Probabilistic Thermal Analysis Method for CMC Material Turbine Blades Based on Mesostructure Feature Statistics

Abstract

The present invention discloses a probabilistic thermal analysis method for CMC turbine blades based on the statistical characteristics of mesoscopic structural features. For woven structure CMC materials, XCT is used to obtain mesoscopic structural feature images of different cross-sections inside the materials, and the probability distribution characteristics of mesoscopic geometric parameters such as fiber bundle cross-sectional dimensions, fiber bundle spacing, and weaving angles are statistically analyzed. Based on the mesoscopic structure parameterization model of woven structure CMC materials, the probability distribution characteristics of anisotropic equivalent thermal conductivity are obtained. On this basis, the spatial distribution change and probability distribution of anisotropic thermal conductivity are introduced into the thermal analysis model of woven structure CMC turbine blades, and the Monte Carlo stochastic finite element method is used to statistically analyze the probabilistic characteristics of the blade temperature field. The present invention obtains the random characteristics of the internal geometric structure of CMC materials and the corresponding probabilistic distribution of anisotropic thermal properties based on actual mesoscopic structure images, and can more truly and effectively obtain the characteristics of potential high-temperature regions of woven structure CMC material turbine blades.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering thermophysics, and in particular relates to a probabilistic thermal analysis method for CMC material turbine blades based on microscopic structural feature statistics. Background Art

[0002] Foreign countries have been studying ceramic matrix composites (CMC) for a long time. With the gradual improvement of material performance and the gradual maturity of preparation technology, Europe and the United States have carried out simulation assessments of typical and simulated CMC parts and even engineering applications. Among them, foreign countries have also established corresponding engineering design methods for the application of CMC in aircraft engine turbine blades. According to public information, the most representative one is the research on SiC conducted by NASA Glenn Research Center in the UEET program. f / SiC turbine blade simulation parts preparation and assessment. The center not only proved through experiments that the three-dimensional five-way woven SiC f / SiC turbine guide blades have excellent performance in high-temperature gas impact environments, and a reliability prediction method under actual working conditions has been established for the blades, and corresponding software has been developed. In the above reliability calculation process, NASA researchers have fully considered the discreteness of material mechanical and thermodynamic properties, the uncertainty of internal and external pressure loads of blades, the fluctuation of blade structural parameters, the discreteness of critical loads of material failure, etc. from the perspective of probability analysis. The discrete data of material performance parameters are derived from the results of physical property tests on the materials. In addition, in the finite element modeling of blades, the anisotropy of CMC physical properties and the spatial distribution of the main directions of material physical properties caused by the bending of the blade surface have been carefully considered. Finally, it was found through calculation that for the current blade design, the probability of not meeting the design requirements is 1.6%. Facts have proved that the above research work has provided SiC f / Lays a solid foundation for the commercial application of SiC turbine blades.

[0003] Since the research on ceramic-based composites in my country started relatively late, the current research on CMC is still at the material level. There is little research on the engineering-level application design methods of CMC turbine blades, and most of them only focus on certain specific technical difficulties.

[0004] Sun Jie et al. combined the prediction of the stiffness performance of plain woven composites with the thermal-solid coupling analysis of turbine guide vanes, and combined material optimization with structural optimization. Starting from two scales of material and structure, they established an integrated optimization design method for the structure and material of ceramic matrix woven composite turbine guide vanes. The above method took material stress and blade displacement limits as constraint conditions and the minimum blade mass as the optimization goal, and obtained good optimization results. However, the discreteness of the physical properties of the composite material was not considered in the calculation process of this method. Therefore, this method needs to be improved to achieve engineering applications.

[0005] Based on the research on the calculation method of the thermal conductivity of unidirectional composites, Xu Rui et al. took the Mark II turbine blade as the object and used self-programmed finite element and Fluent simulation methods to focus on the influence of the anisotropy of thermal conductivity and the random fluctuation of thermal conductivity on the blade temperature distribution, especially the high-temperature regions of the leading edge and trailing edge. They obtained the sensitivity of the blade temperature field to the thermal conductivity in different principal directions and the variation law of the high-temperature regions of the blade. The above research results provide a reference technical solution for considering the discreteness of material physical properties in the thermal analysis of CMC turbine blades. However, the research object in the paper can be regarded as a Mark II turbine blade composed of unidirectional fibers, which is quite different from the structure of the three-dimensional woven CMC turbine blades that have been commercially used internationally.

[0006] Sun et al. established a method for integrated optimization and reliability assessment of material-structure for 2.5D C f / SiC guide vanes from two scales of material and structure. The authors first used the Monte Carlo method to study the randomness of the mechanical properties of 2.5D C f / SiC composites and found that the macroscopic mechanical properties of 2.5D C f / SiC composites are closely related to the randomness of material components and microstructures. Then they established a finite element model for the structural optimization of 2.5D C f / SiC guide vanes considering the discreteness of material properties and carried out optimization calculations. Finally, through the integral analysis of the distribution model of the calculated results of the blade mechanical properties, the reliability of the optimization results was verified. Generally speaking, the above method already has strong engineering practicability. Although its purpose is blade structural optimization and mechanical property analysis, it still has good reference significance for the establishment of the thermal analysis model of CMC turbine blades.

[0007] However, due to the inevitable randomness of geometric features during the weaving and composite processes of CMC materials, which brings about the anisotropic and inhomogeneous characteristics of the overall material, there are few relevant thermal analysis studies. This is because compared with the thermal analysis of traditional metal turbine blades, the establishment of a thermal analysis model for CMC material turbine blades requires considering more influencing factors. The two most prominent problems are the influence of the probability distribution of mesoscopic structure geometric features on the anisotropic thermal conductivity coefficient, and the influence of the probability distribution of anisotropic heat conduction on the macroscopic blade temperature field. The key problems that this study focuses on solving for the above two issues are how to identify and post-process the mesoscopic structure geometric features through existing image recognition technology to establish a database of the probability distribution of geometric features; and how to introduce the probability distribution of the anisotropic thermal conductivity coefficient obtained from the mesoscopic structure into the macroscopic blade to calculate the temperature field.

[0008] Most of the above studies on the probability distribution characteristics of the anisotropic thermal conductivity coefficient of composite materials are aimed at the random changes in the position of fiber bundles and the differences in volume fraction, and have not systematically explored the influence law of the randomness of the geometric feature parameters of the mesoscopic structure of woven CMC materials. Therefore, based on the Monte-Carlo simulation method and aiming at obtaining the equivalent thermal conductivity of the material, this invention systematically calculates and analyzes the influence law of the geometric feature parameters such as the warp width, weft width, fiber bundle gap, and weaving angle in the typical mesoscopic structure of the material on the probability distribution characteristics of the equivalent thermal conductivity of the woven structure CMC material. Summary of the Invention

[0009] This invention obtains the probability distribution characteristics of the internal mesoscopic geometric parameters of the woven structure CMC material based on XCT, and combines the mesoscopic structure parameterization model to obtain the probability distribution characteristics of the anisotropic equivalent thermal conductivity of the material. On this basis, the spatial distribution change and probability distribution of the anisotropic thermal conductivity coefficient are introduced into the thermal analysis model of the woven structure CMC turbine blade, and the Monte Carlo stochastic finite element method is used to statistically analyze the probabilistic characteristics of the blade temperature field to obtain the potential high-temperature region characteristics of the CMC material turbine blade.

[0010] To achieve the above object, the technical solution adopted by this invention is as follows:

[0011] A probabilistic thermal analysis method for CMC material turbine blades based on the statistics of mesoscopic structure characteristics, comprising the following steps:

[0012] Step 1: Carry out mesoscopic structure tests on the woven structure CMC material sample using XCT to obtain the mesoscopic structure images of different directions and positions of the cross-section of the material;

[0013] Step 2: For a certain number of mesoscopic structure images, statistically analyze the probability distribution characteristics of geometric feature parameters such as the cross-sectional length and width of warp and weft yarns, the warp spacing, and the weaving angle inside the material, and characterize them using corresponding probability distribution functions;

[0014] Step 3: Establish a parametric model of the mesoscopic braided structure of CMC materials. The parametric geometric features include the cross-sectional length and width of warp and weft yarns, the warp spacing, and the weaving angle. Input the geometric feature parameters in Step 2 into the parametric model of the mesoscopic braided structure of CMC materials, and calculate and obtain the probability distribution characteristics of the anisotropic thermal conductivity of the material based on the Monte Carlo stochastic finite element method;

[0015] Step 4: For CMC turbine blades, use the anisotropic equivalent thermal conductivity to characterize the thermal physical properties of the braided structure CMC materials. The direction of the anisotropic thermal conductivity changes with the blade profile. Use a curvilinear coordinate system to realize the conversion of the principal coordinate system of the anisotropic thermal conductivity to the space coordinate system. Use tetrahedral meshes to generate blade meshes in the calculation, and apply the third-kind convective heat transfer boundary conditions on the inner and outer wall surfaces of the blade respectively, and carry out the finite element calculation of the temperature field of the CMC blade;

[0016] Step 5: Based on the Monte Carlo stochastic finite element method, sample from the probability distribution of the anisotropic thermal conductivity of the material obtained in Step 3, repeat the finite element calculation of the temperature field of the CMC blade in Step 4, and then obtain the probability distribution characteristics of the temperature field of the CMC blade, and conduct statistical analysis on key parameters such as the maximum temperature of the blade.

[0017] Preferably: In the above Step 2, the probability distribution functions of the cross-sectional length and width of warp and weft yarns, the warp spacing, and the weaving angle are characterized using normal distribution functions.

[0018] Preferably: In the above Step 3, the process of calculating the probability distribution of the anisotropic thermal conductivity of the material based on the Monte Carlo finite element method is as follows: For the parametric model of the mesoscopic braided structure of CMC materials generated by sampling geometric feature parameters each time, use tetrahedral meshes to generate calculation meshes, apply fixed-temperature boundaries on the upper and lower surfaces of the model, apply periodic boundary conditions around, carry out finite element simulation of the temperature field, obtain the temperature gradient and the mean value of heat flux density of the model, and calculate the equivalent thermal conductivity of the material based on the Fourier heat conduction equation.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] The probabilistic thermal analysis method and process of the woven structure CMC material turbine blade established by the present invention can obtain the random characteristics of the internal geometric structure of the CMC material and the corresponding anisotropic thermal property probability distribution based on the actual mesoscopic structure image, and can more truly and effectively obtain the characteristics of potential high-temperature regions of the woven structure CMC material turbine blade, improve the prediction accuracy of the temperature field of the CMC turbine blade, and provide thermal analysis method support for the engineering design and application of the CMC blade. Description of the Drawings

[0021] Figure 1 is a 2.5D woven structure CMC material sample;

[0022] Figure 2 is an XCT model of the CMC mesoscopic structure;

[0023] Figure 3 is an image of the cross-sectional characteristics of the CMC mesoscopic structure;

[0024] Figure 4 is a predicted model of the thermal conductivity of the CMC mesoscopic structure;

[0025] Figure 5 is a normal distribution histogram of the equivalent thermal conductivity of CMC;

[0026] Figure 6 is a schematic diagram of the change in the anisotropic thermal conductivity of the CMC material turbine blade;

[0027] Figure 7 is a schematic diagram of the partition of the CMC material turbine blade;

[0028] Figure 8 is a contour map of the temperature field distribution of the CMC material turbine blade;

[0029] Figure 9 is a schematic diagram of the fluctuation range of the thermal conductivity of the CMC material;

[0030] Figure 10 is a normal distribution histogram of the highest temperature of the CMC material turbine blade. Detailed Embodiments

[0031] The present invention will be further described below in conjunction with embodiments.

[0032] Embodiment: The present invention takes the 2.5D woven structure ceramic matrix composite turbine blade as an example to elaborate the probabilistic thermal analysis method of the CMC material turbine blade based on the statistics of mesoscopic structure characteristics.

[0033] In this paper, for Figure 1The 2.5D woven structure CMC material sample shown is photographed and reconstructed for its internal mesostructure using XCT (X-ray Computed Tomography), and a three-dimensional model of the true characteristics of the mesostructure of the woven structure CMC material as shown in Figure 2 is obtained. Further, for the three-dimensional mesostructure model in Figure 2 , two-dimensional images of cross-sections in different directions and positions are intercepted, as shown in Figure 3 . Statistical analysis is performed on 1104 two-dimensional mesostructure images represented by Figure 3 to obtain the normal distribution characteristics and characterization functions of mesostructure geometric feature parameters such as weft yarn length L1, weft yarn width L2, warp yarn length I1, warp yarn width I2, warp yarn spacing Id, and weaving angle a1. Their means and standard deviations are shown in Table 1.

[0034] Table 1 Normal distribution means and standard deviations of mesostructure geometric feature parameters

[0035]

[0036] A parametric model of the mesoscopic woven structure of the 2.5D woven structure CMC material as shown in Figure 4 is established. The parametric geometric model parameters include weft yarn length L1, weft yarn width L2, warp yarn length I1, warp yarn width I2, warp yarn spacing Id, and weaving angle a1, and the fluctuations of the above parametric geometric parameters obey the probability distribution function obtained in the previous text. The following assumptions are made for the established parametric model of the mesoscopic woven structure: (1) The fiber bundle and the matrix are in full contact; (2) The central position of the fiber bundle does not change randomly, only the fiber geometric characteristics change randomly. The Monte-Carlo method is used, that is, samples are randomly drawn for the geometric characteristics to be studied, and the corresponding parametric models are generated; (3) There are no cracks and pores in the material, and the material as a whole is considered a continuous body.

[0037] For the thermal conductivity estimation model established, tetrahedral mesh is used for mesh division, and the mesh is locally encrypted at the junction of the fiber and the matrix. The number of meshes is 2317707, the maximum size of the mesh unit is 0.660mm, the minimum size is 0.048mm, and the mesh growth rate is 1.4. In the calculation, constant temperature boundary conditions are added to the upper and lower surfaces in the thickness direction of the model. The temperatures of the upper and lower surfaces are set to 283K and 273K respectively, and periodic boundary conditions are used on the surrounding walls. The CMC material used in this embodiment has an axial thermal conductivity of 8.63W / (m·K) and a radial thermal conductivity of 1.175W / (m·K) for the SiC fiber bundle, and a thermal conductivity of 4.25W / (m·K) for the matrix. A finite element simulation of the temperature field is carried out for the above model to obtain the heat flux density and temperature gradient distribution inside the model. According to the Fourier heat conduction equation, the equivalent thermal conductivity of the material can be calculated. Based on the Monte Carlo random finite element method, a specific thermal conductivity estimation model is randomly generated each time, and the above calculation process is repeated to obtain the normal distribution characteristics of the material equivalent thermal conductivity, such as Figure 5 As shown in , its mean is 2.9123W / (m·K) and its standard deviation is 0.0305W / (m·K). The Monte-Carlo method used in this paper for 2.5-dimensional CMC materials has the following specific steps: 1) First, the microstructure of the CMC sample is photographed, all slices are reconstructed in three dimensions, the probability distribution of the geometric features is extracted, and the distribution function is calculated; 2) A parameterized model is constructed based on the parameters with geometric feature fluctuations, and a random distribution function is introduced into the model to randomly generate sample values until the maximum sample value is reached; 3) Thermal boundary conditions are applied, and finite element thermal analysis of the model is performed based on Fourier's law; 4) A set of equivalent thermal conductivity coefficients in the thickness direction of the material are calculated, and the above process is repeated to obtain the probability distribution of the equivalent thermal conductivity of the material. Finally, the data is processed using probabilistic statistics.

[0038] On this basis, a 2.5D braided structure CMC material turbine blade equivalent model is established, such as Figure 6 As shown in , the anisotropic equivalent thermal conductivity is used to characterize the thermophysical properties of CMC materials, and the direction of the anisotropic thermal conductivity varies along the blade profile. Therefore, it is necessary to first obtain the contour fitting function of each region of the blade to provide a basis for calculating the spatial deflection angle of the local ETC main direction coordinate system of the blade relative to the blade temperature field calculation coordinate system. On this basis, the blade is divided into the leading edge, reinforcement rib and blade body for contour fitting and solve the spatial deflection angle, as shown in Figure 6. The calculation model of the CMC turbine blade is divided by tetrahedral grids, and the number of grids is 239240. The thermal boundary condition for the blade temperature field calculation adopts the third type of convective heat transfer boundary. At the same time, according to the heat transfer characteristics of different regions of the blade, the blade surface is divided into 6 regions, such as Figure 7 The specific heat exchange boundaries of each area are shown in Table 2.

[0039] Table 2 Heat transfer boundary conditions on the CMC blade surface

[0040]

[0041] The calculated cloud chart of the blade temperature field is as shown in Figure 8 the figure. The highest temperature appears in the central part of the blade leading edge. The temperature gradually decreases along the pressure surface and the suction surface. Under the condition of a typical constant thermal conductivity value, the highest and lowest temperatures on the blade surface are 2099.1 K and 1028.1 K respectively. With the random fluctuation of the thermal conductivity (the fluctuation range is 2.817 - 3.021 W / (m·K), as shown in Figure 9 the figure), the fluctuation range of the highest temperature on the blade surface is 2099.1 ± 3.3 K, and it follows a normal distribution, as shown in Figure 10 the figure.

[0042] The temperature field distribution information of the parametric basic model calculated by the above steps can be obtained by applying the third - type boundary condition. Using the Monte Carlo stochastic finite - element method, the probability distribution characteristics of the anisotropic thermal conductivity are introduced through multiple random samplings, and the finite - element calculation of the temperature field of the CMC material turbine blade is repeated multiple times, so as to obtain the probability distribution characteristics of the temperature field of the CMC blade, conduct statistical analysis on the fluctuation characteristics of the temperature field, and achieve the accurate prediction of the fluctuation of the highest temperature point and the potential high - temperature area of the blade.

[0043] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A probabilistic thermal analysis method for CMC material turbine blades based on the statistical characteristics of the mesoscopic structure, characterized in that, It includes the following steps: Step 1: Conduct mesoscopic structure tests on the woven structure CMC material samples using XCT to obtain mesoscopic structure images of the cross-sections of the material in different directions and positions; Step 2: For a certain number of mesoscopic structure images, statistically analyze the probability distribution characteristics of the geometric feature parameters such as the cross-section length and width of warp and weft yarns, warp spacing, and weaving angle inside the material, and characterize them using corresponding probability distribution functions; Step 3: Establish a parametric model of the mesoscopic woven structure of CMC material. The parametric geometric features include the cross-section length and width of warp and weft yarns, warp spacing, and weaving angle. Input the geometric feature parameters in Step 2 into the parametric model of the mesoscopic woven structure of CMC material, and calculate and obtain the probability distribution characteristics of the anisotropic thermal conductivity of the material based on the Monte Carlo stochastic finite element method; Step 4: For the CMC turbine blade, use the anisotropic equivalent thermal conductivity to characterize the thermal physical properties of the woven structure CMC material. The direction of the anisotropic thermal conductivity changes with the blade profile. Use the curvilinear coordinate system to realize the conversion of the principal coordinate system of the anisotropic thermal conductivity to the space coordinate system. Use tetrahedral meshes to generate the blade mesh in the calculation, and apply the third-kind convective heat transfer boundary conditions on the inner and outer wall surfaces of the blade respectively, and conduct the finite element calculation of the temperature field of the CMC blade; Step 5: Based on the Monte Carlo stochastic finite element method, sample from the probability distribution of the anisotropic thermal conductivity of the material obtained in Step 3, repeat the finite element calculation of the temperature field of the CMC blade in Step 4, and then obtain the probability distribution characteristics of the temperature field of the CMC blade, and conduct statistical analysis on key parameters such as the maximum temperature of the blade.

2. The probabilistic thermal analysis method for CMC material turbine blades based on the statistical analysis of mesoscopic structural characteristics according to claim 1, wherein: In Step 2, the probability distribution functions of the cross-section length and width of warp and weft yarns, warp spacing, and weaving angle are characterized using the normal distribution function.

3. The probabilistic thermal analysis method of CMC material turbine blade based on mesoscopic structure feature statistics according to claim 1, characterized in that: In Step 3, the process of calculating the probability distribution of the anisotropic thermal conductivity of the material based on the Monte Carlo finite element method is as follows: For the parametric model of the mesoscopic woven structure of CMC material generated by sampling the geometric feature parameters each time, use tetrahedral meshes to generate the calculation mesh, apply the constant temperature boundary on the upper and lower surfaces of the model, apply the periodic boundary conditions around, conduct the finite element simulation of the temperature field, obtain the temperature gradient and the mean value of the heat flux density of the model, and calculate the equivalent thermal conductivity of the material based on the Fourier heat conduction equation.

Images