A rapid prediction method for particle deposition characteristics inside double-walled blades based on a reduced-order model

Abstract

This invention discloses a rapid prediction method for particle deposition characteristics inside double-walled turbine blades based on a reduced-order model. The method includes model building, mesh generation, numerical simulation, dataset creation, and the establishment of a rapid prediction model combining POD (Positive Distributed Orifice Decomposition) and MLP (Multi-Level Processing). By combining deep learning methods with the internal channels of the cooling structure, and considering three parameters—film cooling hole diameter, air-to-air ratio, and temperature ratio—the high-dimensional data is transformed into low-dimensional modal coefficients characterizing particle deposition features based on POD decomposition. The MLP deep neural network method is then used to fit the modal coefficients and related parameters to establish a rapid prediction model, enabling rapid analysis and evaluation of particle deposition patterns inside the blade. This method can effectively predict particle deposition inside double-walled turbine blades, providing data support and guidance for the design and timely cleaning of internal cooling channels.

Description

Technical Field

[0001] This invention belongs to the field of engineering thermophysics technology, specifically relating to a rapid prediction method for particle deposition characteristics inside double-walled blades based on a reduced-order model. Background Technology

[0002] When gas turbines operate in dusty environments, airborne particulate matter such as PM2.5, dust, and sand are inevitably drawn into the turbine. Under high temperature and pressure, these particles easily deposit in the internal cooling channels of the turbine blades, altering the blade profile and clogging the film cooling pores, leading to decreased heat transfer performance and even high-temperature burnout. Therefore, improving the cooling efficiency of turbine blades and understanding the deposition characteristics of fine particles in the internal cooling channels are of great significance. In particular, with the development of next-generation gas turbines, turbine inlet temperatures are higher, placing higher demands on component cooling performance. Double-walled blades exhibit significant cooling performance potential, but their narrow and complex internal structure presents a more severe risk of deposition and blockage. Therefore, understanding the particle deposition characteristics inside double-walled blades is crucial.

[0003] While numerical simulations can yield effective and high-precision results within limited computational resources, conducting numerical or experimental studies on different combinations of parameters before fitting empirical relationships and optimizing structural parameters is extremely time-consuming and labor-intensive. Therefore, to quickly predict the particle deposition characteristics on turbine blade surfaces, especially under conditions of limited computational resources, introducing efficient prediction models as an effective alternative to traditional large-scale numerical simulations is of great significance for subsequent research. Summary of the Invention

[0004] This invention proposes a rapid prediction method for particle deposition characteristics inside double-walled blades based on a reduced-order model. A rapid prediction model is constructed, while ensuring that the relative prediction error is less than 10%. This invention develops a rapid prediction method for particle deposition characteristics inside double-walled blades based on a reduced-order model to solve the technical problems existing in the background art.

[0005] To achieve the above objectives, the present invention employs the following technical solution: a rapid prediction method for particle deposition characteristics inside double-walled blades based on a reduced-order model, comprising:

[0006] Step 1: Select the middle region of the chord length of the double-walled turbine blade as the research object, simplify the middle region of the chord length of the double-walled turbine blade into a double-walled flat plate model, mesh the flat plate model, and establish the corresponding mathematical model;

[0007] Step 2: Select the film orifice diameter, blowing ratio, and temperature ratio as characteristic parameters. Use Latin hypercube (LHS) to sample within the characteristic parameter range and extract 65 samples as the characteristic dataset. Import the mesh model obtained by flat plate meshing into Ansys-Fluent software, set the numerical simulation boundary conditions, and input the parameters of the characteristic dataset into the boundary conditions of the example. Use the SST k-ω turbulence model to perform steady-state calculation of the flow field.

[0008] Step 3: Load the user-defined function (UDF) for deposition, and use a deposition model combining the critical velocity model and the particle stripping model to calculate the particle deposition characteristics of the deposition surface, obtaining deposition rate contour maps of the impact plate and the gas film plate, and establishing a label dataset corresponding to the feature dataset; divide the dataset into training set, test set and validation set in a ratio of 8:1:1; construct a color scale mapping by uniform interpolation in the color space, and convert the color images of the deposition rate distribution of 65 samples into a three-dimensional numerical matrix;

[0009] Step 4: Perform Orthogonal Eigenvalue Decomposition (POD) on the numerical matrix based on Singular Value Decomposition (SVD), extract orthogonal decomposition mode coefficients from the dataset, determine the number of modes to be retained through the cumulative variance contribution rate, and achieve data compression and feature extraction; when the energy ratio reaches 95%, select the top... k Image reconstruction is performed using orthogonal decomposition basis vectors;

[0010] Step 5: Input the feature parameters as input and the modal coefficients δ as output, and feed them into a multilayer perceptron network (MLP) to establish the mapping relationship between the feature parameters and the modal coefficients; through the connection relationship between nodes in the hidden layer and the nonlinear activation function, learn the nonlinear relationship between the operating condition parameters and the coefficients, and establish a fast prediction proxy model;

[0011] Step 6: When using the fast prediction surrogate model to predict new working conditions, input the feature parameters to obtain the corresponding predicted modal coefficients, and then reconstruct the feature coefficients into a deposition rate distribution cloud map through the inverse process of orthogonal decomposition of POD to achieve a fast prediction effect.

[0012] Step 7: Evaluate the accuracy of the fast prediction surrogate model by extracting examples from the training set and comparing the prediction results of the fast prediction model with the CFD calculation results; quantitatively evaluate the computational cost of different methods by comparing the average time taken to obtain deposition rate cloud maps of the same accuracy level by traditional CFD simulation and fast prediction model.

[0013] Step 8: Evaluate the generalization ability of the fast prediction surrogate model, make predictions for conditions not included in the sample dataset using the fast prediction model, and evaluate regions with different deposition rate distributions using qualitative and quantitative evaluation metrics.

[0014] Furthermore, in step 1, the double-walled flat plate model is verified to be independent of the mesh, and the average temperature of the upper and lower coupled surfaces of the turbulence column remains unchanged, indicating that the mesh has met the independence requirements.

[0015] Furthermore, in step 2, the Latin Hypercube (LHS) sampling within the feature variable range specifically includes the following steps: dividing each feature variable into several equally spaced intervals, and randomly selecting a point within each interval as a sampling point; unlike traditional random sampling methods, in the Latin Hypercube (LHS), each variable has only one chance to be selected, and the number of sampling points corresponding to each variable is equal. This method can effectively avoid the problem of some areas not being covered or being repeatedly covered due to randomness.

[0016] Furthermore, in step 2, the turbulence model selected for numerical calculation is:

[0017] The simulation was performed using a shear stress transport (SST) k-ω turbulence model, the specific form of which is as follows:

[0018] ;

[0019] ;

[0020] In the formula For turbulent kinetic energy, For specific dissipation rate, For fluid density, Represents fluid velocity. Represents the turbulent kinetic energy caused by the average velocity gradient. The generation rate representing the specific dissipation rate, The effective diffusion coefficient of turbulent kinetic energy. The effective diffusion coefficient is the specific dissipation rate. This is the partial derivative operator; To calculate the partial derivative of the displacement direction; i and j represent coordinate information; This represents the dissipation of turbulent kinetic energy caused by turbulent flow. Dissipation represents the specific dissipation rate caused by turbulence. For custom representatives The source item, For custom representatives The source terms; among which and The specific calculation formula is as follows:

[0021] ;

[0022] ;

[0023] In the formula It is turbulent kinetic energy The turbulent Prandtl number, It is the specific dissipation rate The turbulent Prandtl number, For dynamic viscosity, For turbulent viscosity, Numerical and and The relevant relationship is:

[0024] ;

[0025] In the formula, This is the Reynolds number correction factor.

[0026] Furthermore, in step 3, the deposition model combining the critical velocity model and the particle stripping model is as follows:

[0027] The El-Batsh critical velocity model was used as the deposition criterion; the critical trapping velocity of particles is the key parameter for determining whether they can be deposited after colliding with the wall; the normal collision rate of particles was used as the deposition criterion. V n With critical capture rate V cr The comparison is used to determine whether particles have deposited; if the normal collision rate of the particles... V n Less than the critical capture rate V cr Particles deposit on the collision surface; otherwise, they bounce off. The specific form of the critical capture rate was derived by comparing it with a semi-empirical formula.

[0028] ;

[0029] in, E For mixed Young's modulus, D p The particle diameter is determined based on the Young's modulus of the particle surface.

[0030] ;

[0031] ;

[0032] ;

[0033] in E s For surface Young's modulus, E p Let be the Young's modulus of the particle. v s For surface Poisson's ratio, vp For the particle Poisson's ratio, It is particle density;

[0034] To determine stable particle deposition using a particle stripping model, if the wall shear velocity at the point of particle impact is greater than the shear velocity near the wall, then even if the normal collision velocity of the particle impact satisfies the critical trapping velocity condition, the particle will still escape. The critical wall shear velocity in this case is calculated using the following formula:

[0035] ;

[0036] After conversion and simplification, it can be represented as:

[0037] ;

[0038] In the formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, The work done by particle adhesion is measured experimentally. For wall shear stress, d p K is the particle diameter. c For El-Batsh parameters;

[0039] When particles no longer meet the deposition conditions, they will rebound. The particle rebound rate is calculated as follows:

[0040] ;

[0041] In the formula, The normal velocity of the particle before the collision is... The normal velocity after the particle collision. The tangential velocity before particle collision. The tangential velocity after particle collision. The angle between the particle's velocity before collision and the tangential angle of the wall; according to and Find the angle after the particle collision: .

[0042] Furthermore, in step 3, the expression for the deposition rate is: ;

[0043] In the formula C denoted as deposition rate, CR as cumulative deposition mass of particles, A as current grid area, and t as service duration.

[0044] Furthermore, in step 4, the specific steps for performing eigenorthogonal decomposition (POD) on the numerical matrix based on singular value decomposition (SVD) are as follows:

[0045] Mapping the cloud maps of each working condition into a deposition rate matrix X :

[0046] ;

[0047] in Let be the deposition rate distribution matrix for the i-th working condition;

[0048] For high-dimensional datasets X Singular Value Decomposition (SVD) decomposes it into a product of three matrices, as shown in the following equation:

[0049] ;

[0050] ;

[0051] in, U For a left singular matrix, its column vectors They are orthogonal, representing the spatial fundamental schema;

[0052] diagonal elements of the singular value matrix These are singular values ​​arranged from largest to smallest, collectively representing the importance of each mode;

[0053] The right singular basis vectors constitute n × n An orthogonal matrix represents the weighting coefficients of spatial patterns under different operating conditions;

[0054] Energy percentage interception As shown in the following formula:

[0055] ;

[0056] The data is compressed into an approximate matrix as shown in the following equation. Improve computational efficiency:

[0057] .

[0058] Furthermore, in step 5, the MLP (Multi-Layer Perceptron) is a feedforward artificial neural network composed of multiple neurons (neural nodes) arranged in a hierarchical structure, including an input layer, a hidden layer, and an output layer. Neurons between layers are connected by weights, and information propagates sequentially from the input layer to the output layer without feedback connections. The input to the MLP network is... , No. The weights of the neurons are The bias is ， The computational process of each neuron from input to output is shown in the following formula: ;

[0059] ;

[0060] In the formula, The inputs to neural tube j are weighted and summed, and a bias is added. The value after activation is used to obtain the output. .

[0061] Furthermore, in step 6, the predicted image is reconstructed using the inverse POD process:

[0062] The predicted mode coefficients With the original spatial fundamental model Multiplication yields an approximate matrix Then, the numerical matrix is ​​transformed into an image to obtain the predicted image:

[0063] .

[0064] Furthermore, in step 7, the accuracy of the fast prediction model is evaluated by extracting examples from the training set, qualitatively comparing the prediction results of the fast prediction model with the CFD calculation results, evaluating areas with large differences in deposition rate cloud maps, and performing error analysis.

[0065] Furthermore, in step 7, the computational cost is quantitatively evaluated. The time required to obtain deposition rate cloud maps with the same accuracy level using both traditional CFD simulation and fast prediction models for the extracted training set samples is recorded, and the average time is compared to evaluate the computational cost.

[0066] Furthermore, in step 8, the generalization ability metric for evaluating the fast prediction model is:

[0067] Pixel-level difference and Structural Similarity Index (SSIM) are selected as evaluation metrics. When one of two images is undistorted and the other is distorted, their structural similarity is considered a measure of the image quality of the distorted image. Pixel-level difference compares the RGB values ​​of two images pixel by pixel and calculates the difference to generate an image representing the difference. Two identical images will generate a pure black image (0, 0, 0) after pixel-level difference calculation. The range of the SSIM value is [0, 1], with a larger value indicating greater similarity. If two images are completely identical, the SSIM value is 1.

[0068] The formula for calculating the SSIM index is as follows:

[0069] ;

[0070] in yes x The average value, yes y The average value, yes x variance yes y variance yes x and y covariance; , , is a constant used to maintain stability; L It is the dynamic range of pixel values; , The structural similarity index uses the mean as an estimate of brightness, the standard deviation as an estimate of contrast, and the covariance as a measure of the degree of structural similarity.

[0071] The present invention provides a rapid prediction method for the internal particle deposition characteristics of a double-walled blade based on a reduced-order model, which has the following advantages:

[0072] (1) The prediction method of this invention is based on the deposition characteristics of intrinsic orthogonal decomposition (POD) and multilayer perceptron (MLP) for rapid prediction. Using user-defined functions (UDFs) in Ansys-Fluent, the deposition process of impact plates and film plates is numerically simulated using Fluent software. The rapid prediction model is trained to achieve rapid deposition prediction, and the results are compared with simulation results to verify the reliability and superiority of the proposed method. The method of this invention avoids cumbersome physical model construction and mesh generation, reduces computational costs, improves computational efficiency, and better meets the needs of practical engineering applications.

[0073] (2) The prediction method of the present invention takes a typical double-wall cooling structure as the research object. The critical velocity model combined with the particle stripping model realizes the judgment of whether the collision particles are deposited stably. At the same time, the rapid prediction model is used to predict unknown working conditions and is compared and verified with the simulation deposition rate results to evaluate the generalization ability of the model. Subsequently, the model can be used to predict the particle deposition distribution under different characteristic parameters so as to carry out subsequent optimization processing.

[0074] (3) The present invention provides a rapid prediction model for the upper and lower plates of the turbulence column in a flat film gas. The difference in deposition rate on the plate is within 0.05, and the error between the average deposition rate of the prediction result and the simulation result is within 10%, indicating that the model has a certain effectiveness in predicting the deposition rate of the upper and lower plates of the turbulence column in a flat film gas. Attached Figure Description

[0075] Figure 1 The flowchart below shows the implementation of a rapid prediction method for particle deposition characteristics inside a double-walled blade based on a reduced-order model, according to the present invention.

[0076] Figure 2 This is a schematic diagram of the calculation area for the double-walled cooling structure of the turbine blades in this invention;

[0077] Figure 3 This is a schematic diagram of the tag dataset of the present invention;

[0078] Figure 4 This is a flowchart of the POD-MLP model training process of the present invention;

[0079] Figure 5 This is a flowchart of the POD-MLP model prediction process of the present invention;

[0080] Figure 6 This is a comparison chart of particle deposition rates in the training set of this invention;

[0081] Figure 7 This is a comparison chart of the computational costs of the present invention;

[0082] Figure 8 This is a comparison chart of particle deposition rates in the examples;

[0083] Figure 9 This is a diagram showing the SSIM error distribution in the embodiment;

[0084] Figure 10 This is a distribution diagram of the deposition rate difference in the embodiment;

[0085] Figure 11 This is a graph showing the average deposition rate error of the present invention. Detailed Implementation

[0086] The following is in conjunction with the appendix Figure 1 The process shown in the diagram provides a further explanation of the present invention.

[0087] Step 1: Select the middle region of the chord length of the double-walled turbine blade as the research object. Since the curvature of the middle region of the blade chord is small and changes gradually, it is simplified to a double-walled flat plate model, such as... Figure 2 This is a schematic diagram of the computational domain for a double-walled flat plate model. The flat plate model is meshed, and the corresponding mathematical model is established.

[0088] Step 2: Select the film orifice diameter, blowing ratio, and temperature ratio as characteristic variables. Use Latin hypercube (LHS) to sample within the range of characteristic variables, and extract a total of 65 samples as the characteristic dataset. Import the mesh model obtained by flat plate meshing into Ansys-Fluent software, set the boundary conditions for numerical simulation, and input the parameters of the characteristic dataset into the boundary conditions of the example. Use the SST k-ω turbulence model to perform steady-state calculation of the flow field.

[0089] Step 3: Load the deposition UDF, calculate the particle deposition characteristics of the deposition surface, obtain the deposition rate contour maps of the impact plate and film plate, and establish a label dataset corresponding to the feature dataset, such as... Figure 3 As shown, the dataset was divided into training, testing, and validation sets in an 8:1:1 ratio. A color scale mapping was constructed using uniform interpolation in the color space, converting the color images of the deposition rate distribution of 65 samples into a three-dimensional numerical matrix.

[0090] Step 4: Perform Orthogonal Eigenvalue Decomposition (POD) on the numerical matrix based on Singular Value Decomposition (SVD), extract orthogonal POD mode coefficients from the dataset, and determine the number of modes to be retained based on the cumulative variance contribution rate, thus achieving data compression and feature extraction. When the energy ratio reaches 95%, select the... k Image reconstruction is performed using POD basis vectors;

[0091] Step 5: Input the feature parameters and output the modal coefficients δ into a multilayer perceptron (MLP) network to establish a mapping relationship between the operating parameters and the modal coefficients. Through the connections between nodes in the hidden layers and the nonlinear activation function, the nonlinear relationship between the operating parameters and the coefficients is learned, establishing a fast prediction proxy model. This fast prediction proxy model is named the POD-MLP model. The POD-MLP model training flowchart is shown below. Figure 4 As shown, the POD-MLP model prediction flowchart is as follows: Figure 5 As shown;

[0092] Step 6: When using the fast prediction model to predict new working conditions, input the feature parameters to obtain the corresponding predicted modal coefficients (k-order coefficients), and then reconstruct the feature coefficients into a deposition rate distribution cloud map through the inverse process of POD to achieve a fast prediction effect.

[0093] Step 7: Evaluate the accuracy of the fast prediction model. Extract examples from the training set (labeled as cases 1-5), and compare the prediction results of the fast prediction model with the numerical simulation (CFD) calculation results, such as... Figure 6As shown, the computational cost of different methods is quantitatively evaluated, comparing the average time taken by traditional CFD simulation and fast prediction models to obtain deposition rate contour maps of the same accuracy level. The time evaluation refers to the CPU time required for execution. For example... Figure 7 As shown;

[0094] Step 8: Evaluate the generalization ability of the POD-MLP fast prediction model, predict working conditions not included in the sample dataset using the fast prediction model, and evaluate regions with different deposition rate distributions using qualitative and quantitative evaluation metrics.

[0095] In step 8, before evaluating the generalization ability, numerical simulation is used to obtain the particle deposition rate cloud map on the plate under the new working condition, as shown in the figure. Figure 8 As shown in the figure. The average deposition rate on the impact plate and the film plate under each working condition was calculated to prepare for subsequent error calculations. The SSIM error distribution diagram is shown in the figure. Figure 9 As shown in the figure, the distribution of deposition rate difference is as follows: Figure 10 As shown in the figure, the average deposition rate error (Relative error) is as follows: Figure 11 As shown.

[0096] In step 1, the double-walled flat plate model is verified to be independent of the mesh, and the average temperature of the upper and lower coupled surfaces of the turbulence column remains unchanged, so the mesh is considered to have met the independence requirements.

[0097] In step 2, the Latin Hypercube (LHS) sampling within the range of feature variables specifically includes the following steps: dividing each feature variable into several equally spaced intervals, and randomly selecting a point within each interval as a sampling point; each variable has only one chance to be selected, and the number of sampling points corresponding to each variable is equal.

[0098] In step 2, the selected turbulence model is the SST k-ω turbulence model:

[0099] The SST k-ω turbulence model was used for simulation, and its specific form is as follows:

[0100] ;

[0101] ;

[0102] In the formula For turbulent kinetic energy, For specific dissipation rate, For fluid density, Represents fluid velocity. Represents the turbulent kinetic energy caused by the average velocity gradient. The generation rate representing the specific dissipation rate, The effective diffusion coefficient of turbulent kinetic energy. The effective diffusion coefficient is the specific dissipation rate. This is the partial derivative operator; To calculate the partial derivative of the displacement direction; i and j represent coordinate information; This represents the dissipation of turbulent kinetic energy caused by turbulent flow. Dissipation represents the specific dissipation rate caused by turbulence. For custom representatives The source item, For custom representatives The source terms; among which and The specific calculation formula is as follows:

[0103] ;

[0104] ;

[0105] In the formula It is turbulent kinetic energy The turbulent Prandtl number, It is the specific dissipation rate The turbulent Prandtl number, For dynamic viscosity, For turbulent viscosity, Numerical and and The relevant relationship is:

[0106] ;

[0107] In the formula, This is the Reynolds number correction factor.

[0108] In step 3, the deposition model combining the critical velocity model and the particle stripping model is as follows:

[0109] In the study of particle deposition behavior in a double-layer flat-panel film-cooled structure, the El-Batsh critical velocity model was used as the deposition criterion. The critical trapping velocity of a particle is a key parameter for determining whether it can deposit after colliding with the wall; this is determined by the particle's normal collision rate. V n With critical capture rate V cr The comparison is used to determine whether particles have deposited; if the normal collision rate of the particles... V n Less than the critical capture rate V cr Particles deposit on the collision surface; otherwise, they bounce off. The specific form of the critical capture rate was derived by comparing it with a semi-empirical formula.

[0110] ;

[0111] in, E For mixed Young's modulus, D p The particle diameter is determined based on the Young's modulus of the particle surface.

[0112] ;

[0113] ;

[0114] ;

[0115] in E s For surface Young's modulus, E p Let be the Young's modulus of the particle. v s For surface Poisson's ratio, v p For the particle Poisson's ratio, It is particle density;

[0116] To determine stable particle deposition using a particle stripping model, if the wall shear velocity at the point of particle impact is greater than the shear velocity near the wall, then even if the normal collision velocity of the particle impact satisfies the critical trapping velocity condition, the particle will still escape. The critical wall shear velocity in this case is calculated using the following formula:

[0117] ;

[0118] After conversion and simplification, it can be represented as:

[0119] ;

[0120] In the formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, The work done by particle adhesion is measured experimentally. For wall shear stress, d p K is the particle diameter. c For El-Batsh parameters;

[0121] When particles no longer meet the deposition conditions, they will rebound. The particle rebound rate is calculated as follows:

[0122] ;

[0123] In the formula, The normal velocity of the particle before the collision is... The normal velocity after the particle collision. The tangential velocity before particle collision. The tangential velocity after particle collision. The angle between the particle's velocity before collision and the tangential angle of the wall; according to and Find the angle after the particle collision: .

[0124] In step 3, the expression for the deposition rate is: ;

[0125] In the formula C denoted as deposition rate, CR as cumulative deposition mass of particles, A as current grid area, and t as service duration.

[0126] In step 4, the specific steps for performing Orthogonal Eigenvalue Decomposition (POD) on the numerical matrix based on Singular Value Decomposition (SVD) are as follows: to balance computation time and prediction accuracy, the eigenvalues ​​are arranged in descending order, and to determine the number of modes to be retained... k The energy contribution of each mode was analyzed.

[0127] Mapping the cloud maps of each working condition into a deposition rate matrix X :

[0128] ;

[0129] in Let be the deposition rate distribution matrix for the i-th working condition;

[0130] Singular Value Decomposition (SVD), a classic dimensionality reduction method, decomposes high-dimensional data into a combination of orthogonal bases. By preserving the principal singular values ​​and their corresponding basis vectors, it significantly reduces the dimensionality of the data. This method is particularly useful for high-dimensional datasets. X Singular Value Decomposition (SVD) decomposes it into a product of three matrices, as shown in the following equation:

[0131] ;

[0132] ;

[0133] in, U For a left singular matrix, its column vectors They are orthogonal, representing the spatial fundamental schema;

[0134] diagonal elements of the singular value matrix These are singular values ​​arranged from largest to smallest, collectively representing the importance of each mode;

[0135] The right singular basis vectors constituten × n An orthogonal matrix represents the weighting coefficients of spatial patterns under different operating conditions;

[0136] To balance computation time and prediction accuracy, the eigenvalues ​​are arranged in descending order, and to determine the number of modes to retain... k The energy contribution of each mode was analyzed, and the energy percentage was extracted. As shown in the following formula:

[0137] ;

[0138] The data is compressed into an approximate matrix as shown in the following equation. Improve computational efficiency:

[0139] .

[0140] In step 5, the MLP (Multi-Layer Perceptron) is a feedforward artificial neural network composed of multiple neurons (neural nodes) arranged in a hierarchical structure, including an input layer, hidden layers, and an output layer. Neurons between layers are connected by weights, and information propagates sequentially from the input layer to the output layer without feedback connections. The input to the MLP network is... , No. The weights of the neurons are The bias is ， The computational process of each neuron from input to output is shown in the following formula: ;

[0141] ;

[0142] In the formula, The inputs to neural tube j are weighted and summed, and a bias is added. The value after activation is used to obtain the output. .

[0143] In step 6, the predicted image is reconstructed using the inverse POD process:

[0144] The predicted mode coefficients With the original spatial fundamental model Multiplication yields an approximate matrix Then, the numerical matrix is ​​transformed into an image to obtain the predicted image:

[0145] .

[0146] In step 7, the prediction results of the fast prediction model are qualitatively compared with the CFD calculation results to assess areas with significant differences in deposition rate contour maps and to perform error analysis. The computational cost is quantitatively evaluated by using both traditional CFD simulation and the fast prediction model to obtain deposition rate contour maps with the same level of accuracy from the extracted training set samples. The CPU time required for these maps is recorded, and the average execution time is compared to assess the computational cost.

[0147] In step 8, the generalization ability metric for evaluating the fast prediction model is:

[0148] Pixel-level difference and Structural Similarity Index (SSIM) are chosen as evaluation metrics. When one image is undistorted and the other is distorted, their structural similarity is considered a measure of the distorted image's quality. Pixel-level difference involves comparing the RGB values ​​of two images pixel by pixel and calculating the difference to generate an image representing the difference. Two identical images, after pixel-level difference calculation, will generate a pure black image (0, 0, 0). The SSIM value ranges from [0, 1], with a larger value indicating greater similarity. If two images are completely identical, the SSIM value is 1. Figure 8 The figure shown is the SSIM error distribution diagram under the new operating condition.

[0149] The formula for calculating the SSIM index is as follows:

[0150] ;

[0151] in yes x The average value, yes y The average value, yes x variance yes y variance yes x and y covariance; , , is a constant used to maintain stability; L It is the dynamic range of pixel values; , The structural similarity index uses the mean as an estimate of brightness, the standard deviation as an estimate of contrast, and the covariance as a measure of the degree of structural similarity.

[0152] The present invention provides an embodiment that specifically includes:

[0153] (1) Establish a double-walled blade model

[0154] The study focuses on the central region of the chord of a double-walled turbine blade. Because the curvature in the central region of the blade chord is small and changes gradually, it is simplified to a double-walled flat plate model, as follows: Figure 2 As shown, the mesh was generated using Meshing software. Mesh independence was verified, and the mesh at the fluid-structure interface was refined by dividing it into 15 boundary layers to ensure that the y+ value near the wall was less than 1, thus meeting the requirements for wall reinforcement. When the number of mesh layers is increased or decreased while the average temperature of the coupled surfaces above and below the turbulence column remains essentially unchanged, the mesh can be considered to have met the independence requirement.

[0155] (2) Setting numerical boundary conditions

[0156] The primary and secondary flow fluids are ideal gases, with mass flow rate inlets for both. The mainstream mass flow rate is 0.001437 kg / s, and the mainstream temperature is 818 K. The cold flow inlet mass flow rate is determined by the blowing ratio M based on the impact orifice area, and the cold flow temperature is determined by the mainstream temperature Tg and the temperature ratio. The mixed gas outlet is a pressure outlet with an outlet pressure of 101325 Pa. This paper employs fluid-structure interaction (FSI) calculations, using coupling surface conditions at the fluid and solid domain interface to ensure the continuity of heat flux density and temperature in the overlapping region of the fluid and solid domains. A k-ω, SST turbulence model is used, with second-order upwind schemes used for the momentum and energy equations, and the SIMPLE algorithm is employed for pressure and velocity coupling. Particle injection during the calculation is implemented using a discrete phase model (DPM), with a double R distribution Rosin-Rammler particle size distribution selected, and the particle inlet temperature is consistent with the cold flow temperature.

[0157] (3) Dataset creation

[0158] The operating parameters of blowing ratio (M), film pore diameter (df), and temperature ratio (Tg / Tc) were selected as feature variables. Latin hypercube (LHS) sampling was performed within the range of feature variables, resulting in 65 samples. The parameters of the feature dataset were input into the boundary conditions of the computational example to generate deposition rate contour maps of the impact plate and film plate, thus establishing a label dataset corresponding to the feature dataset.

[0159] (4) Convert the deposition rate cloud image into a three-dimensional numerical matrix, perform POD decomposition on the numerical matrix, and retain the main singular values ​​after singular value decomposition. λ k and its related vectors v k This effectively compresses high-dimensional data into a low-dimensional set of feature mode coefficients δ.

[0160] (5) Using the characteristic parameters as input, the modal coefficients δAs output, the data is fed into a multilayer perceptron network to establish a mapping relationship between operating parameters and modal coefficients. Through the connections between nodes in the hidden layers and the nonlinear activation function, the nonlinear relationship between operating parameters and coefficients is learned, resulting in a fast predictive surrogate model that transforms complex physical problems into data-driven mapping tasks.

[0161] (6) For new working conditions, a fast prediction model is used to input three characteristic parameters: air ratio, air film hole diameter and temperature ratio, to obtain the corresponding 41st modal coefficient δ.

[0162] (7) Input the characteristic parameters of the new working condition into the boundary conditions, perform numerical simulation, obtain the deposition rate cloud map of the impact plate and the air film plate, and compare it with the one obtained by the prediction model to evaluate the generalization of the model.

[0163] (8) Example results analysis: This example studies the particle deposition characteristics of double-walled blades. Three new working conditions were selected, and the SSIM error distribution diagram of particle deposition rate under the new working conditions is shown in the figure. Figure 8 This demonstrates the model's effectiveness in predicting the deposition rates of the plates above and below the turbulence column in a flat film gas structure. It can serve as a supplement or alternative to CFD simulations, providing support for subsequent optimization design of anti-deposition cooling structures. This method ensures high simulation accuracy while saving significant computational resources and time.

[0164] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A rapid prediction method for particle deposition characteristics inside a double-walled blade based on a reduced-order model, characterized in that, include: Step 1: Select the middle region of the chord length of the double-walled turbine blade as the research object, simplify the middle region of the chord length of the double-walled turbine blade into a double-walled flat plate model, mesh the flat plate model, and establish the corresponding mathematical model; Step 2: Select the film orifice diameter, blowing ratio, and temperature ratio as characteristic parameters. Use Latin hypercube (LHS) to sample within the characteristic parameter range and extract 65 samples as the characteristic dataset. Import the mesh model obtained by flat plate meshing into Ansys-Fluent software, set the numerical simulation boundary conditions, and input the parameters of the characteristic dataset into the boundary conditions of the example. Use the SST k-ω turbulence model to perform steady-state calculation of the flow field. Step 3: Load the deposition UDF, use the deposition model combining the critical velocity model and the particle stripping model to calculate the particle deposition characteristics of the deposition surface, obtain the deposition rate cloud map of the impact plate and the gas film plate, and establish a label dataset corresponding to the feature dataset; divide the dataset into training set, test set and validation set in a ratio of 8:1:1; construct the color level mapping by uniform interpolation in the color space, and convert the color image of the deposition rate distribution of 65 samples into a three-dimensional numerical matrix; Step 4: Perform Orthogonal Eigenvalue Decomposition (POD) on the 3D numerical matrix based on Singular Value Decomposition (SVD). Extract orthogonal decomposition mode coefficients from the dataset. Determine the number of modes to retain based on the cumulative variance contribution rate, achieving data compression and feature extraction. When the energy percentage reaches 95%, select the top... k Image reconstruction is performed using orthogonal decomposition of basis vectors; Step 5: Input the feature parameters as input and the modal coefficients δ as output, and feed them into the multilayer perceptron network (MLP) to establish the mapping relationship between the feature parameters and the modal coefficients; through the connection relationship between nodes in the hidden layer and the nonlinear activation function, learn the nonlinear relationship between the working condition parameters and the coefficients, and establish a fast prediction proxy model; Step 6: When using the fast prediction surrogate model to predict new working conditions, input the feature parameters to obtain the corresponding predicted modal coefficients, and then reconstruct the feature coefficients into a deposition rate distribution cloud map through the inverse process of orthogonal decomposition of POD to achieve a fast prediction effect. Step 7: Evaluate the accuracy of the fast prediction surrogate model by extracting examples from the training set and comparing the prediction results of the fast prediction model with the CFD calculation results; quantitatively evaluate the computational cost of different methods by comparing the average time taken to obtain deposition rate cloud maps of the same accuracy level by traditional CFD simulation and fast prediction model. Step 8: Evaluate the generalization ability of the fast prediction surrogate model, make predictions for conditions not included in the sample dataset using the fast prediction model, and evaluate regions with different deposition rate distributions using qualitative and quantitative evaluation metrics.

2. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 1, characterized in that, In step 1, the double-walled flat plate model is verified to be independent of the mesh, and the average temperature of the upper and lower coupled surfaces of the turbulence column remains unchanged, so the mesh is considered to have met the independence requirements.

3. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 2, characterized in that, In step 2, the Latin Hypercube (LHS) sampling within the range of feature variables specifically includes the following steps: dividing each feature variable into several equally spaced intervals, and randomly selecting a point within each interval as a sampling point; each variable has only one chance to be selected, and the number of sampling points corresponding to each variable is equal.

4. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 3, characterized in that, In step 2, the turbulence model selected for numerical calculation is: The SST k-ω turbulence model was used for simulation, and its specific form is as follows: ； ； In the formula For turbulent kinetic energy, For specific dissipation rate, For fluid density, Represents fluid velocity. Represents the turbulent kinetic energy caused by the average velocity gradient. The generation rate representing the specific dissipation rate, The effective diffusion coefficient of turbulent kinetic energy. The effective diffusion coefficient is the specific dissipation rate. This is the partial derivative operator; To calculate the partial derivative of the displacement direction; i and j represent coordinate information; This represents the dissipation of turbulent kinetic energy caused by turbulent flow. Dissipation represents the specific dissipation rate caused by turbulence. For custom representatives The source item, For custom representatives The source terms; among which and The specific calculation formula is as follows: ； ； In the formula It is turbulent kinetic energy The turbulent Prandtl number, It is the specific dissipation rate The turbulent Prandtl number, For dynamic viscosity, For turbulent viscosity, Numerical and and The relevant relationship is: ； In the formula, This is the Reynolds number correction factor.

5. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 4, characterized in that, In step 3, the deposition model combining the critical velocity model and the particle stripping model is as follows: The El-Batsh critical velocity model was used as the deposition criterion; the critical trapping velocity of particles is the key parameter for determining whether they can be deposited after colliding with the wall; the normal collision rate of particles was used as the deposition criterion. V n With critical capture rate V cr The comparison is used to determine whether particles have deposited; if the normal collision rate of the particles... V n Less than the critical capture rate V cr Particles deposit on the collision surface; otherwise, they bounce off. The specific form of the critical capture rate was derived by comparing it with a semi-empirical formula. ； in, E For mixed Young's modulus, D p The particle diameter is determined based on the Young's modulus of the particle surface. ； ； ； in E s For surface Young's modulus, E p Let be the Young's modulus of the particle. v s For surface Poisson's ratio, v p For the particle Poisson's ratio, It is particle density; To determine stable particle deposition using a particle stripping model, if the wall shear velocity at the point of particle impact is greater than the shear velocity near the wall, then even if the normal collision velocity of the particle impact satisfies the critical trapping velocity condition, the particle will still escape. The critical wall shear velocity in this case is calculated using the following formula: ； After conversion and simplification, it can be represented as: ； In the formula, The critical wall shear rate of the fluid is denoted as . For Cunningham correction factor, The work done by particle adhesion is measured experimentally. For wall shear stress, d p K is the particle diameter. c For El-Batsh parameters; When particles no longer meet the deposition conditions, they will rebound. The particle rebound rate is calculated as follows: ； In the formula, The normal velocity of the particle before the collision is... The normal velocity after the particle collision. The tangential velocity before particle collision. The tangential velocity after particle collision. The angle between the particle's velocity before collision and the tangential angle of the wall; according to and Find the angle after the particle collision: .

6. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 5, characterized in that, In step 3, the expression for the deposition rate is: ; In the formula C denoted as deposition rate, CR as cumulative deposition mass of particles, A as current grid area, and t as service duration.

7. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 6, characterized in that, In step 4, the specific steps for performing the eigenorthogonal decomposition (POD) of the numerical matrix based on singular value decomposition (SVD) are as follows: Mapping the cloud maps of each working condition into a deposition rate matrix X : ； in Let be the deposition rate distribution matrix for the i-th working condition; For high-dimensional datasets X Singular Value Decomposition (SVD) decomposes it into a product of three matrices, as shown in the following equation: ； ； in, U For a left singular matrix, its column vectors They are orthogonal, representing the spatial fundamental schema; diagonal elements of the singular value matrix These are singular values ​​arranged from largest to smallest, collectively representing the importance of each mode; The right singular basis vectors constitute n × n An orthogonal matrix represents the weighting coefficients of spatial patterns under different operating conditions; Energy percentage interception As shown in the following formula: ； The data is compressed into an approximate matrix as shown in the following equation. Improve computational efficiency: 。 8. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 7, characterized in that, In step 5, the Multilayer Perceptron (MLP) network is a feedforward artificial neural network composed of multiple neurons arranged in a hierarchical structure, including an input layer, hidden layers, and an output layer. Neurons between layers are connected by weights, and information propagates sequentially from the input layer to the output layer without feedback connections. The input to the MLP network is... , No. The weights of the neurons are The bias is ， The computational process of each neuron from input to output is shown in the following formula: ; ； In the formula, The inputs to neural tube j are weighted and summed, and a bias is added. The value after activation is used to obtain the output. .

9. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 8, characterized in that, In step 6, the predicted image is reconstructed using the inverse POD process: The predicted mode coefficients With the original spatial fundamental model Multiplication yields an approximate matrix Then, the numerical matrix is ​​transformed into an image to obtain the predicted image: 。 10. The method for rapid prediction of particle deposition characteristics inside a double-walled blade based on a reduced-order model according to claim 9, characterized in that, In step 8, the generalization ability metric for evaluating the fast prediction model is: Pixel-level difference and structural similarity index (SSIM) are selected as evaluation metrics. When one of two images is a distortion-free image and the other is a distorted image, their structural similarity is considered as a measure of the image quality of the distorted image. Pixel-level difference compares the RGB values ​​of two images pixel by pixel and calculates the difference to generate an image representing the difference. Two identical images will generate a pure black image (0, 0, 0) after pixel-level difference calculation. The range of the SSIM value is [0, 1], with a larger value indicating greater similarity. If two images are completely identical, the SSIM value is 1. The formula for calculating the SSIM index is as follows: ； in yes x The average value, yes y The average value, yes x variance yes y variance yes x and y covariance; , , is a constant used to maintain stability; L It is the dynamic range of pixel values; , The structural similarity index uses the mean as an estimate of brightness, the standard deviation as an estimate of contrast, and the covariance as a measure of the degree of structural similarity.

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