct a low-dimensional reduced-order solution space.

4. The rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers as described in claim 3, characterized in that, Based on a preset energy cutoff threshold, key modes are selected from the mode set to construct a low-dimensional reduced-order solution space, including: Calculate the energy contribution rate of each mode and sum them up in descending order of energy contribution rate; The minimum number of modes to be retained is determined by comparing the cumulative contribution rate with the preset energy cutoff threshold. The preserved modes are used as key modes for constructing the reduced-order solution space.

5. The rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers as described in claim 1, characterized in that, The iterative update of the network parameters includes: The network is initialized based on the optimal weight threshold, and the network parameters are iteratively updated using training set data. An adaptive step-size optimization algorithm is used to dynamically adjust the learning rate in order to minimize the prediction error function; Training is terminated based on the error convergence condition or the maximum number of iterations, and a mapping model between the operating parameters and the reduced-order solution space is obtained.

6. The rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers as described in claim 1, characterized in that, Calculate heat flux density and energy transfer characteristics, including: The local heat transfer coefficient is calculated piecewise based on the ratio of heat flux density to the temperature difference at the fluid-solid interface. The friction factor is calculated based on the relationship between pressure drop and flow kinetic energy, combined with the flow channel geometric parameters. The calculation results of each segment are weighted and integrated to output the overall heat transfer coefficient and friction factor of the microchannel.

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