CN112149235B - Micro-scale temperature field information correction-based thermal analysis method for woven structure ceramic matrix composite material - Google Patents
Micro-scale temperature field information correction-based thermal analysis method for woven structure ceramic matrix composite material Download PDFInfo
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Abstract
The invention discloses a thermal analysis method of a ceramic matrix composite material with a braided structure based on microscopic temperature field information correction, which comprises the following steps: obtaining geometrical characteristics of the ceramic matrix composite with the woven structure; establishing a microscopic unit cell model and a homogenization calculation model of the ceramic matrix composite material with the braided structure; performing finite element calculation of a temperature field; obtaining the equivalent heat conductivity coefficient of the braided structure ceramic matrix composite material in the thickness direction of the thin-wall member and the equivalent heat conductivity coefficients of the two directions; performing finite element calculation to obtain a microcosmic temperature field; fitting the temperature fluctuation information through a two-dimensional Fourier series of a finite term to obtain a fitting expression; and D, obtaining temperature fluctuation information corresponding to the homogenization calculation model, and superposing the temperature fluctuation information to the macroscopic equivalent temperature field obtained in the step five to carry out local correction so as to reconstruct the temperature field. The method can obtain the surface temperature value of the knitted CMC material part with higher precision.
Description
Technical Field
The invention belongs to the technical field of engineering thermophysics, and particularly relates to a thermal analysis method for a CMC (CMC) material of a braided structure based on microscopic-scale temperature field information correction.
Background
With the increase of the thrust-weight ratio of the aeroengine, the inlet temperature of the turbine is continuously increased, the heat resistance limit of the existing high-temperature alloy is far exceeded, and the novel high-temperature resistant material represented by the fiber-toughened ceramic matrix composite (Ceramic Matrix Composite, CMC) is increasingly focused and applied. CMC materials are composite materials which adopt fibers such as C or SiC to toughen ceramic matrixes, and have the advantages of high strength, high temperature resistance, good toughness and the like.
Over the years, integrally formed ceramic matrix composites have gained the favor of more and more aircraft engine manufacturers, and CMC hot end components have gradually gained engineering application on rotor/stator components of aircraft gas turbine engines. Core hot end components such as the high pressure turbine primary outer ring, low pressure turbine guide vanes, and tail cone of LEAP-X engines all employ CMC materials (Li Jie. Application and development of composite materials in new generation commercial engines. Aviation science and technology 2012 (1): 22-26.). In 2015, the GE company website revealed that GE company developed the world's first CMC low pressure turbine rotor blade and successfully passed 500 severe cycle tests on the validator of the F414 engine.
When the CMC material with the woven structure is applied to a hot end component of an aeroengine, thermal analysis and design are required to be carried out on the CMC material. The woven CMC material has larger difference with the traditional homogeneous metal material, is formed by compounding a matrix and reinforcing fibers, and is arranged in a staggered way. Because of the thermal physical property difference between the matrix and the fiber and the thermal physical property difference between the fiber in the axial direction, the heat conductivity coefficient of the woven CMC material presents anisotropy, the heat transmission mode in the material is very complex, and the thermal physical fields such as a temperature field, a heat flux density field and the like have larger dispersibility and fluctuation, so that a thermal analysis method suitable for the hot end part of the CMC material with the woven structure needs to be established.
At present, when thermal analysis is performed on a CMC material hot end component, researchers often adopt a calculation method based on homogenization, namely, based on the trend of fibers (woven yarns), macroscopic equivalent heat conductivity coefficients of the material in three directions are obtained according to test or numerical calculation results, and then the macroscopic equivalent heat conductivity coefficients are assigned to the macroscopic component so as to finish calculation of a temperature field. For example, zhao Hongli et al simulate the temperature field of a rocket engine jet nozzle for C/C braided composite materials by setting equivalent thermal conductivity coefficients in three directions (Zhao Hongli. Finite element analysis of carbon/carbon braided composite temperature field, jinan: qilu university of industries, 2012). Zhang et al conducted thermal response studies on unidirectional fibers and woven fiber toughened CMC material plates, in which fiber toughened materials were homogenized, and the overall anisotropic thermal conductivity of the materials was characterized by thermal conductivity in three directions, and the temperature field distribution and internal heat transfer characteristics of the materials were calculated and analyzed (Zhang D X, hayhurst D.Informance of applied in-plane strain on transverse thermal conductivity of/90 DEG and plain weave ceramic matrix composites, international Journal of Solids and Structures,2011, 48:828-842). In the research of L.M.Chen et al, the equivalent heat conductivity coefficients of three directions are also given, and the temperature field of a certain medium caliber artillery composite material gun barrel is calculated by using a finite difference method. The research result shows that the heat conductivity coefficient perpendicular to the length direction of the tube is increased, the heat dissipation capacity of the tube can be obviously enhanced, and the temperature field distribution uniformity of the composite material tube can be improved (Chen L M, qian L F, hu H S. numerical heat transfer analysis and experiment of composite material barrel,6th International Symposium on Test and Measurement,2005:4526-4529). Xu Rui for MarkII turbine blade, the influence of anisotropy and dispersibility of the heat conductivity coefficient on the temperature field distribution of the turbine blade is studied, the macroscopic equivalent heat conductivity coefficients of the turbine blade in three directions are given in the study, and the law of the change of the high temperature region of the blade along with the heat conductivity coefficient is obtained (Xu Rui. The calculation method of the heat conductivity coefficient of the unidirectional fiber reinforced ceramic matrix composite material, nanjing: nanjing aviation aerospace university, 2013).
Based on the research, tu, mao and the like are used for CMC material turbine blades, the influence of the complex type of the parts on the spatial distribution of the anisotropic heat conductivity coefficient of the materials is further considered, a function of the anisotropic heat conductivity coefficient of the materials along with the change of the profile of the turbine blades is initially established, CMC turbine blade temperature field estimation is carried out, the research shows that the change of the anisotropic heat conductivity coefficient of the blade materials has obvious influence on the estimation of the blade temperature field, especially in the area with larger curvature change such as the front edge of the blade, the calculated value of the comprehensive cold effect of the blade with the spatial change of the anisotropic heat conductivity coefficient is not considered to be close to 108% compared with the experimental value, the calculated value with the spatial change of the anisotropic heat conductivity coefficient of the materials is considered to be not more than 9% compared with the experimental value, the precision is greatly improved, but microstructure temperature field fluctuation information (TuZ C, mao J K, han X S, et al. Numerical method for the thermal analysis of a CMC turbine vane considering the spatial variation of the ATC, applied Thermal Engineering,2017, 127:436-452) which is not considered in the research.
However, the macroscopic homogenization thermal analysis method based on the anisotropic equivalent heat conductivity coefficient is difficult to obtain temperature field fluctuation information of the micro-woven structure of the CMC material, cannot reflect the influence caused by the inner woven structure of the hot end part, and has a large defect. However, for the hot end component with large geometric dimension and complex geometric feature of the turbine blade, if microstructure modeling is completely adopted, the calculated amount is too large to be well applied to engineering calculation. Therefore, a mapping method of information between a microscopic temperature field and a macroscopic temperature field needs to be explored, and a high-precision thermal analysis method of the CMC material of the braided structure based on the information correction of the microscopic temperature field is established.
Disclosure of Invention
The invention aims to provide a thermal analysis method for a ceramic matrix composite material with a braided structure based on microscopic temperature field information correction, which aims to solve the problems that in the prior art, fluctuation information of a microscopic temperature field of a braided CMC material is difficult to obtain by adopting a homogenizing thermal analysis method based on anisotropic equivalent heat conductivity coefficient, larger defects exist, a model of a real microscopic structure of a hot end part with larger geometric dimension is established, the calculated amount is increased rapidly, and the requirement of thermal analysis engineering calculation of the CMC hot end part with the braided structure is not met.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a thermal analysis method of a ceramic matrix composite of a braided structure based on microscopic-scale temperature field information correction comprises the following steps:
step one, performing microstructure test on a ceramic matrix composite material with a woven structure to obtain geometric characteristics of the ceramic matrix composite material;
step two, establishing a microstructure unit cell model and a homogenization calculation model of the ceramic matrix composite material of the braided structure according to the geometric characteristics obtained in the step one and by combining the actual thickness of the ceramic matrix composite material of the braided structure and the periodic distribution characteristics of the internal fiber bundles;
thirdly, carrying out finite element calculation of a temperature field on the microscopic unit cell model established in the second step;
obtaining average heat flux density in the thickness direction according to a finite element calculation result of a temperature field of the micro unit cell model, calculating to obtain equivalent heat conductivity coefficients in the thickness direction of the thin-wall component of the ceramic matrix composite material of the woven structure according to a Fourier formula by combining the thickness and boundary temperature difference value of the homogenization calculation model established in the second step, and obtaining the equivalent heat conductivity coefficients in the remaining two directions of the ceramic matrix composite material of the woven structure by the same method;
step five, carrying out flow thermosetting coupling calculation on the homogenization calculation model to obtain a macroscopic equivalent temperature field;
step six, extracting the temperature and the convective heat transfer coefficient of the surface of the homogenizing calculation model according to the calculation result of the step five, and applying the extracted temperature and heat transfer coefficient distribution to the surface of the microscopic unit cell model for finite element calculation to obtain a microscopic temperature field;
step seven, obtaining microscopic temperature fluctuation information based on the macroscopic equivalent temperature field and the microscopic temperature field obtained by calculation in the step five and the step six;
step eight, introducing the geometric characteristics of the ceramic matrix composite with the braided structure into the temperature fluctuation information obtained in the step seven, defining the geometric characteristics as fluctuation information containing position information, and fitting the temperature fluctuation information according to the periodic characteristics of the ceramic matrix composite with the braided structure through a two-dimensional Fourier series of finite terms to obtain a fitting expression;
step nine, a full-size knitting structure model with the same size as the homogenization calculation model in the step two is established, the position information of the full-size knitting structure model is brought into the fitting expression obtained in the step eight, the temperature fluctuation information corresponding to the homogenization calculation model is obtained, the temperature fluctuation information is overlapped into the macroscopic equivalent temperature field obtained in the step five for local correction, and the reconstruction of the temperature field is realized.
In the first step, the geometric features include the cross-sectional size, spacing and material braiding angle of the fiber bundles.
In the third step, the microscopic unit cell model is led into Comsol Multiphysics software, the matrix, the axial fiber bundles and the woven fiber bundles of the microscopic unit cell model are subjected to thermophysical parameter assignment and grid division, the upper surface and the lower surface of the microscopic unit cell model are subjected to temperature boundary conditions, the periphery of the microscopic unit cell model is subjected to period boundary conditions, and then finite element calculation of a temperature field is performed.
In the fifth step, the homogenization calculation model established in the second step is imported into Comsol Multiphysics software, thermophysical parameter setting is performed according to the equivalent heat conductivity coefficients in different directions obtained in the fourth step, grid division is performed, the boundary conditions of the primary flow inlet and the secondary flow outlet of the homogenization calculation model are given, and flow thermosetting coupling calculation is performed.
In the seventh step, parameterizing the macroscopic equivalent temperature field and the microscopic temperature field obtained by calculation in the fifth step and the sixth step, importing MATLAB software, and obtaining microscopic temperature fluctuation information by differentiating the corresponding areas of the macroscopic equivalent temperature field and the microscopic temperature field.
In the eighth step, the temperature fluctuation information is fitted through a two-dimensional fourier series of a finite term, and the following formula is adopted:
in the above, K x ，K y Representing the number of finite terms along the x, y direction; a, a 00 ，a 0k (k＝1,…,K x )，b ok (k＝1,…,K y )，A kj ，B kj ，C kj ，D kj (k＝1,…,K x ，j＝1,…,K y ) Is an expression coefficient; omega 1 ，ω 2 Represents angular frequency, ω, along the x-direction and y-direction 1 ＝2π/T 1 ，ω 2 ＝2π/T 2 ，T 1 ，T 2 A single period length along the x and y directions for the composite internal braid structure.
Compared with the prior art, the invention has the following beneficial effects:
according to the geometric characteristics of the woven CMC material, the microscopic unit cell model and the homogenization calculation model of the component, the mapping between the microscopic temperature field and the macroscopic temperature field is established based on the two models, the macroscopic equivalent temperature field is locally corrected through microscopic temperature fluctuation information, the reconstruction of the temperature field is realized, and the temperature distribution of the surface of the woven CMC material which is closer to an actual measurement value is obtained.
Drawings
FIG. 1 is a 2.5D woven structure composite material;
FIG. 2 is a schematic diagram of a single cell model. Wherein: (a) is a yarn section schematic, (b) is a woven structure schematic, (c) is a matrix schematic, and (d) is a calculation model schematic;
FIG. 3 is a schematic diagram of a homogenization calculation model;
FIG. 4 is a principal direction coordinate system of heat conduction;
FIG. 5 is a boundary condition and grid division;
FIG. 6 is a macroscopic equivalent temperature field calculation model;
FIG. 7 is a macroscopic equivalent temperature field;
FIG. 8 is a feature region division;
FIG. 9 is a microscopic single cell model boundary condition;
FIG. 10 is a flow chart of temperature fluctuation information calculation;
FIG. 11 is a schematic diagram of zone 1 temperature fluctuation information;
FIG. 12 is a full-size woven structural model;
FIG. 13 is a reconstructed temperature field of the present invention;
fig. 14 is a graph of calculated temperature fields for a full-size woven structure model.
Detailed Description
The invention discloses a thermal analysis method of a ceramic matrix composite of a braided structure based on microscopic-scale temperature field information correction, which comprises the following steps:
step one, performing microstructure test on a ceramic matrix composite material with a braided structure to obtain geometric characteristics of the ceramic matrix composite material, wherein the geometric characteristics comprise the cross-sectional dimension of fiber bundles, the spacing and the braiding angle of the material;
step two, establishing a microstructure unit cell model and a homogenization calculation model of the ceramic matrix composite material of the braided structure according to the geometric characteristics obtained in the step one and by combining the actual thickness of the ceramic matrix composite material of the braided structure and the periodic distribution characteristics of the internal fiber bundles;
step three, introducing Comsol Multiphysics software into the micro unit cell model, carrying out thermophysical parameter assignment and grid division on a matrix, an axial fiber bundle and a woven fiber bundle of the micro unit cell model, setting temperature boundary conditions on the upper surface and the lower surface of the micro unit cell model, setting period boundary conditions on the periphery of the micro unit cell model, and further carrying out finite element calculation of a temperature field;
obtaining average heat flux density in the thickness direction according to a finite element calculation result of a temperature field of the micro unit cell model, calculating to obtain equivalent heat conductivity coefficients in the thickness direction of the thin-wall component of the ceramic matrix composite material of the woven structure according to a Fourier formula by combining the thickness and boundary temperature difference value of the homogenization calculation model established in the second step, and obtaining the equivalent heat conductivity coefficients in the remaining two directions of the ceramic matrix composite material of the woven structure by the same method;
step five, importing the homogenization calculation model established in the step two into Comsol Multiphysics software, carrying out thermophysical parameter setting and grid division according to the equivalent heat conductivity coefficients in different directions obtained in the step four, giving boundary conditions of a main flow inlet and a secondary flow outlet of the homogenization calculation model, and carrying out flow thermosetting coupling calculation to obtain a macroscopic equivalent temperature field;
step six, extracting the temperature and the convective heat transfer coefficient of the surface of the homogenizing calculation model according to the calculation result of the step five, and applying the extracted temperature and heat transfer coefficient distribution to the surface of the microscopic unit cell model for finite element calculation to obtain a microscopic temperature field;
step seven, parameterizing the macroscopic equivalent temperature field and the microscopic temperature field obtained by calculation in the step five and the step six, importing MATLAB software, and carrying out difference between the macroscopic equivalent temperature field and the corresponding area of the microscopic temperature field to obtain microscopic temperature fluctuation information;
step eight, introducing the geometric characteristics of the ceramic matrix composite with the braided structure into the temperature fluctuation information obtained in the step seven, defining the geometric characteristics as fluctuation information containing position information, and fitting the temperature fluctuation information according to the periodic characteristics of the ceramic matrix composite with the braided structure through a two-dimensional Fourier series of finite terms to obtain a fitting expression;
step nine, a full-size knitting structure model with the same size as the homogenization calculation model in the step two is established, the position information of the full-size knitting structure model is brought into the fitting expression obtained in the step eight, the temperature fluctuation information corresponding to the homogenization calculation model is obtained, the temperature fluctuation information is overlapped into the macroscopic equivalent temperature field obtained in the step five for local correction, and the reconstruction of the temperature field is realized.
The present invention will be further described with reference to examples and comparative examples.
Examples
In this embodiment, as shown in fig. 1, the fiber bundle material in the sample is SiC, the trade name is SLF-SiC-NF, the thermal conductivity of the SiC fiber bundle in the axial direction is 9.66W/(m·k), the radial thermal conductivity is 1.48W/(m·k), and the thermal conductivity of the material matrix is 0.2W/(m·k), for example, according to the basic data provided by the material supplier.
The material fiber bundles were obtained by microstructural SEM electron microscopy with a width of 1.6mm and a thickness of 0.2mm, the shape being as shown in fig. 2 (a). The distance between two adjacent X-direction wefts in the Z direction was 2mm, the distance between two adjacent Z-direction warps in the X direction was 0.6mm, the distance between two adjacent woven yarns in the Y direction was 0.1mm, the weaving angle was 34 °, and a microscopic unit cell model was established according to the geometric characteristics of the material, and a homogenization calculation model was as shown in fig. 2 and 3, wherein the specific dimensions of the unit cell model were length (Z) ×width (X) ×thickness (Y) =10×4.8×3.3 (mm), and the size of the homogenization calculation model was length (Z) ×width (X) ×thickness (Y) =70×4.8×3.3 (mm).
In the research, the anisotropy of the fiber bundle is characterized by adopting the heat conductivity coefficients in 3 directions, namely, the axial zeta (main direction of the heat conductivity coefficient) of the fiber bundle with larger heat conductivity coefficient and two directions v and eta perpendicular to the axial direction of the fiber bundle, and a main coordinate system (zeta, v and eta) of the heat conductivity coefficient is established, as shown in fig. 4, wherein: lambda (lambda) ζ ＝9.66W/(m·K)、λ ν ＝λ η =1.48W/(m·k). The anisotropic thermal conductivity of the woven yarns changes as the yarns spatially deflect.
In the calculation, the upper surface and the lower surface of the unit cell model are set as constant temperature boundaries, the upper surface is 273K, the lower surface is 373K, and the periphery is the periodic boundary condition to calculate the equivalent heat conductivity coefficient of the material in the Y direction, as shown in figure 5. In the Comsol, the unit cell model is subjected to grid division, the maximum unit of the grid is 0.8mm, the minimum unit of the grid is 0.1mm, the maximum growth rate is 1.45, the curvature factor is 0.5, and finally the grid division model shown in fig. 5 is constructed.
The calculation part is mainly completed by adopting a steady-state solid heat transfer module in Comsol Multiphysics software, a PARDISO solver is selected in the calculation, after the finite element calculation of a single cell model temperature field is completed, the average heat flow density of the whole material in the Y direction is obtained, and the equivalent heat conductivity coefficient of the material can be calculated according to a Fourier equation shown in a formula (1).
Wherein: lambda (lambda) effective For the equivalent coefficient of thermal conductivity,the average heat flux density, T is the temperature and x is the distance.
The equivalent heat conductivity coefficient of the material in the Y direction is lambda through calculation YY = 0.3539W/(m.K), the thermal conductivity coefficient lambda of the material in the other two directions is calculated by the same method XX ＝2.0177W/(m·K)，λ ZZ = 0.8342W/(m·k) and used in the calculation of the subsequent macroscopic equivalent temperature field.
Then, based on the obtained anisotropic equivalent thermal conductivity coefficient, a calculation model of thermal coupling of the flow is shown in fig. 6, wherein the calculation model comprises a main flow area, a solid area and a secondary flow area, and the sizes of the main flow area and the secondary flow area are as follows: length x width x height = 235 x 4.8 x 16mm, to ensure adequate fluid development, the leading edge of the solid domain is placed 200mm downstream of the inlet of the fluid domain, and the trailing edge of the solid domain is flush with the outlets of the primary and secondary fluid domains.
The upper and lower walls of the solid domain are respectively connected with the main flow area and the secondary flow area, the periphery of the solid domain is set as a periodic boundary condition, and in the main flow channel, the inlet speed U h Inlet temperature t=120 m/s h =1200k, turbulence intensity of 0.2%, outlet pressure P h-out =101325 Pa; in the secondary flow path, the inlet velocity U c Inlet temperature t=20m/s c =300K, turbulence intensity of 0.2%, outlet pressure P c-out =101325 Pa. In addition to the boundaries, the solid and fluid contact areas are calculated by coupling, two side walls are set as symmetrical boundaries, and the rest are set as heat insulation.
The meshing uses a Comsol-Multiphysics self-contained unstructured meshing tool. The method comprises the steps of carrying out fine division on the surface of a solid domain by adopting a free triangle mesh, carrying out free tetrahedral mesh division on the rest matrix of the solid domain, yarn fiber bundles and other parts, carrying out two-side sweeping on the mesh of the solid domain and the wall surface to obtain the mesh division of the fluid domain, wherein the contact part of the fluid domain, the solid domain and the wall surface needs a boundary layer mesh, and carrying out delta-shaped division on the upper wall surface of the solid domain according to a k-omega model ω + Is calculated to have a boundary layer first layer grid height of 2.8e-5m, dividing the boundary layer grids of the up-and-down river basin into 12 layers respectively, wherein the grid growth scale factor is 1.2, and the number of grids of the whole model is 737887.
Fig. 7 shows the calculation result of the macroscopic equivalent temperature field, and the temperature flow direction of the solid domain surface is uniform in the spanwise distribution (X direction) without great fluctuation. In order to facilitate extraction of the heat exchange boundary of the surface of the micro unit cell model, the solid domain of the homogenizing calculation model is divided into 7 local feature areas according to the size of the unit cell model, the feature areas are divided from the front edge of the solid domain of the equivalent model to the tail edge of the solid domain, and the size of each feature area is the same as that of the micro weave structural model shown in fig. 2, as shown in fig. 8.
Then, for 7 local areas, the heat exchange coefficients of the upper surface and the lower surface are respectively extracted to average and respectively recorded as H i And h i (i=1, 2,3,4,5,6, 7), and the temperatures Th and Tc of the inlet and outlet of the model are added to the upper and lower surfaces of the model of the micro-weave structure in combination with the homogenization calculation, as shown in fig. 9, the model is surrounded by a periodic boundary. The temperature field of the micro-weave structure model is calculated by adopting a heat transfer module in the Comsol-Multiphysics, and the grid division adopts the same division strategy as that in fig. 5.
After the temperature field of the micro-weave structure and the macroscopic equivalent temperature field of the homogenization model are obtained through calculation, the extraction and description of the temperature fluctuation information are carried out, and a detailed flow for solving the temperature field fluctuation information is given in fig. 10. In the Comsol-Multiphysics, a parameterized surface (parameter-surface) is built in an X-Z plane for each characteristic region and microstructure woven unit cell model in a homogenizing calculation model solid domain, wherein 20 data nodes are divided along the X-axis direction, 36 data nodes are divided along the Z-axis direction, a parameterized surface containing 720 data nodes is obtained, according to calculation results of different characteristic regions, temperature data of a solid domain of a corresponding region equivalent model and temperature data of a microstructure woven unit cell model high-temperature surface are derived and are imported into Matlab, temperature data of two models in the same region are subjected to difference at corresponding positions through Matlab, the numerical value delta T of temperature fluctuation information in the region is calculated, and the temperature fluctuation information delta T and position parameters X and Z of the corresponding surface are placed in the same matrix to be regarded as a temperature fluctuation sequence containing spatial position information and are used for subsequent calculation analysis.
Fig. 11 shows, as an example, a cloud of temperature fluctuation information distribution over area 1, for which the present invention proposes to describe temperature field fluctuation information by a two-dimensional fourier series of finite terms, expressed as follows:
wherein, the angular frequencies along the x-direction and the y-direction are respectively: omega 1 ＝2π/T 1 ，ω 2 ＝2π/T 2 . The different coefficients in formula (2) are as follows:
the temperature fluctuation information has a certain periodicity along the direction of the knitting structure of the material, so the invention analogizes the position information of the knitting structure along the periodic variation into time variation, regards the temperature fluctuation information as the periodic variation along with the periodic extension of the solid domain along the knitting structure, applies the expression of the limited two-dimensional Fourier series given by the formula (2), and expands the temperature fluctuation information in the area into the form of the two-dimensional Fourier series. Period T of microscopic unit cell model along warp direction wrap A period T along the weft direction of 0.01m weft 0.0048m, corresponding to a period of time series, i.e. T 1 ＝T wrap ，T2＝T weft Since the temperature fluctuation information is in the Z-X plane, the angular frequencies along the Z direction and the X direction are respectively: omega 1 ＝2π/T wrap ，ω 2 ＝2π/T weft . According to the definition of Fourier series, the expansion of series generally needs infinite multiple terms to completely approximate the original function, but in the practical application of engineering, the original function is generally approximated by adopting finite term series, so that the invention also selects finite term series (K x ＝K y =3, 4,5, 6). Based on the obtained temperature fluctuation information, the known angular frequencies omega in the Z direction and the X direction are obtained 1 And omega 2 And substituting the position information corresponding to the temperature fluctuation information into the expression, and obtaining the coefficients of the expression through the Matlab custom function and fitting and solving, so as to obtain the expressions of the temperature fluctuation information in different areas, namely, at a given angular frequency omega 1 And omega 2 In the case of (a), a set of upper and lower boundaries corresponds to the coefficients of a set of expressions.
By fitting the expressions of the temperature fluctuation information under different levels, the level is increased after the level reaches 4, the difference between the coefficients of the temperature fluctuation information expressions is not more than 1%, and when the level is overlarge, the temperature fluctuation information of the local area obtained by the expression calculation shows a certain fluctuation at the boundary, and in order to ensure the accuracy of the expression and simplify the calculation as much as possible, the level of the finite item is selected to be 4. The form of the temperature fluctuation information expression in the final local area is as follows:
the fitting result shows that the difference between the fitting data of the rest part except the front part and the rear part of the area 1 and the original temperature fluctuation information data is not more than 8.5% of the amplitude of the original temperature fluctuation information, the difference between the fitting data of nearly 90% and the original signal is not more than 5%, the average difference between the fitting data and the original data is only 0.1681K, and the overall fitting accuracy of the area 1 is higher. The accuracy of the fitting expression of each remaining area is gradually improved from the area 1, the difference between the fitting data and the original temperature fluctuation information is gradually reduced when the determining coefficient of the expression exceeds 0.95 (the accuracy is higher when the coefficient is closer to 1), and the average relative error of each area is not more than 4.93%, so that the finite-term two-dimensional Fourier series can be considered to effectively fit the periodic characteristic temperature fluctuation information of the woven structure with the material.
After the corresponding relation between the temperature fluctuation information and the knitting geometry is obtained, the macroscopic equivalent temperature field is locally corrected to realize the reconstruction of the temperature field. Firstly, a full-size knitting structure model shown in fig. 12 is established, the calculated temperature fluctuation information in each position area of the surface of the full-size knitting structure model is overlapped to a new temperature field obtained by reconstructing a uniform temperature field on the surface of an equivalent model according to a fitting expression, the calculation of the temperature fluctuation and the overlapping of the equivalent temperature field are carried out in Matlab, different expressions are adopted for calculation in different areas through judging the position information of the full-size knitting structure, the corresponding equivalent temperature field is derived according to the spatial position information of data points of the surface of the full-size knitting structure, the temperature fluctuation information corresponds to the equivalent temperature field, and the new temperature field is obtained by reconstruction, as shown in fig. 13.
Comparative example
To verify the reliability of the mapping method between microstructure temperature information and macroscopic equivalent model and the accuracy of the reconstructed temperature field, the temperature distribution of the surface of the full-size woven structure model (shown in fig. 12) under the same heat exchange boundary was calculated to compare with the reconstructed temperature field. And applying the actual heat exchange coefficients H (z) and H (z) of the equivalent model surface and the inlet temperatures Th and Tc of the upper and lower channels of the equivalent model fluid domain to the upper and lower surfaces of the model, wherein periodic boundary conditions are arranged around the model.
Fig. 14 shows a temperature field corresponding to a full-size knitting structure model, and comparing fig. 13 and 14, it can be found that the distribution rule of the reconstructed temperature field and the calculated temperature field is consistent, the temperature is continuously and alternately changed along the flow direction, the reconstructed temperature is higher than the calculated temperature at the front edge of the solid domain and the base region of the second half of the first period, the reconstructed temperature and the calculated temperature have certain deviation, at the position of z=0mm, the highest temperature difference of the two approaches 17K, but with the deep flow direction, the temperature difference of the two gradually decreases, after z=10mm, i.e. the second period of the knitting structure starts, the temperature difference between the reconstructed temperature field and the calculated temperature field is within 10K, and the temperature difference at the position exceeding 65% is smaller than 5K. The average temperature of the calculated temperature field is 1069.15K, the average temperature of the reconstructed temperature field is 1069.84K, the calculated temperature field and the reconstructed temperature field are almost identical, and the absolute value of the average deviation of the calculated temperature field and the reconstructed temperature field is only 0.7K. Therefore, the thermal analysis method for the CMC material of the braided structure based on the microscopic temperature field information correction, which is established by the invention, can accurately estimate the temperature distribution of the material, can rapidly estimate the structural complex and large-size components through the equivalent model and the microscopic braided structure, meets the requirements of practical application, and has good engineering value.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (5)
1. A thermal analysis method of a ceramic matrix composite with a braided structure based on microscopic temperature field information correction is characterized by comprising the following steps of: the method comprises the following steps:
step one, performing microstructure test on a ceramic matrix composite material with a woven structure to obtain geometric characteristics of the ceramic matrix composite material;
step two, establishing a microstructure unit cell model and a homogenization calculation model of the ceramic matrix composite material of the braided structure according to the geometric characteristics obtained in the step one and by combining the actual thickness of the ceramic matrix composite material of the braided structure and the periodic distribution characteristics of the internal fiber bundles;
thirdly, carrying out finite element calculation of a temperature field on the microscopic unit cell model established in the second step;
obtaining average heat flux density in the thickness direction according to a finite element calculation result of a temperature field of the micro unit cell model, calculating to obtain equivalent heat conductivity coefficients in the thickness direction of the thin-wall component of the ceramic matrix composite material of the woven structure according to a Fourier formula by combining the thickness and boundary temperature difference value of the homogenization calculation model established in the second step, and obtaining the equivalent heat conductivity coefficients in the remaining two directions of the ceramic matrix composite material of the woven structure by the same method;
step five, carrying out flow thermosetting coupling calculation on the homogenization calculation model to obtain a macroscopic equivalent temperature field;
step six, extracting the temperature and the convective heat transfer coefficient of the surface of the homogenizing calculation model according to the calculation result of the step five, and applying the extracted temperature and heat transfer coefficient distribution to the surface of the microscopic unit cell model for finite element calculation to obtain a microscopic temperature field;
step seven, obtaining microscopic temperature fluctuation information based on the macroscopic equivalent temperature field and the microscopic temperature field obtained by calculation in the step five and the step six;
step eight, introducing the geometric characteristics of the ceramic matrix composite with the braided structure into the temperature fluctuation information obtained in the step seven, defining the geometric characteristics as fluctuation information containing position information, and fitting the temperature fluctuation information according to the periodic characteristics of the ceramic matrix composite with the braided structure through a two-dimensional Fourier series of finite terms to obtain a fitting expression;
step nine, establishing a full-size knitting structure model with the same size as the homogenization calculation model in the step two, bringing the position information of the full-size knitting structure model into the fitting expression obtained in the step eight to obtain temperature fluctuation information corresponding to the homogenization calculation model, and superposing the temperature fluctuation information into the macroscopic equivalent temperature field obtained in the step five to carry out local correction so as to realize the reconstruction of the temperature field;
in the seventh step, parameterizing the macroscopic equivalent temperature field and the microscopic temperature field obtained by calculation in the fifth step and the sixth step, importing MATLAB software, and obtaining microscopic temperature fluctuation information by differentiating the corresponding areas of the macroscopic equivalent temperature field and the microscopic temperature field.
2. The micro-scale temperature field information correction-based woven structure ceramic matrix composite thermal analysis method according to claim 1, wherein the method comprises the following steps of: in the first step, the geometric features include the cross-sectional size, spacing and material braiding angle of the fiber bundles.
3. The micro-scale temperature field information correction-based woven structure ceramic matrix composite thermal analysis method according to claim 1, wherein the method comprises the following steps of: in the third step, the microscopic unit cell model is led into Comsol Multiphysics software, the matrix, the axial fiber bundles and the woven fiber bundles of the microscopic unit cell model are subjected to thermophysical parameter assignment and grid division, the upper surface and the lower surface of the microscopic unit cell model are subjected to temperature boundary conditions, the periphery of the microscopic unit cell model is subjected to period boundary conditions, and then finite element calculation of a temperature field is performed.
4. The micro-scale temperature field information correction-based woven structure ceramic matrix composite thermal analysis method according to claim 1, wherein the method comprises the following steps of: in the fifth step, the homogenization calculation model established in the second step is imported into Comsol Multiphysics software, thermophysical parameter setting is performed according to the equivalent heat conductivity coefficients in different directions obtained in the fourth step, grid division is performed, the boundary conditions of the primary flow inlet and the secondary flow outlet of the homogenization calculation model are given, and flow thermosetting coupling calculation is performed.
5. The micro-scale temperature field information correction-based woven structure ceramic matrix composite thermal analysis method according to claim 1, wherein the method comprises the following steps of: in the eighth step, the temperature fluctuation information is fitted through a two-dimensional fourier series of a finite term, and the following formula is adopted:
in the above, K x ，K y Representing the number of finite terms along the x, y direction; a, a 00 ，a 0k ，b 0k Where k=1, …, K y ，A kj ，B kj ，C kj ，D kj Where k=1, …, K x ，j＝1,…,K y Is an expression coefficient; omega 1 ，ω 2 Represents angular frequency, ω, along the x-direction and y-direction 1 ＝2π/T 1 ，ω 2 ＝2π/T 2 ，T 1 ，T 2 A single period length along the x and y directions for the composite internal braid structure.
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