Turbine blade thermal barrier coating thickness distribution optimization method, electronic equipment and medium

Abstract

The invention provides a turbine blade thermal barrier coating thickness distribution optimization method, electronic equipment and a medium, and the method comprises the following steps: dividing a turbine blade thermal barrier coating into a plurality of areas, and changing the thermal barrier coating thickness of at least one area to obtain a plurality of different thermal barrier coating thickness distributions; a machine learning network model is adopted to construct a prediction model of a target value, the multiple different thermal barrier coating thickness distributions serve as input of the machine learning network model, the machine learning network model is trained, and a target value prediction model is obtained; and adopting a multi-target genetic algorithm to obtain a Pareto optimal solution of the thickness distribution of the thermal barrier coating. The thickness distribution of the thermal barrier coating is reasonably optimized to optimize the thermal load distribution on the surface of the coating, so that the comprehensive cooling effect of the turbine blade is improved; according to the method, the high comprehensive cooling efficiency and the low pressure loss coefficient are both considered, and the service performance and economical efficiency of the turbine blade are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of surface coating protection, and particularly relates to a method for optimizing the thickness distribution of a thermal barrier coating for a turbine blade, an electronic device, and a medium. Background Art

[0002] Thermal efficiency is one of the key indicators for evaluating the performance of an aeroengine. Increasing the turbine inlet temperature is the main technical means to improve the thermal efficiency of an aeroengine. At present, the inlet temperature of advanced aeroengines has exceeded 1700 °C, far exceeding the melting point of advanced single-crystal alloys. Advanced cooling technologies and thermal barrier coating technologies (TBCs) are crucial for ensuring the normal operation of turbine blades. Currently, in F-class and G-class gas turbines, the flow rate of cooling air accounts for 16% to 20% of the compressor inlet flow rate, while in aeroengines, this ratio is as high as 20% to 30%. It has become very difficult to further increase the bleeding flow rate. Therefore, thermal barrier coatings are considered the most practical way to significantly increase the service temperature of turbine blades.

[0003] The thickness of the thermal barrier coating is usually 0.1 - 0.7 mm. Currently, in the research on thermal barrier coatings, it is generally approximated that the coating thickness is evenly distributed on the surface of the alloy substrate. However, due to the complex curved surface structure of the turbine blade, it is difficult to completely eliminate the thickness variation of the thermal barrier coating on the complex curved surface through processing methods such as air plasma spraying (APS) and electron beam - physical vapor deposition (EB–PVD), resulting in uneven distribution of the coating thickness on the substrate surface. In the leading edge and trailing edge regions of the turbine blade, the thickness of the thermal barrier coating is often 1.2 - 1.3 times that of other regions of the blade. This thickness variation directly affects the heat insulation effect of the thermal barrier coating and may also have an adverse impact on the mechanical properties of the blade. In addition, heat insulation is one of the main functions of the thermal barrier coating. The heat insulation effect of the thermal barrier coating depends not only on the properties and thickness of the coating itself but also on various factors such as the overall structural design of the blade, coating characteristics, cooling air film distribution, and gas flow environment. Due to the complex internal cooling structure and external high - temperature service environment of the turbine blade, the temperature drop generated by the evenly distributed thermal barrier coating on the blade surface is not evenly distributed. Research shows that the temperature drop generated by the coating in the suction side and leading edge regions of the blade is generally higher than that in the pressure side and trailing edge. This indicates that even if the thermal barrier coating thickness distribution is the same, its heat insulation effect will show regional differences due to the differences in air flow and heat load distribution. Therefore, the coating thickness distribution should vary according to the different and changing heat loads in different regions. Finally, increasing the thickness of the thermal barrier coating can, to a certain extent, improve the heat insulation effect, especially in high - heat - load regions, where a thicker coating can effectively reduce the substrate temperature and extend the service life of the blade. However, thicker TBCs will not only significantly increase the manufacturing cost and technical complexity but also reduce the effective flow area of the blade channel, increase the aerodynamic loss, and thus have an adverse impact on the overall turbine efficiency. This makes a thinner thermal barrier coating the preferred option in actual engineering design to achieve a balance between service performance and economy.

[0004] Patent application CN106649934A discloses a method for optimizing the design of the thermal barrier coating thickness of a turbine blade. In this method, the thermal barrier coating thickness is evenly distributed in all calculation conditions, and the thickness value of the thermal barrier coating corresponding to the minimum maximum stress of the representative node is obtained through optimization calculation, and this value is used as the thickness of the thermal barrier coating on the blade surface. Due to the complex internal cooling structure and external high - temperature service environment of the turbine blade, even if the thermal barrier coating thickness distribution is the same, its heat insulation effect will show regional differences due to the differences in air flow and heat load distribution. Therefore, the coating thickness distribution should vary according to the different and changing heat loads in different regions. An evenly distributed thermal barrier coating thickness is difficult to improve the comprehensive cooling effect of the turbine blade and achieve a balance between service performance and economy. Summary of the Invention

[0005] The object of the present invention is to provide a method for optimizing the thickness distribution of a thermal barrier coating for a turbine blade, an electronic device, and a medium, aiming at the deficiencies of the existing technology, so as to improve the comprehensive cooling effect of the turbine blade.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for optimizing the thickness distribution of a thermal barrier coating for a turbine blade, comprising the following steps:

[0008] S1. Divide the thermal barrier coating of the turbine blade into multiple regions, change the thickness of the thermal barrier coating in at least 1 region, and obtain multiple different thickness distributions of the thermal barrier coating;

[0009] S2. Use multiple different thickness distributions of the thermal barrier coating as the input of a machine learning network model, train the machine learning network model, and obtain a target value prediction model.

[0010] The present invention considers the influence of different thickness distributions of the thermal barrier coating on the target value, and can reasonably optimize the thickness distribution of the thermal barrier coating to optimize the surface heat load distribution of the thermal barrier coating, thereby improving the comprehensive cooling effect of the turbine blade.

[0011] Further, in S3, input multiple different thickness distributions of the thermal barrier coating into the target value prediction model to obtain the target value of each thickness distribution of the thermal barrier coating, and the target value includes the comprehensive cooling efficiency and the pressure loss coefficient;

[0012] S4. Taking maximizing the comprehensive cooling efficiency and minimizing the pressure loss coefficient as the goal, and using multiple different thickness distributions of the thermal barrier coating as the population, adopt a multi-objective genetic algorithm to obtain the Pareto optimal solution of the thickness distribution of the thermal barrier coating.

[0013] The present invention takes into account both a relatively high comprehensive cooling efficiency and a relatively low pressure loss coefficient, improving the service performance and economy of the turbine blade.

[0014] Further, in S2, establish a finite element model of the turbine blade with multiple different thickness distributions of the thermal barrier coating. The finite element model of the turbine blade includes a blade substrate and a thermal barrier coating on the surface of the blade substrate;

[0015] Perform a simulation analysis on each finite element model of the turbine blade to obtain the actual target value of each finite element model of the turbine blade;

[0016] Evaluate the performance of the target value prediction model through the relative error RE, mean square error MSE, and determination coefficient R between the actual target value and the predicted target value 2 of the target value prediction model.

[0017] Further, the expression of the comprehensive cooling efficiency is as follows:

[0018]

[0019] Among them, T in is the temperature of the high-temperature gas, and T w,e is the average temperature of the blade base wall, and T c is the temperature of the cooling air.

[0020] Furthermore, the expression of the pressure loss coefficient C p,t is as follows:

[0021]

[0022] Among them, p t,in is the total pressure averaged over the inlet cross-sectional area of the turbine blade, and p s,out is the static pressure of the characteristic cross-section, and p t is the total pressure of the characteristic cross-section. Taking the leading edge point of the turbine blade as the coordinate origin, the cross-section at a distance of 1.09 times the axial chord length from the origin and parallel to the inlet plane is the characteristic cross-section.

[0023] Furthermore, the implementation process of the simulation analysis for each turbine blade finite element model includes:

[0024] Assign material properties to the blade base and thermal barrier coating in the turbine blade finite element model;

[0025] Set the high-temperature condition and the cooling temperature condition;

[0026] Dynamically update the particle deposition layer thickness, the thermal conductivity of the particle deposition layer, and the heat transfer process, and perform simulation analysis and calculation on the turbine blade finite element model;

[0027] After the calculation is completed, the actual target value is obtained.

[0028] During the operation of ground gas turbines and aero-engines, they are inevitably affected by external particle deposition, erosion, and corrosion. Particle deposition changes the aerodynamic shape of the blade, increases aerodynamic losses, enhances the convective heat transfer between the blade and the mainstream, blocks the cooling channels, and reduces the effectiveness of the gas film coverage. The thickness of the thermal barrier coating is usually several hundred micrometers, and the deposits on the fixed components can reach several hundred micrometers or even several millimeters. The deposition layer simultaneously conducts conjugate heat transfer and mass transfer with the high-temperature mainstream and the coating system, and its own conjugate heat transfer effect cannot be ignored. The distribution of the coating on the surface of the turbine blade affects the distribution of the surface heat load, and further affects the distribution of the deposition layer. The present invention considers the influence of the conjugate heat transfer of the particle deposition layer on the particle dynamic deposition in the simulation analysis, effectively utilizes the heat insulation effect of the deposition layer, can further improve the comprehensive cooling effect of the blade, and has the potential to further increase the service temperature of the turbine blade.

[0029] Further, in S1, control points are set in each area of the thermal barrier coating, and the positions of the control points are adjusted by using a free-form deformation method to change the thickness of the thermal barrier coating.

[0030] Further, the machine learning network model is one of the following models: Kriging surrogate model, radial basis function (RBF), support vector regression (SVR), Gaussian process regression, and deep neural network model.

[0031] Further, the implementation process of obtaining the Pareto optimal solution of the thermal barrier coating thickness distribution by using the multi-objective genetic algorithm includes:

[0032] A1: Using multiple different thermal barrier coating thickness distributions as the population;

[0033] A2: Selecting parents from the population based on non-dominated sorting and crowding distance calculation;

[0034] A3: Performing crossover and mutation on the parents to generate a new population;

[0035] A4: Repeating steps A2 - A3, continuously updating the population until the maximum number of iterations is reached;

[0036] A5: Taking maximizing the comprehensive cooling efficiency and minimizing the pressure loss coefficient as the objectives, and extracting the Pareto optimal solution of the thermal barrier coating thickness distribution from the final population.

[0037] Based on the same inventive concept, the present invention also provides an electronic device, including:

[0038] One or more processors;

[0039] A memory storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the steps of the method for optimizing the thermal barrier coating thickness distribution of a turbine blade.

[0040] Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for optimizing the thermal barrier coating thickness distribution of a turbine blade.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] The present invention optimizes the surface heat load distribution of the coating by reasonably optimizing the thermal barrier coating thickness distribution, and improves the comprehensive cooling effect of the turbine blade; the present invention takes into account both a high comprehensive cooling efficiency and a low pressure loss coefficient, improves the service performance and economy of the turbine blade, and meets the application requirements of aeroengines in higher temperature and more complex environments. Description of the Drawings

[0043] Figure 1 Schematic diagram of the method for optimizing the thermal barrier coating thickness of the turbine blade of the present invention;

[0044] Figure 2 Schematic diagram of the selection of control points in the embodiment of the present invention;

[0045] Figure 3 Schematic diagram of the movement of control points in the embodiment of the present invention;

[0046] Figure 4 Schematic diagram of the particle deposition process in the embodiment of the present invention. Detailed implementation manners

[0047] The present invention will be described in detail below with reference to embodiments. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. For the convenience of narration, words such as "upper", "lower", "left", and "right" in the following text only represent the same directions as the upper, lower, left, and right directions of the accompanying drawings themselves, and do not limit the structure.

[0048] Embodiment

[0049] As Figure 1 , the multi-objective optimization method for the thermal barrier coating thickness distribution of the gas turbine turbine blade considering the heat insulation effect of the deposition layer in this embodiment performs multi-objective optimization on the thickness distribution of the thermal barrier coating (TBCs) on the blade surface under deposition conditions. First, taking the thickness of the thermal barrier coating on the blade substrate surface as the optimization variable and the comprehensive cooling efficiency and pressure loss coefficient of the blade as the objective functions. The thermal barrier coating is divided into 36 regions, and control points are set in the thermal barrier coating region. The distance range of the control points from the substrate surface is 0.1 - 0.7 mm. Based on the Free-Form Deformation (FFD) method, the positions of the control points are adjusted to achieve the deformation of the thermal barrier coating in the local or global range; secondly, based on the Latin hypercube design method, experimental design is carried out, samples within the design variable range are sampled, and 360 samples are obtained; thirdly, based on the ANSYS Workbench platform, automated numerical simulation is carried out. Through scripts, parametric modeling and mesh generation of the samples of the experimental design are realized. Combining the critical viscosity model and the dynamic mesh technology, numerical solutions and result post-processing are carried out for different samples, and the target results are output; thirdly, a preliminary surrogate model is constructed based on the results of the automated numerical calculation. The verification point results of the randomly generated surrogate model are compared with the numerical calculation results for verification, the prediction accuracy of the surrogate model is evaluated and improved, and other samples are calculated based on the surrogate model; finally, the multi-objective genetic algorithm is used to obtain the Pareto optimal solution of the thermal barrier coating thickness distribution, taking into account a higher cooling efficiency and a lower pressure loss coefficient to meet the application requirements of aero-engines in a higher temperature and more complex environment.

[0050] The method includes the following steps:

[0051] Step 1: Define the optimization problem.

[0052] Take the thickness of the thermal barrier coating on the blade base surface as the optimization variable, and take the comprehensive cooling efficiency and pressure loss coefficient of the blade as the objective functions. Divide the thermal barrier coating into 36 regions. In the places where the blade curvature is large, the region division is denser to ensure covering the entire blade surface. Set control points in the thermal barrier coating regions. The distance range of the control points from the blade base surface is 0.1 - 0.7 mm. Based on the Free-Form Deformation (FFD) method, adjust the positions of the control points to achieve local or global deformation of the thermal barrier coating (such as Figure 2 , Figure 3 ). To understand the contribution of the increase in the thickness of the thermal barrier coating at different positions under the existing internal cooling channel configuration to the cooling efficiency; the movement of the control points drives the change in the geometric shape of the thermal barrier coating, and the heat insulation performance of the part where the coating thickness increases is better and the cooling efficiency is higher.

[0053] The comprehensive cooling efficiency of the turbine blade is defined as follows:

[0054]

[0055] where T in is the temperature of the high-temperature gas, T w,e is the average temperature of the blade base wall, and T c is the temperature of the cooling air.

[0056] Take the leading edge point of the turbine blade as the coordinate origin, and take the cross-section at a distance of 1.09 times the axial chord length from the origin and parallel to the inlet plane as the characteristic cross-section. The pressure loss coefficient is defined as:

[0057]

[0058] In the formula, p t,in is the total pressure averaged over the turbine inlet cross-section area, p s,out is the static pressure of the characteristic cross-section, and p t is the total pressure of the characteristic cross-section.

[0059] Free-Form Deformation (FFD) is a flexible and general geometric deformation and parameterization method, which is widely used in fields such as engineering design, computer graphics, optimization problems, and aerodynamic shape design. Its core idea is to parametrically deform geometric shapes through a control grid nested within a reference geometric body, without directly modifying the expression of the geometric body or the grid structure. This method is efficient and flexible in dealing with complex geometric shapes, and is particularly suitable for complex design requirements in aerospace, mechanical design, and medical simulation, etc.

[0060] The FFD method is based on the free deformation of an initial geometric body, and its specific implementation process can be divided into the following steps:

[0061] (1) Define the control grid

[0062] The FFD method describes the space of shape deformation through a multi-dimensional control grid. The control grid is usually a regular Cartesian grid that contains a number of control points. The movement of these control points will drive the deformation of the entire nested geometric body.

[0063] (2) Geometric mapping

[0064] The core of FFD is to bind each point of the target geometric body to the control grid through a mapping relationship. Common mapping methods include:

[0065] Local coordinate transformation: By converting the coordinates of geometric points into the local coordinates of the control grid;

[0066] Cubic interpolation functions (B-spline or Bezier basis functions): Using interpolation functions to calculate the deformed coordinates.

[0067] The mapping formula can be expressed as:

[0068]

[0069] where P is the point on the deformed geometric body, P ijk is the control point in the control grid, and B i (ξ), B j (η), B k (ζ) are interpolation basis functions, and l, m, n are respectively the number of points of the B i (ξ), B j (η), B k (ζ) interpolation basis functions.

[0070] (3) Control point movement

[0071] By moving the control points in the control grid, the target geometric body is driven to deform in shape. FFD ensures the smoothness and continuity of the deformation, and at the same time provides a high degree of local and global control capabilities.

[0072] Step 2: Experimental design.

[0073] Based on the Latin Hypercube Design (LHD) method, conduct experimental design, sample the samples within the design variable range, and obtain 360 samples;

[0074] Latin Hypercube Design (LHD) is a commonly used experimental design method, especially suitable for the research of complex systems within the scope of multiple variables and multiple parameters. It ensures that the sample covers the entire parameter space by evenly distributing sampling points in the parameter space, improving the efficiency and representativeness of the experiment. Compared with traditional completely random sampling or other design methods, the LHD method has significant advantages in reducing the sample size and optimizing the calculation cost, and is widely used in fields such as engineering optimization, computational experiments, and multidisciplinary design optimization. Its specific implementation process can be divided into the following steps:

[0075] (1) Determine the experimental range and variables

[0076] Determine the number of parameters k to be studied and the value range of each parameter. The range of each parameter can be discrete or continuous.

[0077] (2) Divide the interval

[0078] Divide the value range of each parameter into n 1 equal intervals.

[0079] (3) Random sampling

[0080] For each parameter, randomly select a value as the sample point in each interval. By randomly arranging the sample points of each parameter, a k-dimensional hypercube sample is formed.

[0081] (4) Ensure uniform sample distribution

[0082] Adjust the arrangement order of the sample points so that the samples are evenly distributed in the high-dimensional space, thus avoiding the samples being too concentrated or repeated.

[0083] In multi-objective optimization, there is usually the following empirical relationship between the number of samples and the number of optimization parameters to ensure the optimization accuracy and the coverage of the sample space. The number of samples (or the number of experimental design points) generally should increase with the increase in the number of optimization parameters, but considering the calculation cost, the following several guiding principles are usually adopted:

[0084] 1. Empirical formula

[0085] The common empirical formula is:

[0086] N = 10 × k (4)

[0087] Among them, N is the number of samples, and k is the number of optimization parameters.

[0088] If the complexity of the optimization problem is high or the change of the objective function is fast, the coefficient can be increased to 15 or 20. For multi-dimensional optimization problems, efficient sampling methods such as Latin Hypercube Design (LHD) can help reduce the number of samples. At this time, the number of samples can be selected slightly lower than the value of the empirical formula. For example, the number of samples can be selected as 5 to 10 times the number of parameters, and the optimization design can be used to make up for the reduction of the number of samples.

[0089] Step 3: Automatic simulation calculation.

[0090] Based on the ANSYS Workbench platform, carry out automated numerical simulation. Through scripts, parametric modeling and mesh generation of the samples of the experimental design are realized. Combining the critical viscosity model with the dynamic mesh technology, numerical solutions and result post-processing are carried out for different samples (different thermal barrier coating distributions), and the target results are output.

[0091] Realizing automated numerical simulation in ANSYS Workbench through scripts can greatly improve work efficiency, especially in the case of multiple runs of simulation. By writing Python scripts, the entire process from geometry import, mesh generation, boundary condition setting, running the solution to result extraction can be controlled. In large-scale parametric design or multi-objective optimization, automated scripts have irreplaceable advantages. The specific implementation process can be divided into the following steps:

[0092] (1) Prepare the environment

[0093] In ANSYS Workbench, Python scripts can be directly written and run in the "Scripting" window, or the script file (.py) can be imported into Workbench for execution. In the script, the Workbench project file can be controlled, components can be created, parameters can be set, the solution can be run, and results can be exported, etc.

[0094] (2) Create and set the project

[0095] The project file can be controlled and the fluid analysis module can be added through scripts.

[0096] (3) Load the geometric model

[0097] The geometric model can be imported into Workbench through scripts, and the generation and setting of parametric geometry can also be controlled. Suppose there is an external CAD file (such as a.step or.iges file).

[0098] (4) Set the mesh generation parameters

[0099] The relevant parameters of mesh division can be set through scripts, such as the global mesh size, local mesh refinement, etc. Different types of analysis modules have different mesh setting methods.

[0100] (5) Set materials and boundary conditions

[0101] The material properties, boundary conditions, and initial conditions can be assigned to the model and set through scripts.

[0102] (6) Define parametric design and parameter sweep

[0103] Some parameters such as geometry, materials, boundary conditions, etc. can be parameterized to perform parametric design and parameter sweep.

[0104] (7) Run simulation to solve

[0105] After the settings are completed, the solution can be automatically started through a script. The solution commands for different modules may be different.

[0106] (8) Extract and save results

[0107] The simulation results can be extracted through a script and saved in a specified file format, such as CSV or Excel format.

[0108] (9) Execute multiple simulations in a loop

[0109] In multi-objective optimization or parameter sweep, it is usually necessary to automatically execute multiple simulations. The entire solution process can be placed in a loop to automatically iterate each set of parameters.

[0110] (10) Save and close the project

[0111] After the simulation is completed, save and close the project.

[0112] In the Fluent software, the dynamic deposition calculation of particles considering conjugate heat transfer in the deposition layer can be realized by using user-defined functions (UDF). The following is how to use the UDF method to achieve this goal, including the dynamic update of the deposition layer, conjugate heat transfer calculation, and the implementation of the particle dynamic deposition model.

[0113] Such as Figure 4 , particle dynamic deposition: In the flow field, due to effects such as inertia and diffusion, particles collide with the wall and deposit on the wall, and the deposition layer will thicken dynamically over time. Conjugate heat transfer: The thermal conductivity characteristics of the deposition layer affect the wall temperature distribution, and the heat transfer between the fluid, deposition layer, and substrate needs to be considered. UDF implementation: Dynamically update the deposition layer thickness, thermal conductivity, and heat transfer process through UDF, and real-time couple the particle deposition model in Fluent.

[0114] The specific implementation process of the UDF method can be divided into the following steps:

[0115] (1) Define macros and data structures

[0116] Use the UDF macros of Fluent to define and control the physical properties of the deposition layer on the wall surface. For example, define the thickness and thermal conductivity of the deposition layer.

[0117] (2) Define the particle deposition logic

[0118] Process the interaction between particles and the wall surface through the DEFINE_DPM_BC macro, and determine whether the particles are deposited and update the thickness of the deposition layer.

[0119] (3) Dynamically update the thermal conductivity and thickness of the deposition layer

[0120] Use the DEFINE_PROFILE macro to update the thermal conductivity and thickness of the deposition layer in real time.

[0121] (4) Couple the heat transfer on the fluid side and the solid side

[0122] Couple the heat flux on the fluid side and the heat conduction on the solid side through the conjugate heat transfer model. Use the DEFINE_HEAT_FLUX macro to calculate the heat transfer between the fluid side and the deposition layer.

[0123] Load and run the UDF in Fluent:

[0124] (1) Compile the UDF

[0125] Save the above code as a.c file, such as particle_deposition.c, and compile it through the UDF compiler of Fluent:

[0126] Open Fluent.

[0127] In the Fluent interface, select Define>User-Defined>Functions>Compile.

[0128] Load the particle_deposition.c file.

[0129] (2) Associate with the Fluent model

[0130] Associate the deposition logic (DEFINE_DPM_BC) with the target wall surface.

[0131] In the material properties, set the thermal conductivity as a dynamically updated variable.

[0132] Set the conjugate heat transfer model and apply the DEFINE_HEAT_FLUX macro to the wall surface.

[0133] (3) Enable the DPM module

[0134] Ensure that the Discrete Phase Model (DPM) module is enabled in Fluent and define the particle properties (diameter, density, etc.).

[0135] (4) Run the simulation

[0136] Set the simulation parameters (time step, maximum number of iterations, etc.), run the simulation, and observe the deposit layer thickness, temperature distribution, and particle deposition behavior in the post-processing stage.

[0137] Step 4: Construct a surrogate model.

[0138] Construct a preliminary surrogate model based on the results of automated numerical calculations. Use the results of the verification points of the randomly generated surrogate model to compare and verify with the numerical calculation results, evaluate and improve the prediction accuracy of the surrogate model, and calculate other sample points based on the surrogate model.

[0139] A surrogate model is a lightweight model used to approximate complex numerical calculations, which can significantly reduce the computational cost. After constructing the preliminary surrogate model, the model accuracy can be evaluated by comparing the results of the randomly generated verification points with the numerical calculation results, and the model can be improved according to the evaluation results. The following are the specific steps:

[0140] (1) Construction of the surrogate model

[0141] Determine the range of input parameters X = [x 1 , x 2 , …, x x , 36 control points on the surface of the thermal barrier coating, and use the Latin Hypercube Design (LHD) method to generate 360 samples (different thermal barrier coating thickness distributions). Calculate the comprehensive cooling efficiency and pressure loss coefficient of the blade corresponding to these samples in the numerical calculation tool. Select a suitable type of surrogate model to construct the surrogate model and fit the model using the training data. Randomly generate verification points (Xval) in the input parameter space. Usually, the number of verification points is 20% - 30% of the number of samples. Calculate the true value Ytrue = f(Xval) of the verification points using the numerical calculation tool. Use the surrogate model to predict the output Ypred = f(Xval) of the verification points. Use accuracy evaluation metrics such as Mean Squared Error (MSE), Relative Error (RE), and Coefficient of Determination (R 2 ) to evaluate the accuracy of the surrogate model. Improve the surrogate model according to the evaluation results, and improve the local prediction accuracy by increasing the number of samples, optimizing the sampling strategy, and constructing sub-models separately for high-error regions. Re-evaluate the improved model until the accuracy reaches the target.

[0142] The Pareto optimal solution of the thermal barrier coating thickness distribution is obtained by using a multi-objective genetic algorithm, taking into account higher cooling efficiency and lower pressure loss coefficient to meet the application requirements of aero-engines in higher temperature and more complex environments.

[0143] (2) Verification of the surrogate model

[0144] Verification points (X val ) are randomly generated within the input parameter space. Usually, the number of verification points is 20%-30% of the sample number. Use a numerical calculation tool to calculate the true value Y true = f(X val ) of the verification points. Use the surrogate model to predict the output Y pred = f(X val ) of the verification points. Precision evaluation metrics, common metrics include: mean square error (MSE), relative error (RE), and coefficient of determination (R 2 ).

[0145] (3) Improving the prediction accuracy of the surrogate model

[0146] Improve the surrogate model according to the evaluation results, including: increasing the sample number; optimizing the sampling strategy, such as adaptive sampling for high-error regions; trying more complex models (such as Gaussian process regression, deep neural network); adjusting model parameters, such as kernel function parameters in Kriging, the number of hidden layers in NN, etc. Build a sub-model separately for the high-error region to improve the local prediction accuracy. Re-evaluate the improved model until the accuracy reaches the target.

[0147] Step Five: Optimization problem.

[0148] The Pareto optimal solution of the thermal barrier coating thickness distribution is obtained by using a multi-objective genetic algorithm, taking into account higher cooling efficiency and lower pressure loss coefficient to meet the application requirements of aero-engines in higher temperature and more complex environments. The specific steps are as follows:

[0149] (1) Construct a surrogate model

[0150] Construct a surrogate model for optimization, such as Kriging, radial basis function (RBF), support vector regression (SVR), etc. Assume the goal is two objective functions f 1 (x) and f 2 (x), which represent the comprehensive cooling efficiency and pressure loss coefficient respectively, and the objective functions are approximated by the surrogate model.

[0151] (2) Define the multi-objective genetic algorithm

[0152] Implement multi-objective optimization using a genetic algorithm library in Python (such as DEAP or pygmo). The following are the implementation steps:

[0153] Initialize the population: Randomly generate a set of solutions in the parameter space, which are different thermal barrier coating thickness distributions, and use these different thermal barrier coating thickness distributions as the population.

[0154] Fitness evaluation: Use a surrogate model to predict the objective values of each thermal barrier coating thickness distribution in the population. The objective values are the comprehensive cooling efficiency and pressure loss coefficient.

[0155] Selection: Select parents from the population based on non-dominated sorting and crowding distance calculation. Crossover and mutation: Generate a new population through genetic operations.

[0156] Iterative optimization: Continuously update the population until the maximum number of iterations is reached to generate the Pareto front.

[0157] (3) Extract the Pareto front

[0158] Extract the Pareto optimal solutions of the thermal barrier coating thickness distribution from the final population.

[0159] (4) Result analysis and optimization

[0160] Pareto front distribution: Analyze the trade-off relationship between different objective values in the Pareto solution set.

[0161] Select the optimal solution: Select a certain solution in the Pareto set as the optimal solution according to the design requirements, that is, consider the relatively better thermal barrier coating thickness distribution under these two objective functions (maximizing the cooling efficiency and minimizing the pressure loss coefficient).

[0162] Optimize the surrogate model: If the accuracy of the Pareto front is insufficient, samples can be increased to improve the accuracy of the surrogate model.

[0163] The non-dominated sorting genetic algorithm is based on different classifications of the individuals in the population, as follows: Before selection, the population is first sorted according to non-dominance. All non-dominated individuals are divided into the same category, given a Dummy fitness value (this value is proportional to the population size), and equal replication opportunities are given to the individuals in the same category. To maintain the diversity of the population, these classified individuals are shared according to their Dummy fitness values. Then, ignore these individuals that have been classified into different categories, and continue this step for the remaining individuals in the population until all individuals are classified into a certain category. Based on these categories, random residual sampling selection is performed to move the population towards the Pareto front.

[0164] The purpose of crowding distance sorting is to sort the individuals in the same category, and finally select the individuals with high level and large crowding distance as the next generation.

[0165] The calculation formula of crowding distance is as follows:

[0166]

[0167] Among them, CD im represents the crowding degree of the i-th individual in the m-th objective function, and f m (x i+1 ), f m (x i-1 ) represent the m-th objective function values of the (i + 1)-th individual and the (i - 1)-th individual respectively, and f m (x max ), f m (x min ) represent the maximum and minimum values of the m-th objective function among all individuals respectively.

[0168] Thermal barrier coatings are considered to be the most practical way to significantly increase the service temperature of turbine blades at present. The thickness of thermal barrier coatings is usually 0.1 - 0.7 mm. At present, the research on thermal barrier coatings approximately assumes that the coating thickness is evenly distributed. However, it is difficult to completely eliminate the thickness variation of thermal barrier coatings on complex surfaces through traditional processing means, resulting in uneven distribution of the coating thickness on the substrate surface. In addition, due to the complex internal cooling structure and external high-temperature service environment of turbine blades, the temperature drop ΔT generated by the evenly distributed thermal barrier coating on the blade surface is not evenly distributed. This shows that even if the thermal barrier coating thickness distribution is the same, its heat insulation effect will show regional differences due to the differences in air flow and heat load distribution. Therefore, the coating thickness distribution should vary according to the different heat loads in different regions. Thicker TBCs will not only significantly increase the manufacturing cost and technical complexity, but also reduce the effective flow area of the blade channel, increase the aerodynamic loss, and thus have an adverse impact on the overall turbine efficiency. The optimal thermal barrier coating distribution should be able to balance its service performance and economy. The distribution of the coating on the turbine blade surface will also affect the distribution of its surface heat load, and further affect the distribution of the deposition layer. The thickness of thermal barrier coatings is usually several hundred micrometers, and the deposits on fixed components can reach several hundred micrometers or even several millimeters. The deposition layer is conjugated with the high-temperature mainstream and the coating system for heat and mass transfer, and its own conjugated heat transfer effect cannot be ignored. This method optimizes the surface heat load distribution of the coating by reasonably optimizing the thermal barrier coating thickness distribution, effectively utilizes the heat insulation effect of the deposition layer, and further improves the comprehensive cooling effect of the blade, having the potential to further significantly increase the service temperature of turbine blades.

[0169] Another embodiment of the present invention provides an electronic device, including:

[0170] One or more processors;

[0171] A memory storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the steps of the method for optimizing the thickness distribution of the thermal barrier coating of the turbine blade.

[0172] In some implementations, the memory may be a high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk memory.

[0173] In other implementations, the processor may be various types of general-purpose processors such as a central processing unit (CPU) or a digital signal processor (DSP), which is not limited herein.

[0174] Another embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for optimizing the thickness distribution of the thermal barrier coating of the turbine blade.

[0175] The content clarified in the above embodiments should be understood that these embodiments are only used to more clearly illustrate the present invention, rather than to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification made by those skilled in the art to the present invention all fall within the scope defined by the appended claims of this application.

Claims

1. A method for optimizing thickness distribution of thermal barrier coating on turbine blades, characterized in that: The following steps are involved: S1. Dividing the thermal barrier coating of the turbine blade into a plurality of regions, and changing the thickness of the thermal barrier coating in at least one region to obtain a plurality of different thermal barrier coating thickness distributions; S2. Using a plurality of different thermal barrier coating thickness distributions as inputs of a machine learning network model, training the machine learning network model, and obtaining a target value prediction model.

2. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 1, characterized in that: S3, inputting a plurality of different thermal barrier coating thickness distributions into the target value prediction model to obtain a target value for each thermal barrier coating thickness distribution, wherein the target value includes a comprehensive cooling efficiency and a pressure loss coefficient; S4. With the goal of maximizing the comprehensive cooling efficiency and minimizing the pressure loss coefficient, multiple thermal barrier coating thickness distributions are used as the population, and a multi-objective genetic algorithm is used to obtain the Pareto optimal solution of the thermal barrier coating thickness distribution.

3. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 1, characterized in that: In S2, a plurality of turbine blade finite element models with different thermal barrier coating thickness distributions are established, and the turbine blade finite element model includes a blade substrate and a thermal barrier coating on the surface of the blade substrate; Perform simulation analysis on each turbine blade finite element model to obtain an actual target value of each turbine blade finite element model; The relative error RE, mean square error MSE and determination coefficient R between the actual target value and the predicted target value are used. 2 Evaluate the performance of the target value prediction model.

4. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 2, characterized in that: Overall cooling efficiency The expression is as follows: Pressure loss coefficient C p,t The expression is as follows: Among them, T in is the temperature of the high temperature gas, T w,e is the average temperature of the blade base wall, T c is the temperature of the cooling air, p t,in is the total pressure averaged over the turbine blade inlet cross-sectional area, p s,out is the static pressure of the characteristic cross section, p t is the total pressure on the characteristic cross section.

5. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 3, characterized in that: The implementation process of the simulation analysis of each turbine blade finite element model includes: Assign material properties to the blade substrate and thermal barrier coating in the turbine blade finite element model; Set high temperature conditions and cooling temperature conditions; Dynamically update the particle deposition layer thickness, particle deposition layer thermal conductivity, and heat transfer process, and perform simulation analysis and calculation on the turbine blade finite element model; After the calculation is completed, the actual target value is obtained.

6. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 1, characterized in that: In S1, a control point is set in each area of ​​the thermal barrier coating, and the position of the control point is adjusted by a free deformation method to change the thickness of the thermal barrier coating.

7. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 1, characterized in that: The machine learning network model is one of the following models: Kriging proxy model, radial basis function, support vector regression, Gaussian process regression, deep neural network model.

8. The method for optimizing thickness distribution of thermal barrier coating for turbine blades according to claim 2, characterized in that: The implementation process of obtaining the Pareto optimal solution of thermal barrier coating thickness distribution using a multi-objective genetic algorithm includes: A1: multiple different TBC thickness distributions are used as populations; A2: Select parents from the population based on non-inferiority sorting and crowding distance calculation; A3: Perform crossover and mutation on the parent generation to generate a new population; A4: Repeat steps A2-A3 and continuously update the population until the maximum number of iterations is reached; A5: With the goal of maximizing the comprehensive cooling efficiency and minimizing the pressure loss coefficient, the Pareto optimal solution of the thickness distribution of the thermal barrier coating is extracted from the final population.

9. An electronic device, characterized in that: include: one or more processors; A memory having one or more programs stored thereon, which, when the one or more programs are executed by the one or more processors, enables the one or more processors to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The computer program is stored therein, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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