CN115795968A - Probabilistic thermal analysis method for CMC material turbine blades based on statistics of mesostructure characteristics - Google Patents

Abstract

The invention discloses a CMC turbine blade probability thermal analysis method based on mesoscopic structure characteristic statistics, which is characterized in that for a woven structure CMC material, XCT is adopted to obtain mesoscopic structure characteristic images of different sections in the material, the probability distribution characteristics of mesoscopic geometric parameters such as the section size of a fiber bundle, the space of the fiber bundle, the weaving angle and the like are statistically analyzed, the probability distribution characteristic of anisotropic equivalent thermal conductivity is obtained based on a woven structure CMC material mesoscopic structure parameterized model, on the basis, the spatial distribution change and the probability distribution of the anisotropic thermal conductivity are introduced into the woven structure CMC turbine blade thermal analysis model, and the probability characteristic of a blade temperature field is statistically analyzed by adopting a Monte Carlo random finite element method. The method obtains the random characteristics of the internal geometric structure of the CMC material and the corresponding anisotropic thermophysical property probability distribution based on the actual microscopic structure image, and can more truly and effectively obtain the potential high-temperature region characteristics of the turbine blade of the CMC material with the braided structure.

Description

Probabilistic Thermal Analysis of CMC Material Turbine Blades Based on Mesostructure Characteristic Statistics method

technical field

The invention belongs to the technical field of engineering thermophysics, and in particular relates to a probabilistic thermal analysis method for a CMC material turbine blade based on statistics of mesostructure characteristics.

Background technique

Research on ceramic matrix composites (CMC) abroad was earlier. With the gradual improvement of material performance and the gradual maturity of preparation technology, countries such as Europe and the United States have carried out simulation assessment and even engineering application of CMC typical parts and simulated parts. For the application research on aeroengine turbine blades, corresponding engineering design methods have been established abroad. From the public information, the most representative one is the preparation and assessment of SiC _f /SiC turbine blade simulation parts carried out by NASA Glenn Research Center in the UEET program. The center not only proved the excellent performance of the three-dimensional five-directional braided SiC _f /SiC turbine guide vane in the high-temperature gas impingement environment, but also established a reliability prediction method for the blade under actual working conditions, and developed a For the corresponding software, NASA researchers fully considered the discreteness of mechanical and thermodynamic properties of materials, the uncertainty of internal and external pressure loads of blades, fluctuations of blade structural parameters, and material failure from the perspective of probability analysis in the above reliability calculation process. The impact of the discreteness of the critical load on the reliability of the blade, where the discrete data of the material performance parameters are derived from the physical property test results for the material. In addition, in the finite element modeling of the blade, the anisotropy of the physical properties of the CMC and the Phenomena such as the spatial distribution of the main direction of material properties caused by blade surface curvature have been carefully considered. Finally, it was found through calculation that the probability of not meeting the design requirements for the current blade design scheme is 1.6%. Facts have proved that the above research work has laid a solid foundation for the commercial application of SiC _f /SiC turbine blades.

Due to the late start of research on ceramic matrix composites in my country, the current research on CMC is still at the material level, and there are few studies on engineering-level application design methods of CMC turbine blades, and most of them only focus on some specific technical difficulties.

Based on the air-cooled turbine blade profile in the literature and the consideration method of material anisotropy in the paper, Sun Jie combined the stiffness performance prediction of the plain weave composite material with the thermal-solid coupling analysis of the turbine guide vane, and optimized the material and structure. Combined, starting from the two scales of material and structure, a structural and material integrated optimization design method for ceramic matrix braided composite turbine guide vanes is established. The above method takes the material stress and blade displacement limitation as the constraint conditions, and takes the minimum blade mass as the optimization goal, and obtains a good optimization effect. However, the discreteness of the physical parameters of the composite material is not considered in the calculation process of this method. The realization of engineering application also needs to be improved.

On the basis of the research on the calculation method of thermal conductivity of unidirectional composite materials, Xu Rui et al. took Mark II turbine blades as the object, adopted the self-programming finite element and Fluent simulation methods, and focused on the anisotropy of thermal conductivity and the random fluctuation of thermal conductivity. The blade temperature distribution, especially the influence of the leading and trailing edge high-temperature regions, obtains the sensitivity of the blade temperature field to the thermal conductivity in different main directions and the variation law of the blade high-temperature regions. The above research results provide a technical solution for considering the discreteness of material properties in the thermal analysis of CMC turbine blades, but the research object in this paper can be regarded as a Mark II turbine blade composed of unidirectional fibers, which is different from the international commercial The 3D braided CMC turbine blade structure has large differences.

Starting from two scales of material and structure, Sun et al. established a set of methods for material-structure integration optimization and reliability evaluation of 2.5DC _f /SiC guide vanes. The author first used the Monte Carlo method to study the randomness of mechanical properties of 2.5DC _f /SiC composites, and found that the macroscopic mechanical properties of 2.5DC _f /SiC composites are closely related to the randomness of material components and microstructures. Then, a 2.5DC _f /SiC guide vane structure optimization finite element model considering the discreteness of material properties was established, and the optimization calculation was carried out. Finally, the reliability of the optimization results was verified by integral analysis of the distribution model of the calculation results of the blade mechanical properties. sex. Generally speaking, the above methods have strong engineering practicability. Although the purpose is to optimize the blade structure and analyze the mechanical properties, it still has good reference significance for the establishment of the thermal analysis model of the CMC turbine blade.

However, for the randomness of geometric characteristics that inevitably exists in the weaving and compounding process of CMC materials, resulting in the overall anisotropy and heterogeneity of the material, there are few related thermal analysis studies. This is because compared with the thermal analysis of traditional metal turbine blades, the establishment of thermal analysis models of CMC material turbine blades needs to consider more influencing factors. The two most prominent problems are the impact of the probability distribution of mesoscopic structural geometric features on the anisotropic thermal conductivity. , and the effect of the probability distribution of anisotropic heat conduction on the macroscopic blade temperature field. Aiming at the above two problems, the key problem to be solved in this research is how to identify and post-process the geometric features of the mesostructure through the existing image recognition technology, and establish a database of the probability distribution of the geometric features; The probability distribution of anisotropic thermal conductivity is introduced into the macroscopic blade to obtain the temperature field.

Most of the above studies on the probability distribution characteristics of the anisotropic thermal conductivity of composite materials focus on the random changes in the position of the fiber bundles and the differences in volume fractions, and have not systematically explored the influence of the randomness of the geometric characteristic parameters of the mesostructure of woven CMC materials. Therefore the present invention is based on the Monte-Carlo simulation method, aiming at obtaining the equivalent thermal conductivity of the material, systematically calculates and analyzes the effect of the geometric characteristic parameters of the warp width, weft width, fiber bundle gap and braiding angle in the typical mesostructure of the material on the weaving Influence law of probability distribution characteristics of equivalent thermal conductivity of structural CMC materials.

Contents of the invention

The present invention obtains the probability distribution characteristics of the internal mesoscopic geometric parameters of the woven structure CMC material based on XCT, and obtains the probability distribution characteristics of the anisotropic equivalent thermal conductivity of the material in combination with the mesostructure parameterized model. Introduce the spatial distribution and probability distribution of anisotropic thermal conductivity into the thermal analysis model of structural CMC turbine blades, and use the Monte Carlo stochastic finite element method to statistically analyze the probabilistic characteristics of the blade temperature field to obtain the potential high temperature area characteristics of CMC material turbine blades .

To achieve the above object, the technical solution adopted in the present invention is:

A probabilistic thermal analysis method for turbine blades of CMC materials based on statistics of mesostructure features, including the following steps:

Step 1: Use XCT to carry out mesostructure test on the woven structure CMC material sample, and obtain the mesostructure images of the cross section of the material in different directions and positions;

Step 2: For a certain number of mesostructure images, statistically analyze the probability distribution characteristics of the geometric characteristic parameters such as the length and width of the warp and weft yarn sections inside the material, warp yarn spacing and weaving angle, and use the corresponding probability distribution function to characterize;

Step 3: Establish a parametric model of the mesoscopic weaving structure of the CMC material. The parameterized geometric features include the length and width of the warp and weft yarn sections, the distance between the warp yarns and the weaving angle. The geometric feature parameters in step 2 are input into the parameters of the mesoscopic weaving structure of the CMC material The model is based on the Monte Carlo stochastic finite element method to obtain the probability distribution characteristics of the anisotropic thermal conductivity of the material;

Step 4: For CMC turbine blades, the anisotropic equivalent thermal conductivity is used to characterize the thermophysical characteristics of the braided CMC material. The direction of the anisotropic thermal conductivity changes with the blade profile, and the curvilinear coordinate system is used to realize the anisotropic thermal conductivity. The conversion from the principal coordinate system to the space coordinate system, the tetrahedron grid is used to generate the blade grid in the calculation, the third type of convective heat transfer boundary condition is applied on the inner and outer walls of the blade, and the finite element calculation of the temperature field of the CMC blade is carried out;

Step 5: Based on the Monte Carlo stochastic finite element method, perform sampling in the probability distribution of material anisotropic thermal conductivity obtained in step 3, repeat the finite element calculation of the CMC blade temperature field in step 4, and then obtain the probability distribution of the temperature field of the CMC blade Features, statistical analysis of key parameters such as the maximum temperature of the blade.

Preferably: in the second step, the normal distribution function is used to characterize the probability distribution function of the section length and width of the warp and weft yarns, the distance between the warp yarns and the weaving angle.

Preferably: in said step 3, the process of obtaining the probability distribution of material anisotropic thermal conductivity based on Monte Carlo finite element method calculation is as follows: the CMC material mesoscopic weaving structure parameterized model generated for each geometric characteristic parameter sampling, using four-sided The calculation grid is generated by the volume grid, the constant temperature boundary is applied on the upper and lower surfaces of the model, and the periodic boundary conditions are applied around it, and the finite element simulation of the temperature field is carried out to obtain the temperature gradient and the average heat flux density of the model, which are calculated based on the Fourier heat conduction equation The equivalent thermal conductivity of the material.

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

The probabilistic thermal analysis method and process of the turbine blade of the woven structure CMC material established by the present invention can obtain the random characteristics of the internal geometric structure of the CMC material and the corresponding probability distribution of anisotropic thermal properties based on the actual mesoscopic structure image, which can be more realistic and effective. Obtain the potential high-temperature region characteristics of the woven structure CMC material turbine blade, improve the temperature field prediction accuracy of the CMC turbine blade, and provide thermal analysis method support for the engineering design application of the CMC blade.

Description of drawings

Figure 1 is a 2.5-dimensional braided structure CMC material sample;

Figure 2 is the XCT model of CMC mesostructure;

Figure 3 is a characteristic image of the cross-section of the CMC mesostructure;

Figure 4 is a prediction model for the thermal conductivity of the CMC mesostructure;

Fig. 5 is a histogram of the normal distribution of CMC equivalent thermal conductivity;

Fig. 6 is a schematic diagram of the variation of anisotropic thermal conductivity of a CMC material turbine blade;

Fig. 7 is a schematic diagram of CMC material turbine blade partition;

Figure 8 is a cloud map of the temperature field distribution of the CMC material turbine blade;

Fig. 9 is a schematic diagram of the fluctuation range of the thermal conductivity of the CMC material;

Figure 10 is a histogram of the normal distribution of the maximum temperature of the CMC material turbine blade.

Detailed ways

Below in conjunction with embodiment the present invention will be further described.

Embodiment: The present invention takes a 2.5-dimensional woven structure ceramic matrix composite material turbine blade as an example to illustrate a probabilistic thermal analysis method for a CMC material turbine blade based on statistics of mesostructure characteristics.

In this paper, for the 2.5-dimensional woven structure CMC material sample shown in Figure 1, XCT (X-ray Computed Tomography, X-ray CT) was used to photograph and reconstruct the internal mesoscopic structure, and the woven structure CMC as shown in Figure 2 was obtained. The 3D model of the real characteristics of the material mesostructure. Further, for the three-dimensional model of the mesostructure in Fig. 2, two-dimensional images of cross-sections in different directions and positions are intercepted, as shown in Fig. 3 . Statistical analysis was carried out on 1104 two-dimensional images of mesostructure represented by Fig. 3, and the geometric characteristics of mesostructure such as weft length L1, weft width L2, warp length I1, warp width I2, warp distance Id, and weaving angle a1 were obtained. The normal distribution characteristics and characterization functions of the parameters, and their mean and standard deviation are shown in Table 1.

Table 1 Normal distribution homogeneity and standard deviation of geometric characteristic parameters of mesostructure

Establish a 2.5-dimensional weaving structure CMC material mesoscopic weaving structure parametric model as shown in Figure 4. The parameterized geometric model parameters include weft length L1, weft width L2, warp length I1, warp width I2, warp spacing Id and weaving angle a1, and the fluctuation of the above parameterized geometric parameters obeys the probability distribution function obtained above. The established parametric model of the mesoscopic braided structure makes the following assumptions: (1) The fiber bundles are in complete contact with the matrix; (2) The central position of the fiber bundles does not change randomly, only the geometric characteristics of the fibers change randomly, using the Monte-Carlo method, that is, Samples are randomly selected for the geometric features to be studied, and corresponding parametric models are generated; (3) There are no cracks and pores in the material, and the material as a whole is considered to be a continuum.

For the thermal conductivity estimation model established, the tetrahedral mesh is used for mesh division, and the mesh is locally refined at the junction of the fiber and the matrix. The number of meshes is 2317707, and the maximum size of the mesh unit is 0.660 mm, and the minimum size is 0.048mm, 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 surface and the lower surface are set to 283K and 273K respectively, and the surrounding walls adopt periodic boundary conditions. For the CMC material used in this embodiment, the axial thermal conductivity of the SiC fiber bundle is 8.63W/(m K), the radial thermal conductivity is 1.175W/(m K), and the thermal conductivity of the matrix is 4.25W/ (m·K). Carry out temperature field finite element simulation for the above model, obtain the heat flux density and temperature gradient distribution inside the model, and calculate the equivalent thermal conductivity of the material according to the Fourier heat conduction equation. Based on the Monte Carlo stochastic 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 equivalent thermal conductivity of the material, as shown in Figure 5. The average value is 2.9123W/(m K), the standard deviation is 0.0305W/(m K), and the Monte-Carlo method used in this paper for 2.5-dimensional CMC materials, the specific steps are as follows: 1) Firstly, the mesostructure of the CMC sample Shooting, three-dimensional reconstruction of all slices, extracting the probability distribution of geometric features and calculating the distribution function; 2) Constructing a parametric model based on the parameters with geometric feature fluctuations, and introducing a random distribution function into the model to randomly generate sample values until reaching 3) apply thermal boundary conditions, and conduct finite element thermal analysis on the model based on Fourier's law; 4) calculate a set of equivalent thermal conductivity in the thickness direction of the material, repeat the above process, and obtain the equivalent thermal conductivity of the material Probability distribution, and finally use the method of probability and statistics to process the data.

On this basis, an equivalent model of a 2.5-dimensional woven structure CMC material turbine blade is established, as shown in Fig. Changes in blade profile. Therefore, it is first necessary to obtain the contour fitting function of each region of the blade, which provides 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 leading edge, rib and Contour fitting is performed on the blade body and the spatial deflection angle is solved, as shown in Figure 6. The calculation model of the CMC turbine blade is being divided by tetrahedron grids, and the number of grids is 239240. The thermal boundary condition of the blade temperature field calculation adopts the third type of convective heat transfer boundary, and at the same time, according to the heat transfer characteristics of different regions of the blade, the blade surface is divided into 6 regions, as shown in Figure 7, and the specific heat transfer boundaries of each region are shown in Table 2 shown.

Table 2 CMC blade surface heat transfer boundary conditions

The cloud diagram of the calculated blade temperature field is shown in Fig. 8. The highest temperature appears at the center of the leading edge of the blade, and the temperature gradually decreases along the pressure surface and suction surface. Under typical conditions of constant thermal conductivity, the maximum temperature and The lowest temperatures are 2099.1K and 1028.1K respectively. As the thermal conductivity fluctuates randomly (the fluctuation range is 2.817-3.021W/(m K), as shown in Figure 9), the fluctuation range of the maximum temperature on the blade surface is 2099.1±3.3K, and obeys the normal distribution, as shown in Figure 10 shown in .

The temperature field distribution information of the parametric basic model that can be calculated by applying the third type of boundary conditions in the above steps uses the Monte Carlo stochastic finite element method to introduce the probability distribution characteristics of anisotropic thermal conductivity through multiple random sampling. The finite element calculation of the temperature field of the turbine blade made of CMC material is repeated several times to obtain the probability distribution characteristics of the temperature field of the CMC blade, and the statistical analysis of the fluctuation characteristics of the temperature field is carried out to realize the accurate prediction of the fluctuation of the highest temperature point of the blade and the potential high temperature area.

The above is only a preferred embodiment 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, some improvements and modifications can also be made, and these improvements and modifications are also possible. It should be regarded as the protection scope of the present invention.

Claims (3)

1. The CMC material turbine blade probability thermal analysis method based on the mesoscopic structure feature statistics is characterized by comprising the following steps of:

the method comprises the following steps: carrying out mesoscopic structure test on a CMC material sample with a braided structure by adopting XCT (X-ray computer tomography), and obtaining mesoscopic structure images of sections of the material in different directions and positions;

step two: according to a certain number of microscopic structure images, the probability distribution characteristics of geometrical characteristic parameters such as the lengths and widths of the cross sections of the warps and the wefts in the material, the warp spacing and the weaving angle are statistically analyzed, and corresponding probability distribution functions are adopted for representing;

step three: establishing a CMC material mesoscopic weaving structure parameterized model, inputting the geometric characteristic parameters in the second step into the CMC material mesoscopic weaving structure parameterized model, and calculating and acquiring the probability distribution characteristics of the anisotropic heat conductivity coefficient of the material based on a Monte Carlo random finite element method, wherein the parameterized geometric characteristics comprise the cross-sectional lengths and widths of the warps and the wefts, the warp spacing and the weaving angle;

step four: aiming at the CMC turbine blade, the thermophysical property characteristic of a woven structure CMC material is represented by adopting an anisotropic equivalent thermal conductivity coefficient, the direction of the anisotropic thermal conductivity coefficient is changed along with the molded surface of the blade, a curve coordinate system is adopted to realize the conversion from a main coordinate system of the anisotropic thermal conductivity coefficient to a space coordinate system, tetrahedral grids are used for generating blade grids in the calculation, a third type of convection heat transfer boundary condition is respectively applied to the inner wall surface and the outer wall surface of the blade, and the finite element calculation of a CMC blade temperature field is carried out;

step five: based on the Monte Carlo random finite element method, sampling is carried out in the material anisotropic thermal conductivity coefficient probability distribution obtained in the third step, the finite element calculation of the CMC blade temperature field in the fourth step is repeated, the probability distribution characteristics of the CMC blade temperature field are further obtained, and statistical analysis is carried out on key parameters such as the highest temperature of the blade.

2. The CMC material turbine blade probabilistic thermal analysis method based on mesoscopic structural feature statistics as recited in claim 1, wherein: in the second step, a normal distribution function is adopted to represent the probability distribution functions of the section lengths and widths of the warp yarns and the weft yarns, the warp yarn spacing and the weaving angle.

3. The CMC material turbine blade probabilistic thermal analysis method based on mesoscopic structural feature statistics as recited in claim 1, wherein: in the third step, the probability distribution process of the anisotropic thermal conductivity coefficient of the material calculated and obtained based on the Monte Carlo finite element method is as follows: aiming at a CMC material mesoscopic woven structure parameterized model generated by sampling geometric characteristic parameters every time, tetrahedral meshes are adopted to generate calculation meshes, constant temperature boundaries are applied to the upper surface and the lower surface of the model, periodic boundary conditions are applied to the periphery, temperature field finite element simulation is carried out, the temperature gradient and the heat flow density mean value of the model are obtained, and the equivalent thermal conductivity coefficient of the material is calculated based on a Fourier thermal conductivity equation.

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