Method for rapidly predicting flow heat transfer characteristics of supercritical carbon dioxide of micro-channel heat exchanger

Abstract

The invention relates to the technical field of thermal hydraulic power, in particular to a rapid prediction method for flow heat transfer characteristics of supercritical carbon dioxide of a micro-channel heat exchanger, and the method comprises the steps: dividing a training set and a test set according to a preset working condition parameter space, and generating a full-order flow field database under multiple working conditions through numerical simulation; performing eigenorthogonal decomposition on the full-order flow field database, and extracting a key mode of a dominant flow heat transfer feature to construct a reduced-order solution space; training an optimized neural network model by using the training set, and establishing a mapping relationship between the working condition parameters and the reduced-order solution space; and reconstructing flow field and temperature field information based on the mapping relation, and calculating and outputting a flow heat transfer characteristic prediction result. The method aims at solving the technical problem that the heat transfer characteristic prediction calculation efficiency of the supercritical carbon dioxide heat transfer flow of the micro-channel heat exchanger is low.

Description

Technical Field

[0001] The present invention relates to the field of thermal hydraulic technology, and in particular to a method for quickly predicting flow heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger. Background Art

[0002] Supercritical carbon dioxide (S-CO2), due to its abrupt change in properties near its critical point, can significantly reduce compression work and improve energy conversion efficiency. The supercritical CO2 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), as key thermal equipment, must meet design requirements for high heat loads, large temperature differences, and a small size. MCDs include various flow channel configurations, including straight channels, zigzag channels, airfoil channels, and S-shaped channels. The flow channel configuration and structural parameters directly impact the heat transfer performance of MCDs, but the multivariable, multi-objective design optimization process is highly complex and requires high-precision flow and heat transfer analysis to identify the optimal flow channel configuration and structural parameters for specific operating conditions. Currently, numerical simulations of S-CO2 flow and heat transfer in microchannels primarily rely on refined computational fluid dynamics (CFD) methods. These methods exhibit highly nonlinear governing equations, requiring an ultra-dense grid to ensure solution accuracy and exponentially increasing computational resource consumption. Furthermore, optimizing parameters for multiple flow channel configurations requires traversing a vast number of operating condition combinations, resulting in a long, single, full-order CFD simulation, which in turn limits the efficiency of design iterations. Summary of the Invention

[0004] In order to solve the technical problem of low calculation efficiency in predicting the heat transfer characteristics of supercritical carbon dioxide flow in a microchannel heat exchanger, the present invention provides a method for quickly predicting the heat transfer characteristics of supercritical carbon dioxide flow in a microchannel heat exchanger. The technical solution adopted is as follows: The technical solution of the present invention provides a method for quickly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger, the method comprising: 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; Performing intrinsic orthogonal decomposition on the full-order flow field database to extract key modes that dominate flow and heat transfer characteristics to construct a reduced-order solution space; Use the training set to train the optimized neural network model and establish the mapping relationship between the working condition parameters and the reduced-order solution space; The flow field and temperature field information are reconstructed based on the mapping relationship, and the flow and heat transfer characteristics prediction results are calculated and output.

[0005] Furthermore, a full-order flow field database under multiple working conditions is generated through numerical simulation, including: Conduct 3D geometric modeling based on the microchannel flow configuration and perform mesh independence analysis; Calling the variable physical property parameter data of supercritical carbon dioxide and combining it with the turbulence model to perform batch numerical simulation calculations for multiple working conditions; Extract flow field, temperature field and pressure field data under various working conditions and generate a set of multi-dimensional physical field information snapshots.

[0006] Furthermore, the full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes that dominate flow and heat transfer characteristics to construct a reduced-order solution space, including: Performing de-meaning processing on the full-order flow field data; The mode set representing the flow and heat transfer characteristics is extracted by orthogonal matrix decomposition method; Based on a preset energy cutoff threshold, key modes are screened from the mode set to construct a low-dimensional reduced-order solution space.

[0007] Furthermore, based on a preset energy cutoff threshold, key modes are screened from the mode set to construct a low-dimensional reduced-order solution space, including: Calculate the energy contribution rate of each mode and accumulate them in descending order; Determine the minimum number of retained modes based on the comparison between the cumulative contribution rate and the preset energy cutoff threshold; The retained modes are used as key modes for constructing the reduced-order solution space.

[0008] Furthermore, the optimized neural network model is trained using the training set to establish a mapping relationship between the operating parameters and the reduced-order solution space, including: Generate a candidate range of hidden layer node numbers based on the empirical relationship between the number of input and output layer nodes; Traverse all node number configurations within the candidate range and determine the optimal network structure by comparing training errors; A global search algorithm is used to optimize the initial weights and thresholds of the neural network; The network parameters are iteratively updated based on the training set data, and the model accuracy is verified through the test set.

[0009] Furthermore, a global search algorithm is used to optimize the initial weights and thresholds of the neural network, including: Normalize the input and output data and initialize multiple sets of random weight threshold combinations; Calculate the prediction error of each weight threshold as the fitness value, and select high-fitness individuals for parameter crossover and perturbation; The optimal weight threshold value is output by iteratively updating the weight threshold combination until the preset termination condition is met.

[0010] Furthermore, the iterative update of the network parameters includes: Initialize the network based on the optimal weight threshold, and iteratively update the network parameters through the training set data; Adaptive step size optimization algorithm is used to dynamically adjust the learning rate to minimize the prediction error function; The training is terminated according to the error convergence condition or the maximum number of iterations to obtain a mapping relationship model between the working condition parameters and the reduced-order solution space.

[0011] Furthermore, the flow field and temperature field information are reconstructed based on the mapping relationship, including: Obtaining corresponding modal coefficients according to the key modes in the reduced-order solution space; Linearly combining the modal coefficients with the key modes and superimposing the mean fields to generate reconstructed flow fields and temperature fields; The reconstructed field information is spatially interpolated to restore the full-order physical field distribution.

[0012] Furthermore, the flow field and temperature field information are reconstructed based on the mapping relationship, and the flow and heat transfer characteristics prediction results are calculated and output, including: Based on the reconstructed flow field information, multiple calculation sections are divided along the axial direction of the microchannel to divide the flow channel into several continuous segments; Extract the mass flow, average temperature, velocity and pressure parameters of the fluid in each segment; The heat flux and energy transfer characteristics are calculated based on the relationship between enthalpy change and pressure drop of adjacent segments.

[0013] Furthermore, the heat flux and energy transfer characteristics are calculated, including: The local heat transfer coefficient is calculated segmentally based on the ratio of heat flux density to the temperature difference at the fluid-solid interface; Based on the relationship between pressure drop and flow kinetic energy, the friction factor is calculated in combination with the flow channel geometric parameters; The calculation results of each segment are weighted and integrated to output the heat transfer coefficient and friction factor of the microchannel as a whole The present invention has the following beneficial effects: The present invention provides a rapid prediction method for the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger. This method extracts key modes through intrinsic orthogonal decomposition to construct a reduced-order solution space, reducing model complexity while retaining the main characteristics of the flow and temperature fields, ensuring high-precision restoration of the physical field. Furthermore, an optimized neural network is used 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, the flow and heat transfer characteristics prediction results are calculated and output through field information reconstruction and piecewise integration methods, taking into account the rapid acquisition of both global and local parameters. This method achieves rapid and high-precision predictions in multi-configuration, wide-parameter scenarios without the need to construct complex reduced-order control equations. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions and advantages of the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0015] Figure 1 A flow chart of a method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger provided by one embodiment of the present invention; Figure 2 An algorithm flow chart of a method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger provided by one embodiment of the present invention; Figure 3 A schematic diagram of a geometric model of a broken line microchannel provided in one embodiment of the present invention; Figure 4 A schematic diagram of grid division provided by an embodiment of the present invention; Figure 5 A cold fluid friction factor distribution diagram provided by one embodiment of the present invention; Figure 6 A distribution diagram of the friction factor of a thermal fluid provided by one embodiment of the present invention; Figure 7 A distribution diagram of the heat transfer coefficient of a cold fluid provided by one embodiment of the present invention; Figure 8 A heat transfer coefficient distribution diagram of a thermal fluid provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0016] To further illustrate the technical means and effectiveness of the present invention in achieving its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effectiveness of a method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to the present invention. In the following description, references to different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.

[0017] Unless defined otherwise, 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 belongs.

[0018] The specific scheme of the method for quickly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger provided by the present invention is described in detail below with reference to the accompanying drawings.

[0019] The interior of a microchannel heat exchanger includes a flow field, a temperature field, and a pressure field. The flow field describes the flow state of the fluid in the microchannel heat exchanger, including the fluid's velocity, direction, and flow trajectory. The temperature field represents the temperature distribution at various locations within the microchannel heat exchanger. Different regions have different temperatures due to different degrees of heat exchange. By studying the temperature field, we can determine the heat transfer effect between hot and cold fluids, and whether there are local overheating or overcooling areas within the heat exchanger. The pressure field reflects the pressure distribution at various locations within the microchannel heat exchanger. When a fluid flows in a microchannel, the pressure changes due to factors such as changes in the shape and size of the channel and the friction between the fluid and the channel wall. Therefore, the flow field, temperature field, and pressure field are crucial for optimizing the design of a microchannel heat exchanger and improving its heat exchange efficiency and operating performance.

[0020] Although the Proper Orthogonal Decomposition (POD) method has applications in the field of flow and heat transfer, its traditional idea is to project high-dimensional problems into low-dimensional space for solution based on POD combined with the Galerkin projection method, thereby reducing computational costs. Since this method relies on the complex construction of reduced-order control equations, its applicability to highly nonlinear systems is limited. In addition, existing neural network-based prediction technologies mostly focus on global parameters such as heat transfer coefficients, making it difficult to efficiently predict high-dimensional physical quantities such as local temperature fields and velocity fields. Directly training neural networks on large-scale grid data is also not feasible. Therefore, the present invention provides an innovative method that takes into account both computational efficiency and prediction accuracy to break through the technical bottleneck of rapid analysis of S-CO2 flow and heat transfer in microchannels.

[0021] See also Figure 1 and Figure 2 , which shows a method flow chart and algorithm flow chart of a method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger provided by one embodiment of the present invention, the method comprising: Step S100: Divide the training set and the 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 working condition parameter sampling range, as shown in Table 1:

[0022] Table 1 Sampling range of operating parameters In Table 1, represents the cold fluid inlet temperature, Hot fluid inlet temperature, Cold fluid outlet pressure, Indicates the outlet pressure of the hot fluid, represents the inlet mass flow rate; according to the sampling range of the 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 to ensure coverage of extreme operating conditions; 332 groups of samples are generated by the above method and then the samples are randomly divided into training and test sets in a ratio of 5:1, with 282 groups in the training set and 50 groups in the test set.

[0023] Step S100 specifically includes: Step S110: Perform three-dimensional geometric modeling based on the microchannel flow channel configuration and perform grid independence analysis; specifically, use ICEM software to build a three-dimensional geometric model based on the microchannel flow channel configuration, which can be found in Figure 3 As shown, Figure 3 is a schematic diagram of the three-dimensional geometric model of the broken line flow channel. Figure 3 The red in the middle is the hot runner and the blue is the cold runner. Then the mesh is divided for the 3D geometric model. Figure 4 As shown, a hybrid network partitioning strategy is adopted, and different types of grids are used for different areas; the grid independence analysis specifically analyzes the degree of influence of the grid partitioning method on the calculation results. This embodiment uses grids of different densities and types for calculation. If the calculation results do not change significantly with the change of the grid within a certain error range, it indicates that the results are grid-independent. For example, in fluid mechanics simulations, coarse grids, medium grids, and fine grids are used to simulate the flow of fluid in a microchannel flow channel. If the calculated values ​​of key parameters such as flow rate and pressure under each grid are similar, it means that the simulation results are grid-independent, which means that the selected grid can effectively and accurately reflect the physical phenomenon. Subsequent calculations can be based on this grid setting without further refining the grid to increase the calculation cost.

[0024] Step S120: Retrieving variable property parameter data of supercritical carbon dioxide and performing batch numerical simulation calculations for multiple working conditions in combination with a turbulence model; specifically, the variable property parameter data of supercritical carbon dioxide can be retrieved from the NIST REFRPROP database. The NIST REFRPROP database refers to the REFPROP database developed by the National Institute of Standards and Technology (NIST) in the United States. REFPROP is a software tool and related database for calculating the thermophysical properties of fluids. The NIST REFRPROP database can be used to obtain parameter data such as density, viscosity, thermal conductivity, and specific heat capacity at constant pressure of S-CO2 in a supercritical state; 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 a Fluent Journal script file, the batch calculation of working condition parameter import, boundary condition setting, solver iteration and result output, as well as the batch extraction of full-order field information, can be automatically completed.

[0025] Step S130: Extract the flow field, temperature field and pressure field data under each working condition and generate a multi-dimensional physical field information snapshot set; specifically, extract the three-dimensional flow field physical data of each working 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 splice the column vectors of all working conditions by column to form a snapshot matrix 、 is the total number of working conditions, i.e. 332, is the physical field dimension, that is, the total number of grids, the snapshot matrix It can be expressed as:

[0026] Where, It is a snapshot matrix that stores the physical field data of all working conditions, and each column corresponds to the full field information of a working condition; Indicates the snapshot matrix Column vector, representing the combination of working condition parameters The physical field distribution under , which can be temperature, velocity or pressure; For the Combination of operating parameters, including cold fluid inlet temperature , hot fluid inlet temperature , cold fluid outlet pressure , hot fluid outlet pressure and inlet mass flow rate , for each working condition , , taking its physical field column vector as the first Column; each column of the snapshot matrix corresponds to the full-field physical quantity distribution of a working condition; is the grid node coordinate set; taking the temperature field snapshot matrix as an example , where each column Indicates working conditions The temperature distribution of all grid nodes under the condition is obtained, the row index corresponds to the grid node position, and the column index corresponds to the working condition number; this embodiment can provide a standard input format for the proper orthogonal decomposition (POD). By performing singular value decomposition (SVD) on the snapshot matrix, the main modes of the flow field across working conditions can be extracted, and then the high-dimensional physical field can be compressed into a low-dimensional space composed of a few key modes.

[0027] This example uses Latin hypercube sampling and boundary point supplementation to ensure that operating conditions cover multiple parameter ranges and extreme conditions. It combines hybrid meshing with mesh independence analysis to achieve a balance between computational accuracy and efficiency. The REFPROP database is coupled with Fluent scripts to achieve automated batch simulation of variable-property S-CO2 flow and heat transfer, ultimately organizing high-dimensional physical field data through a snapshot matrix structure. This process not only provides a high-quality, comprehensive, full-order solution dataset for subsequent POD reduction, but also significantly reduces the manual intervention cost and computational time of traditional CFD simulations through mesh optimization and batch calculations, while ensuring the physical authenticity and reliability of the full-order solution.

[0028] Step S200: performing intrinsic orthogonal decomposition on the full-order flow field database to extract key modes that dominate flow and heat transfer characteristics to construct a reduced-order solution space; Step S200 specifically includes: Step S210: De-mean the full-order flow field data; , calculate the average value of the physical quantity of each grid node under all working conditions by row, and obtain the mean field vector ; The snapshot column vector of each working condition , element-wise subtraction of the mean field vector , we can get the fluctuation field matrix after removing the mean , the wave field vector It can be expressed as:

[0029] Among them, the fluctuation field matrix after removing the mean It only contains the fluctuation information of each working condition relative to the mean field, eliminating the interference of the global mean on the subsequent modal decomposition; Step S220: extracting the mode set that characterizes the flow heat transfer characteristics by orthogonal matrix decomposition method; specifically, the wave field matrix Perform singular value decomposition, which can be expressed as:

[0030] Where, is a left singular vector matrix, whose column vectors are spatial modes, used to characterize the distribution pattern of the physical field in space; It is a diagonal matrix, and the diagonal elements are singular values. The size of the singular value reflects the energy proportion or variance contribution of the corresponding mode; is the right singular vector matrix, the column vector is the parameter mode, which represents the weight distribution of each mode in the working condition parameter space; SVD decomposes high-dimensional physical fields into linear combinations of spatial modes and parameter weights, achieving orthogonal decomposition of complex flow fields. This allows the flow field distribution containing the main features to be reconstructed using only a small number of POD bases.

[0031] Step S230: Based on a preset energy cutoff threshold, key modes are screened from the modal set to construct a low-dimensional reduced-order solution space; wherein, the reduced-order solution space specifically refers to a low-dimensional feature subspace extracted from the full-order flow field database through proper orthogonal decomposition (POD), which is used to reduce the full-order physical field dimension of the million-grid level 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 reconstruction of the flow field.

[0032] Step S231: Calculate the energy contribution rate of each mode and accumulate them in descending order. Specifically, in the singular value decomposition (SVD) of step S220, the diagonal elements of the singular value matrix are sorted from large to small. The square of the singular value corresponds to the modal energy. The modes are sorted from high to low according to the energy contribution rate, and the cumulative energy contribution rate of multiple modes is calculated: 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:

[0033] Where, For the eigenvalues, i.e., modal energies; is the preset energy cutoff threshold; based on this formula, the minimum number of retained modes can be searched using the dichotomy method ; Step S233: The retained mode is used as the key mode for constructing the reduced-order solution space; specifically, the front mode is extracted from the left singular vector matrix. left singular eigenvectors , forming the POD basis matrix ,Right now:

[0034] Among them, each POD basis vector , i.e., the key mode, corresponds to a heat transfer mode; In this embodiment, the global offset of the flow field is eliminated by demeaning processing, ensuring that the subsequent modal decomposition focuses on the difference characteristics between working conditions; then, through singular value decomposition and truncation, the key POD basis can be extracted from the full-order flow field of the million-level grid, reducing the order of magnitude of the physical field dimension; at the same time, the main characteristics are retained by the cumulative energy threshold. This method does not rely on the heat transfer differential equation or turbulence model assumptions, and can construct a reduced-order solution space only through the statistical characteristics of the data. It is suitable for general modeling under complex microchannel configurations and variable physical property conditions. This step serves as a link between full-order simulation and rapid prediction, and provides low-dimensional and efficient input for the subsequent step of the neural network to establish a mapping relationship between working condition parameters and reduced-order solution space. Ultimately, the construction of the reduced-order solution space achieves a balance between computational efficiency and physical reality.

[0035] Step S300: using the training set to train the optimized neural network model, and establishing a mapping relationship between the operating parameters and the reduced-order solution space; Step S300 specifically includes: Step S310: Generate a candidate range of hidden layer node numbers based on the empirical relationship between the number of input and output layer nodes; specifically, the number of input layer nodes corresponds to the dimension of the working condition parameter, i.e., a total of 5 nodes as recorded in Table 1; the number of output layer nodes corresponds to the dimension of the reduced-order solution space. , that is, the number of POD bases; the candidate range of the number of hidden layer nodes can be determined using the following empirical formula:

[0036] Where, is the candidate range of the number of hidden layer nodes; Number of input layer nodes; is the number of nodes in the output layer; is the adjustment factor, which is an integer between 1 and 10; Step S320: traverse all node configurations within the candidate range and determine the optimal network structure by comparing the training errors. Specifically, for the candidate node number determined in step S310, construct a BP neural network one by one to traverse all hidden layer nodes within the candidate range, calculate the network error, and select the neural network configuration with the minimum error. The number of hidden layer nodes of the neural network established for the five variables in this embodiment is as shown in Table 2: Table 2 Number of nodes in the hidden layer of the neural network

[0037] in, is the pressure field; is the temperature field; 、 、 For the three components of the velocity field, the number of nodes in their hidden layers is calculated respectively.

[0038] Step S330: Optimizing the initial weights and thresholds of the neural network using a global search algorithm, including: Step S331: Normalize the input and output data and initialize multiple sets of random weight threshold combinations. Specifically, perform max-min normalization on the input operating parameters and output POD coefficients to ensure that all data are mapped to the [0, 1] interval to avoid gradient update imbalance due to dimensional differences. Then, use a genetic algorithm to randomly generate initial weight threshold combinations as the initial population. Step S332: Calculate the prediction error of each group of weight thresholds as the fitness value, and screen individuals with high fitness for parameter crossover and perturbation; specifically, the roulette wheel selection method can be used to screen the top 50% individuals as parents according to the fitness ratio; then perform single-point crossover on the parent individuals to generate offspring individuals; finally, randomly perturb the individual weight thresholds with a preset low probability to maintain population diversity.

[0039] Step S333: Iteratively update the weight threshold combination until a preset termination condition is met, and output the optimal weight threshold. For example, the maximum number of iterations is set to 50, and the optimal fitness of the population is calculated after each iteration. If there is no significant fitness improvement after 10 consecutive generations, the iteration is terminated early. The optimal individual weight threshold is output as the initial parameter of the BP neural network for subsequent training.

[0040] In this embodiment, the search range of hidden layer nodes is narrowed based on the empirical formula of input and output dimensions, and cross-validation is combined to avoid overfitting, which can ensure that the network structure matches the dimensions of the reduced-order solution space. 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 to adapt to their respective modal energy distribution characteristics.

[0041] Step S340: Iteratively update network parameters based on the training set data, and verify the model accuracy through the test set; The iterative update of the network parameters includes: Step S341: Initialize the network based on the optimal weight thresholds, and iteratively update the network parameters using the training set data. Specifically, the optimal weights and thresholds obtained through genetic algorithm optimization are used as the initial parameters of the neural network. Predictions are calculated using the training set data through forward propagation. Backpropagation is then used to calculate the gradient of the error with respect to the parameters. The network parameters are then iteratively updated using the Levenberg-Marquardt (LM) algorithm. The LM algorithm effectively combines the stability of gradient descent with the rapid convergence of the Newton method. By adaptively adjusting the damping factor to balance the parameter update step size, the LM algorithm can avoid falling into local optima.

[0042] Step S342: Adopting the adaptive step size optimization algorithm to dynamically adjust the learning rate to minimize the prediction error function; the adaptive step size mechanism can avoid oscillation caused by too high a learning rate or slow convergence caused by too low a learning rate, ensuring that the model descends quickly in the early stage of training and fine-tunes in the later stage, thereby accelerating convergence and improving the final accuracy.

[0043] Step S343: Terminate the training according to the error convergence condition or the maximum number of iterations to obtain a mapping relationship model between the operating condition parameters and the reduced-order solution space; the error convergence condition can be configured so that when the loss function of the training set or the validation set decreases by less than a preset threshold for multiple consecutive rounds of iterations, the model is considered to have converged; the error convergence condition can also be configured so that if the model still fails to converge after reaching the preset maximum number of training rounds, the training is forcibly terminated; the model finally generated establishes a nonlinear mapping relationship between the operating condition parameters (input layer) and the reduced-order solution space coefficients (output layer), which can be used to quickly predict the POD coefficient under new operating conditions.

[0044] The model accuracy verification includes: Based on the test set data, the full-field prediction error norm is calculated and the relative error distribution of local spatial points is statistically analyzed; the error evaluation criteria include the full-field two-norm error and the local relative error of each spatial point ; For each working condition in the test set, the trained neural network is used to predict the POD coefficient, and the physical field is reconstructed based on the POD basis matrix of step S200 to obtain a predicted physical field matrix. The predicted physical field matrix is ​​compared with the real physical field matrix obtained by full-order CFD simulation, and the two-norm error of the two is calculated to measure the global prediction accuracy. This error can reflect the overall similarity between the predicted field and the real field. The smaller the value, the higher the global matching degree. On the other hand, for each grid node, the relative error between the predicted value and the real value of the node under all working conditions of the test set is calculated, and the average value is obtained. By analyzing the local error distribution, the prediction defects of the model in specific areas of the microchannel can be located, such as the velocity field error in the flow separation zone or the wall heat flux density error.

[0045] The expressions of the second norm error and local relative error are:

[0046]

[0047] Where, is the predicted physical field matrix; is the full-order numerical simulation result; the second 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 The predicted value of each working condition; Indicates the According to this 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 are adjusted: for example, the number of hidden layer nodes is increased to improve the network expression ability, the sample size of the training set is expanded, the working condition data corresponding to the high error area is supplemented, the number of POD bases is adjusted, and more flow field details are retained by increasing the key modes.

[0048] The two-norm errors of the five field quantities predicted in this example are shown in Table 3: Table 3 Second norm error of each field quantity

[0049] Table 3 records the five predicted field quantities in the rapid prediction method for supercritical carbon dioxide flow heat transfer characteristics in microchannel heat exchangers: For pressure, For temperature, 、 、 is the second-norm error of the velocity component; this error measures the overall similarity between the predicted and true fields; smaller values ​​indicate a higher degree of global match. The data in Table 3 indicate that the second-norm errors for each field are relatively small. The second-norm error for the pressure field is 0.039%, and the error for the temperature field is 0.28%. This indicates that the model has high accuracy in predicting these two field quantities, effectively reflecting the real-world physical field. While the velocity field prediction error is slightly higher than that for the pressure and temperature fields, it remains relatively low in practical applications. This indicates that the model's velocity predictions are also reliable, capturing the key characteristics and changing trends of the velocity field. This meets the precision requirements of practical engineering applications and can be used in engineering scenarios such as the design and optimization of microchannel heat exchangers.

[0050] In summary, this embodiment uses the LM algorithm and adaptive learning rate to accelerate the training process, which improves the convergence speed compared to the traditional BP algorithm. After training, the model can complete the prediction of new working conditions in milliseconds, converting the traditional CFD simulation into real-time response, which significantly improves efficiency. Based on error feedback, the network structure and training strategy are dynamically adjusted so that the model can automatically adapt to complex scenarios such as variable physical properties and multi-channel configurations of supercritical carbon dioxide, avoiding overfitting or underfitting, and enhancing the generalization ability of the model within a wide parameter range. Variable physical properties refer to physical properties such as density, specific heat capacity, and thermal conductivity of supercritical carbon dioxide that change dramatically with temperature or pressure, and the traditional constant physical property assumption is no longer applicable. It is necessary to introduce a physical property correction coefficient, or to establish a coupled correlation model between the physical property field and the flow heat transfer field, so as to quantify the impact of physical property changes on momentum or energy transfer and incorporate it into the constitutive relationship.

[0051] Step S400: reconstructing the flow field and temperature field information based on the mapping relationship, calculating and outputting the flow and heat transfer characteristic prediction results; Among them, the flow field and temperature field information are reconstructed based on the mapping relationship, including: Step S410: According to the key modes in the reduced-order solution space, the corresponding modal coefficients are obtained; the operating parameters are input into the trained neural network model, and the 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 outputs the modal coefficient vector of the reduced-order solution space through forward propagation calculation. For each physical quantity, the output modal coefficient vector contains elements; 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 processing on the reconstructed field information to restore the full-order physical field distribution; specifically, by With each key mode The reconstruction of the physical field can be achieved by linearly superimposing the corresponding POD coefficients. By utilizing the key information in the low-dimensional reduced-order solution space, the reconstruction result of the physical field can be quickly obtained based on the working condition parameters, which can be expressed as:

[0052] Where, Indicates the location and working conditions Under the reconstructed physical field, is the grid node coordinate set; is the average field, i.e., the average value of the physical field such as the flow field or temperature field obtained by the de-averaging process in step S200; is the POD coefficient, which is obtained through the output of the neural network and reflects the working conditions Next The contribution weight of each key mode to the physical field, different working conditions will lead to The values ​​of are different; Represents the POD basis vector, that is, the key mode determined in step S230. Each key mode corresponds to a heat transfer or flow mode, which describes the physical field in space. The distribution characteristics of In this embodiment, reduced-order models are established for three-dimensional velocity, temperature, and pressure. The reduced-order physical field dimensions and the reduction process errors are shown in Table 4: Table 4 Reduced-order physical field dimensions and reduction process errors

[0053] Table 4 records the relevant information after establishing a reduced-order model for three-dimensional velocity, temperature, and pressure in the study of the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger. The reduced-order physical field dimensions show the dimensions of the space in which different physical quantities are located after the reduction process. The reduced-order dimension of pressure is 3, the temperature is 23, and the velocity components are 10, 12, and 21, respectively. These dimensions represent the low-dimensional space dimensions required to describe the corresponding physical quantities after extracting key modes through methods such as proper orthogonal decomposition (POD). The reduction process error: The error generated by each physical quantity in the reduced-order model is given as a percentage. This error reflects the degree of deviation caused by the reduced-order model's approximate representation of the original high-dimensional physical field information.

[0054] As can be seen from Table 4, the reduced-order physical field dimensions compress each physical quantity from a high-dimensional space to a relatively low-dimensional space. This indicates that the POD reduction method effectively reduces the dimensions required to describe the physical field, lowers computational complexity, and improves the efficiency of subsequent computational analysis. Furthermore, the reduced-order model errors for different physical quantities vary, with the pressure field having the smallest error. This indicates that the reduced-order model provides the highest approximation of the pressure field and effectively preserves its original characteristics. Although the reduced-order model exhibits varying accuracy for different physical quantities, it generally ensures an approximate restoration of the original physical field and can be used for subsequent flow and heat transfer analysis. Therefore, while significantly reducing the computational dimensions, this reduced-order model maintains reasonable error, possessing significant value for the study and engineering application of supercritical carbon dioxide flow and heat transfer characteristics in microchannel heat exchangers. It provides an efficient computational model for the rapid prediction of flow and heat transfer characteristics without significant loss of accuracy.

[0055] In summary, this embodiment is based on a trained neural network that has established a mapping relationship between operating parameters and reduced-order solution space. It can quickly obtain modal coefficients based on the input operating parameters, eliminating the need for complex and time-consuming full-order numerical simulations. This greatly shortens the calculation time and achieves a rapid conversion from operating parameters to key information acquisition in the physical field, meeting the real-time requirements in engineering. On the other hand, based on the constructed low-dimensional reduced-order solution space, the modal coefficients output by the neural network are a description of the key features of the physical field in a low-dimensional space. This method avoids processing high-dimensional and complex original flow field data, reduces computational complexity, and at the same time retains the main change patterns of the physical field, improving computational efficiency while ensuring a certain degree of accuracy.

[0056] The calculation and output of the flow and heat transfer characteristics prediction results include: Step S420: Based on the reconstructed flow field information, multiple calculation sections are divided along the axial direction of the microchannel to divide the flow channel into several continuous segments; in order to more accurately analyze the flow and heat transfer characteristics in the microchannel and avoid the influence of complex boundary conditions at the inlet and outlet, the section perpendicular to the channel axis away from the inlet and outlet is selected. In this embodiment, four cross-sections are selected, and the middle section of the flow channel is further divided into three sections. The location of the cross-section can be determined based on factors such as the length of the microchannel and the degree of flow development. Generally, it is required to be in an area where the flow is stable and is less affected by inlet and outlet disturbances.

[0057] Step S421: Extract the average temperature, velocity and pressure parameters of the mass flow of the fluid in each segment; for each section of the flow channel, determine the cross-sectional area of ​​the flow channel based on the flow field information reconstructed in step S410. The inlet mass flow is obtained by measurement or calculation. Due to the conservation of mass in the flow channel, the mass flow in each section of the flow channel can be considered to be approximately equal to the inlet mass flow; in each section of the flow channel, based on the reconstructed temperature field information, the temperatures at different positions in the section are statistically averaged to obtain the average temperature of the fluid in the section. During the specific calculation, the temperature values ​​of all grid nodes in the section can be arithmetic averaged, or weighted averaged according to the weights of different positions. The extraction of velocity and pressure parameters is also based on the reconstructed flow field information, and the velocity and pressure parameters of the fluid in each section of the flow channel are extracted.

[0058] Step S422: Calculate the heat flux and energy transfer characteristics based on the relationship between the enthalpy change and pressure drop of adjacent segments; including: calculating the local heat transfer coefficient segment by segment based on the ratio of the heat flux and the temperature difference between the fluid and solid interface; calculating the friction factor based on the relationship between the pressure drop and the flow kinetic energy, combined with the flow channel geometric parameters; weighted integration of the calculation results of each segment, and outputting the heat transfer coefficient and friction factor of the entire microchannel; wherein, for the first Hot runner, according to the extraction pressure and average temperature By consulting the physical properties table of supercritical carbon dioxide, the corresponding specific enthalpy is obtained , the heat flow enthalpy calculation can be expressed as:

[0059] Where, For the Heat flow enthalpy of hot runner section; is the cross-sectional area of ​​the flow channel; is the inlet mass flow rate; The heat flux density is calculated using the heat flux enthalpy difference between two adjacent sections, which can be expressed as:

[0060] Where, Indicates the Heat flux density of hot runner section; Indicates the The heat flow enthalpy of the hot runner section; that is, the heat flow density of the section per unit time is obtained by subtracting the heat flow enthalpy of the current section from the heat flow enthalpy of the next section, which reflects the heat transfer rate in the section; The calculation of the local heat transfer coefficient can be expressed as:

[0061] Among them, the subscript represents the average value, Indicates hot runner, represents a solid area; express No. part Average temperature of solid wall; Indicates the The average temperature of the fluid in this section; the formula obtains the local heat transfer coefficient through the ratio of heat flux density to the temperature difference of the fluid-solid interface, which reflects the heat transfer capacity between the fluid and the solid wall in this section of the flow channel.

[0062] Finally, based on the relationship between pressure drop and flow kinetic energy, the friction factor is calculated in combination with the geometric parameters of the flow channel. For example, by measuring or calculating the pressure drop between two adjacent sections, combined with 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 to reflect the resistance characteristics of the fluid when flowing in the flow channel. The heat transfer coefficient and friction factor calculated for each segment are weighted and integrated, and finally the heat transfer coefficient and friction factor of the entire microchannel are output, thereby obtaining the heat transfer and flow performance indicators of the entire microchannel heat exchanger.

[0063] See Figures 5 to 8 The scatter plot shown shows the comparative relationship between the predicted value and the true value, where the horizontal axis represents the true value and the vertical axis represents the predicted value; each sub-graph has three lines, the middle dotted line is the ideal situation where the predicted value is equal to the true value; the upper and lower solid lines represent the limits of relative errors of +10% and -10% respectively; the blue scatter points represent the corresponding relationship between the predicted value and the true value under different examples, and one scatter point represents the coordinate position of the predicted value and the true value of one example; it can be understood that the relative error of the convective heat transfer coefficient of 99% of the examples in the test set is within 10%, and the maximum error is 12.7%; the relative error of the friction factor of 97% of the examples is within 10%, and the maximum error is 16.6%. In terms of computational efficiency, the traditional CFD numerical simulation requires tens of minutes to calculate a single example, while the simulation method of the present invention only takes 3 seconds, which increases the computational speed by hundreds of times and reduces the model dimension by about The method of the present invention is effective in significantly improving computational efficiency, can quickly obtain computational results, and meets the computational speed requirements of practical engineering. In summary, the non-invasive POD-based order reduction method proposed in the present invention can meet the accuracy requirements for the S-CO2 flow and heat transfer problem in microchannels, with the error of the second norm of the basic field quantity being below 3%. It can also greatly reduce the physical field dimension and increase the computational speed, and can better predict the field quantity distribution law of S-CO2 flow and heat transfer in microchannels.

[0064] In summary, the method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger, provided by this invention, eliminates the significant computational resources and time required for traditional full-order CFD solutions. By utilizing reconstructed flow and temperature field information, it rapidly performs flow channel segmentation and parameter calculations, reducing reconstruction and parameter calculation time from several hours to seconds. This significantly improves computational efficiency and meets the engineering demand for rapid calculations. This calculation accurately determines key parameters such as the overall microchannel heat transfer coefficient and friction factor, meeting engineering precision requirements.

[0065] It should be noted that the order in which the embodiments of the present invention are described above is for illustrative purposes only and does not necessarily represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0066] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

Claims

1. A method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger, characterized in that: The method comprises: 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; Performing intrinsic orthogonal decomposition on the full-order flow field database to extract key modes that dominate flow and heat transfer characteristics to construct a reduced-order solution space; Use the training set to train the optimized neural network model and establish the mapping relationship between the working condition parameters and the reduced-order solution space; The flow field and temperature field information are reconstructed based on the mapping relationship, and the flow and heat transfer characteristics prediction results are calculated and output.

2. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 1, wherein: Generate a full-order flow field database under multiple working conditions through numerical simulation, including: Conduct 3D geometric modeling based on the microchannel flow configuration and perform mesh independence analysis; Calling the variable physical property parameter data of supercritical carbon dioxide and combining it with the turbulence model to perform batch numerical simulation calculations for multiple working conditions; Extract flow field, temperature field and pressure field data under various working conditions and generate a set of multi-dimensional physical field information snapshots.

3. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 1, wherein: The full-order flow field database is subjected to intrinsic orthogonal decomposition to extract key modes that dominate flow and heat transfer characteristics to construct a reduced-order solution space, including: Performing de-meaning processing on the full-order flow field data; The mode set representing the flow and heat transfer characteristics is extracted by orthogonal matrix decomposition method; Based on a preset energy cutoff threshold, key modes are screened from the mode set to construct a low-dimensional reduced-order solution space.

4. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 3, wherein: Based on a preset energy cutoff threshold, key modes are screened from the mode set to construct a low-dimensional reduced-order solution space, including: Calculate the energy contribution rate of each mode and accumulate them in descending order; Determine the minimum number of retained modes based on the comparison between the cumulative contribution rate and the preset energy cutoff threshold; The retained modes are used as key modes for constructing the reduced-order solution space.

5. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 1, wherein: The optimized neural network model is trained using the training set to establish a mapping relationship between the operating parameters and the reduced-order solution space, including: Generate a candidate range of hidden layer node numbers based on the empirical relationship between the number of input and output layer nodes; Traverse all node number configurations within the candidate range and determine the optimal network structure by comparing training errors; A global search algorithm is used to optimize the initial weights and thresholds of the neural network; The network parameters are iteratively updated based on the training set data, and the model accuracy is verified through the test set.

6. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 5, characterized in that: A global search algorithm is used to optimize the initial weights and thresholds of the neural network, including: Normalize the input and output data and initialize multiple sets of random weight threshold combinations; Calculate the prediction error of each weight threshold as the fitness value, and select high-fitness individuals for parameter crossover and perturbation; The optimal weight threshold value is output by iteratively updating the weight threshold combination until the preset termination condition is met.

7. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 6, wherein: The iterative update of the network parameters includes: Initialize the network based on the optimal weight threshold, and iteratively update the network parameters through the training set data; Adaptive step size optimization algorithm is used to dynamically adjust the learning rate to minimize the prediction error function; The training is terminated according to the error convergence condition or the maximum number of iterations to obtain a mapping relationship model between the working condition parameters and the reduced-order solution space.

8. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to any one of claims 1 to 7, characterized in that: Reconstruct flow field and temperature field information based on mapping relationships, including: Obtaining corresponding modal coefficients according to the key modes in the reduced-order solution space; Linearly combining the modal coefficients with the key modes and superimposing the mean fields to generate reconstructed flow fields and temperature fields; The reconstructed field information is spatially interpolated to restore the full-order physical field distribution.

9. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 8, characterized in that: Based on the mapping relationship, the flow field and temperature field information are reconstructed, and the flow and heat transfer characteristics prediction results are calculated and output, including: Based on the reconstructed flow field information, multiple calculation sections are divided along the axial direction of the microchannel to divide the flow channel into several continuous segments; Extract the mass flow, average temperature, velocity and pressure parameters of the fluid in each segment; The heat flux and energy transfer characteristics are calculated based on the relationship between enthalpy change and pressure drop of adjacent segments.

10. The method for rapidly predicting the flow and heat transfer characteristics of supercritical carbon dioxide in a microchannel heat exchanger according to claim 9, wherein: Calculate heat flux and energy transfer characteristics, including: The local heat transfer coefficient is calculated segmentally based on the ratio of heat flux density to the temperature difference at the fluid-solid interface; Based on the relationship between pressure drop and flow kinetic energy, the friction factor is calculated in combination with the flow channel geometric parameters; The calculation results of each segment are weighted and integrated to output the heat transfer coefficient and friction factor of the entire microchannel.

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