Parameterized modeling-based equivalent thermal conductivity prediction method and system for CMC materials

Abstract

The application provides a CMC material equivalent thermal conductivity prediction method and system based on parameterized modeling, comprising: constructing a unidirectional fiber toughened CMC material single-layer RVE model; constructing a vertical cross arrangement unidirectional fiber toughened CMC material RVE model according to the single-layer RVE model, and performing parameterized definition to obtain a final model; and performing equivalent thermal conductivity prediction according to the final model. Through the creation of the vertical cross arrangement unidirectional fiber toughened CMC material RVE structure parameterized model and simulation calculation thereof conforming to the actual material processing needs of engineering, the application solves the problem of rapid prediction of the thermal conductivity of the CMC material, and the prediction accuracy reaches 3%.

Description

Technical Field

[0001] This invention relates to the field of engineering thermophysics, specifically to a method and system for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling. Background Technology

[0002] Ceramic matrix composites (CMCs) have become an important material for the research, development, processing, and application of high-pressure turbine blades for aero-engines due to their low density and high heat resistance. When studying the heat transfer properties of CMCs, the thermal conductivity in a specific direction is usually measured experimentally. However, the experimental process is lengthy, and the inability to quickly obtain the thermal conductivity in a particular direction can hinder the research progress of engineers and researchers.

[0003] Patent document CN110909495A discloses a method for predicting the equivalent thermal conductivity of thin-walled components made of braided CMC material based on a full-size microstructure model. The method involves obtaining the geometric characteristics of the braided CMC material and establishing a full-size microstructure model of the braided structure based on its actual thickness. This model is then imported into software, and thermal property parameters are assigned to the matrix and fiber bundles. The full-size microstructure model is meshed, with local mesh refinement applied within the fiber bundles and at the interface between the fiber bundles and the matrix. Temperature boundary conditions are applied to the upper and lower surfaces of the full-size microstructure model, while periodic boundary conditions are applied around the perimeter. Finite element analysis of the temperature field is then performed. Based on the finite element analysis results, the average heat flux density in the thickness direction is obtained. Combining the thickness of the calculated model with the boundary temperature difference, the equivalent thermal conductivity in the thickness direction of the thin-walled braided CMC material component is calculated using the Fourier formula.

[0004] However, the weaving structure considered in patent document CN110909495A is different. It is aimed at the full-size modeling of 2.5-dimensional fiber woven materials and does not consider the influence of porosity, etc. In contrast, this application is aimed at the full-size modeling of unidirectional fiber toughened multilayer arrangement processing method, and considers the influence of porosity on the solution of equivalent thermal conductivity through porosity parameter.

[0005] Patent document CN106093108A discloses a method for predicting the equivalent thermal conductivity of unidirectional fiber-reinforced composite materials based on gap defect identification. The method mainly includes the following steps: processing microscopic electron microscope images of the material using image recognition technology to identify the internal structural features and gap defects of the material; establishing a representative unit geometric topology model based on the fiber volume ratio stability criterion using geometric reconstruction technology, while simultaneously determining gap defects; introducing the influence of gap defects by adding contact thermal resistance at the interface inside the representative unit; and simulating the equivalent thermal conductivity using the finite element method.

[0006] However, patent document CN106093108A mainly studies the effect of gap on the equivalent thermal conductivity of unidirectional fiber-toughened CMC materials, without considering the expression of parameters such as fiber volume fraction and interface layer in the modeling, as well as the situation of multi-layer arrangement of unidirectional fiber-toughened materials in actual processing.

[0007] Patent document CN104111270A discloses a rapid thermal conductivity calculation method for a quasi-periodic distributed unidirectional fiber-reinforced composite material, belonging to the field of engineering thermophysics. The rapid thermal conductivity calculation method for this invention includes the following steps: proposing a new theoretical-empirical expression model for anisotropic thermal conductivity calculation, the LNN model, and providing a specific expression form; performing finite element simulation on representative microscopic elements, and obtaining the correction coefficient n in the LNN model through calculation data; transferring the obtained correction coefficient n to the correction term ψnew to determine the final theoretical-empirical expression for the unidirectional fiber anisotropic thermal conductivity calculation of the LNN correction model, and then calculating the rapid thermal conductivity of the unidirectional fiber-reinforced composite material.

[0008] However, patent document CN104111270A uses a modification of the LNN empirical formula to solve for the equivalent thermal conductivity, neglecting the interface phase and pores. This fails to account for the influence of microstructures such as interface phases and pores on the equivalent thermal conductivity at the macroscopic scale. In reality, microstructures such as pores and interface phases are also important components of CMC materials and affect the numerical value of the equivalent thermal conductivity. Furthermore, this patent document's modification of the empirical formula is based on a single-layer model, while actual material processing involves multi-layered structures. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling.

[0010] A method for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling, provided by the present invention, includes:

[0011] Step S1: Construct a single-layer RVE model of unidirectional fiber-toughened CMC material;

[0012] Step S2: Based on the single-layer RVE model, construct the RVE model of the vertically cross-arranged unidirectional fiber-toughened CMC material, and perform parameterization to obtain the final model;

[0013] Step S3: Predict the equivalent thermal conductivity based on the final model.

[0014] Preferably, the single-layer RVE model described in step S1 includes CMC material fibers, matrix, pores and interface phase, and is a three-dimensional model with corresponding thickness in the X direction during modeling;

[0015] The three-dimensional model has a cube shape, and the number of fibers in the model is arranged periodically and uniformly; the pores are through holes, and there is an interface phase of a specific thickness between the fibers and the matrix.

[0016] Preferably, step S2 includes:

[0017] Step S2.1: Arrange the single-layer RVE model constructed in step S1 in a vertically intersecting pattern to form a vertically intersecting unidirectional fiber-toughened CMC material RVE initialization model;

[0018] Step S2.2: Construct geometric associations and generate parameterized templates using parametric expressions, as shown in the following formula:

[0019]

[0020] Among them, D p R is the pore diameter. f R is the fiber radius, a is the side length of the RVE model, b is the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 is the distance between the fiber center in the boundary region and the model boundary, and R i Rt is the outer radius of the interfacial phase, P is the ratio of fiber radius to interfacial phase thickness, and V is the porosity. f n is the volume fraction of the fiber. p and n f These represent the number of pores and the number of fibers, respectively.

[0021] Step 2.3: Parametrically define the geometric parameters of the two-layer model, inputting parameters P and V. f and R t Perform final parameterization to generate the final model.

[0022] Preferably, step S3 includes:

[0023] Step S3.1: Perform unstructured mesh generation on the RVE model obtained in step S2;

[0024] Step S3.2: Obtain and define the thermal conductivity of each part of the microstructure, including the anisotropic thermal conductivity of the fiber, the thermal conductivity of the matrix, the thermal conductivity of the pores, and the thermal conductivity of the interfacial phase;

[0025] Step S3.3: Solve for the equivalent thermal conductivity values ​​in different directions through numerical simulation.

[0026] Preferably, step S3.3 includes:

[0027] The two outer wall surfaces perpendicular to the y-axis are set as high-temperature and low-temperature boundary conditions, respectively, and the other planes are set as adiabatic walls. The heat conduction equation is solved numerically, and the formula is as follows:

[0028]

[0029] In the formula, T is the temperature at the calculation point, and for the matrix κ... xx , κ yy and κ zz All are equal to the thermal conductivity of the matrix; for fibers κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the thermal conductivity in two secondary directions;

[0030] Then, the equivalent thermal conductivity in the y-direction is calculated based on the relationship between heat flow and temperature gradient in Fourier's law, as shown in the following formula:

[0031]

[0032] In the formula, q i and T i Let i be the total heat flux density in the i-direction and the temperature difference between the high and low temperature wall boundary conditions, respectively, where i = x, y, z;

[0033] After solving for the y-direction, the equivalent thermal conductivity in the x and z directions is solved in the same way, and finally the equivalent thermal conductivity values ​​in three different directions are obtained.

[0034] The present invention provides a CMC material equivalent thermal conductivity prediction system based on parametric modeling, comprising:

[0035] Module M1: Construct a single-layer RVE model for unidirectional fiber-toughened CMC materials;

[0036] Module M2: Based on the single-layer RVE model, construct the RVE model of the vertically cross-arranged unidirectional fiber-toughened CMC material, and define the parameters to obtain the final model;

[0037] Module M3: Predicts the equivalent thermal conductivity based on the final model.

[0038] Preferably, the single-layer RVE model described in module M1 includes CMC material fibers, matrix, pores and interface phases, and is a three-dimensional model with corresponding thickness in the X direction during modeling;

[0039] The three-dimensional model has a cube shape, and the number of fibers in the model is arranged periodically and uniformly; the pores are through holes, and there is an interface phase of a specific thickness between the fibers and the matrix.

[0040] Preferably, the module M2 includes:

[0041] Module M2.1: Arrange the single-layer RVE model constructed in Module M1 in a vertically intersecting pattern to form a vertically intersecting unidirectional fiber-toughened CMC material RVE initialization model;

[0042] Module M2.2: Constructs geometric associations and generates parametric templates through parametric expressions, as shown in the following formula:

[0043]

[0044] Among them, D p R is the pore diameter. f R is the fiber radius, a is the side length of the RVE model, b is the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 is the distance between the fiber center in the boundary region and the model boundary, and R i Rt is the outer radius of the interfacial phase, P is the ratio of fiber radius to interfacial phase thickness, and V is the porosity. f n is the volume fraction of the fiber. p and n f These represent the number of pores and the number of fibers, respectively.

[0045] Step 2.3: Parametrically define the geometric parameters of the two-layer model, inputting parameters P and V. f and R t Perform final parameterization to generate the final model.

[0046] Preferably, the module M3 includes:

[0047] Module M3.1: Performs unstructured mesh generation on the RVE model obtained from Module M2;

[0048] Module M3.2: Obtain and define the thermal conductivity of each part of the microstructure, including the anisotropic thermal conductivity of the fiber, the thermal conductivity of the matrix, the thermal conductivity of the pores, and the thermal conductivity of the interfacial phase;

[0049] Module M3.3: Solve for the equivalent thermal conductivity in different directions through numerical simulation.

[0050] Preferably, the module M3.3 includes:

[0051] The two outer wall surfaces perpendicular to the y-axis are set as high-temperature and low-temperature boundary conditions, respectively, and the other planes are set as adiabatic walls. The heat conduction equation is solved numerically, and the formula is as follows:

[0052]

[0053] In the formula, T is the temperature at the calculation point, and for the matrix κ... xx , κ yy and κ zzAll are equal to the thermal conductivity of the matrix; for fibers κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the thermal conductivity in two secondary directions;

[0054] Then, the equivalent thermal conductivity in the y-direction is calculated based on the relationship between heat flow and temperature gradient in Fourier's law, as shown in the following formula:

[0055]

[0056] In the formula, q i and T i Let i be the total heat flux density in the i-direction and the temperature difference between the high and low temperature wall boundary conditions, respectively, where i = x, y, z;

[0057] After solving for the y-direction, the equivalent thermal conductivity in the x and z directions is solved in the same way, and finally the equivalent thermal conductivity values ​​in three different directions are obtained.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] This invention solves the problem of rapid prediction of the thermal conductivity of CMC materials by creating a parametric model of the RVE structure of vertically cross-arranged unidirectional fiber-toughened CMC materials that meets the actual material processing needs in engineering, and through its simulation calculations, thereby improving the prediction accuracy. It obtains equivalent thermal conductivity values ​​that are closer to those of actually processed unidirectional fiber-toughened CMC materials, improving the efficiency and accuracy of scientific research and engineering applications. Furthermore, the parametric modeling process lays an important foundation for further digital and intelligent research and engineering applications of CMC materials. Attached Figure Description

[0060] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0061] Figure 1 A schematic diagram of a two-dimensional cross-section of a single-layer RVE model of unidirectional fiber-toughened CMC material;

[0062] Figure 2 A schematic diagram of a structural model of a vertically cross-arranged unidirectional fiber-toughened CMC material.

[0063] Figure 3 This is a schematic diagram of the parametric modeling process;

[0064] Figure 4 A diagram illustrating the method for defining parameterized variables for a model;

[0065] Figure 5 This is a schematic diagram of the working method of the present invention. Detailed Implementation

[0066] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0067] This invention proposes a parametric modeling-based method for predicting the equivalent thermal conductivity of vertically cross-arranged unidirectional fiber-toughened CMC materials, meeting practical engineering needs. By creating a representative volume element (RVE) model of the microstructure of a double-layer vertically cross-arranged unidirectional fiber-toughened CMC material and performing numerical simulations, the method predicts the equivalent thermal conductivity in three different directions, which closely matches experimental results. This invention provides equivalent thermal conductivity values ​​that more closely approximate those of actually processed unidirectional fiber-toughened CMC materials, improving the efficiency and accuracy of research and engineering applications. Furthermore, the parametric modeling process lays an important foundation for further digital and intelligent research and engineering applications of CMC materials.

[0068] According to the present invention, a method for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling is provided, such as... Figure 5 As shown, it includes:

[0069] Step S1: Construct a monolayer RVE model for unidirectional fiber-toughened CMC material. For example... Figure 1 As shown, the model includes CMC material fibers, matrix, pores, and interface phases. Initial modeling was performed using CAD modeling software such as UG. Figure 1 The diagram presents a two-dimensional cross-sectional view of a single-layer RVE model of a unidirectional fiber-reinforced CMC material, with a magnified view shown on the right. The fibers and pores are assumed to be circles with a certain radius, and the interface phase is assumed to be an annulus with a certain thickness. In actual modeling, this step involves a three-dimensional model with a certain thickness in the X-direction. Figure 1 The corresponding 3D model is a cube with side length 'a'; the model contains n fibers. f =50, verified to be periodically uniformly arranged; pores are assumed to be through holes, number n p =8, there is an interface phase of a certain thickness t between the fiber and the matrix. Figure 1 The dimensions of the specific structure during initial modeling will be constrained after step S2 is completed; therefore, there are no strict dimensional constraints during modeling in step S1.

[0070] Step S2: Based on the single-layer RVE model, construct and parameterize the RVE model of the vertically cross-arranged unidirectional fiber-toughened CMC material. For example... Figure 2 and Figure 3As shown, step S2 includes:

[0071] Step S2.1: Arrange the single-layer RVE model constructed in step S1 in a vertically intersecting pattern to form... Figure 2 The RVE initialization model of the vertically intersecting unidirectional fiber-toughened CMC material is shown.

[0072] Step S2.2: Construct geometric associations and generate parameterized templates using parameterized expressions. For example... Figure 4 The parameterized variables are defined as shown, and the formulas (1) to (4) are entered into the CAE software for parameterized editing. For example, in UG, select "Tools" in the software interface, and then select "Expression" for editing.

[0073]

[0074] Among them, D p R is the pore diameter. f denoted as fiber radius, a as the side length of the RVE model, b as the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 as the distance between the fiber center in the boundary region and the model boundary, Ri as the outer radius of the interface phase, Rt as the ratio of fiber radius to interface phase thickness, P as porosity, and Vf as the volume fraction of the fiber. p and n f These represent the number of pores and the number of fibers, respectively, with an initial definition of a = 1 mm, b = 0.1 mm, and b1 = 0.02 mm.

[0075] Step 2.3: Parametrically define the geometric parameters of the two-layer model, inputting parameters P and V. f and R t The final parameterization is then performed to generate the final model. The porosity P and fiber volume fraction V of the CMC material are obtained through scanning electron microscopy image recognition or material processing parameters. f The ratio R of fiber radius R to interfacial phase thickness t t Alternatively, the material parameters can be obtained from publicly available literature. Using these three input parameters, rapid parametric structural modeling is performed according to step S2.2. The model automatically adjusts the corresponding geometry based on the parameter values ​​of P, Vf, and Rt to generate the final RVE model. For example, currently... Figure 2The model has a porosity of 3% and a single-layer pore size of 8, ensuring uniform pore distribution. The model side length is 1×1×1 mm. The fiber volume fraction is 30%. Rt is 6. (Islam M DR, Pramila A. Thermal conductivity of fiber reinforced composites by the FEM[J].Journal of Composite Materials,1999,33(18):1699-1715.)(Zou M,Yu B,Zhang D.An analytical solution for transverse thermal conductivities of unidirectional fiber composites with thermal barrier[J].Journal of Physics D:Applied Physics,2002,35(15):1867-1874.). In practical use, the specific dimensions of the model can be adjusted according to specific needs and actual process requirements, while meeting parameters such as porosity, fiber volume fraction, and interface layer thickness.

[0076] Step S3: Prediction of equivalent thermal conductivity. Based on... Figure 2 The diagram shows a schematic of the RVE model for a vertically cross-arranged unidirectional fiber-toughened CMC material. The equivalent thermal conductivity in the y-direction is defined as the equivalent thermal conductivity in the thickness direction of the actual engine blade. Figure 2 The model shown is subjected to numerical simulation to solve the heat conduction equation. Step S3 includes:

[0077] Step S3.1: Perform unstructured mesh generation on the RVE model obtained in step S2.

[0078] Step S3.2: Based on existing materials, determine and define the thermal conductivity of each part of the microstructure through experimental means or through publicly available literature, including the anisotropic thermal conductivity of the fiber, the thermal conductivity of the matrix, the thermal conductivity of the pores, and the thermal conductivity of the interfacial phase. For example, in this embodiment, according to literature, the thermal conductivity of the SiC fiber in the primary direction is defined as 9.66 W / (m·K), the thermal conductivity in the secondary direction is defined as 1.48 W / (m·K) (Tu Z, Zhao C, Mao J, et al. Influence of the braided structure on the film cooling performance over the ceramic matrix composite plate[J]. International Journal of Thermal Sciences, 2021, 170: 107112.), and the thermal conductivity of the matrix material is defined as 55 W / (m·K) (Arzig M, Steiner J, Salamon M, et al. Influence of morphological changes in a source material on the growth interface of 4H-SiC single crystals[J]. Materials, 2019, 12(16): 2591.). The pores are treated as air, with a thermal conductivity of 0.067 W / (m·K). The interface phase thermal conductivity is 9W / (m·K)(Islam MDR,Pramila A.Thermal conductivity of fiber reinforced composites by the FEM[J].Journal of Composite Materials,1999,33(18):1699-1715.)(Zou M,Yu B,Zhang D.Ananalytical solution for transverse thermal conductivities of unidirectionalfiber composites with thermal barrier[J].Journal of Physics D:AppliedPhysics,2002,35(15):1867-1874.).

[0079] Step S3.3: Solve for the equivalent thermal conductivity in different directions through numerical simulation. Step S3.3 includes: setting the two outer wall surfaces perpendicular to the y-axis as high-temperature (1300K) and low-temperature (300K) boundary conditions respectively, and setting the other planes as adiabatic walls, and numerically solving the heat conduction equation, as shown in the following formula:

[0080]

[0081] Then, the equivalent thermal conductivity in the y-direction is calculated based on the relationship between heat flow and temperature gradient in Fourier's law, as shown in the following formula:

[0082]

[0083] After solving for the y-direction, the equivalent thermal conductivity in the x and z directions is solved similarly. In equation (5), T is the temperature at the calculation point, and for the matrix, κ... xx , κ yy and κ zz All are equal to the thermal conductivity of the matrix; for fibers, κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the two secondary thermal conductivities. In equation (6), q... i and T i These represent the total heat flux density in direction i (i = x, y, z) and the temperature difference between the high and low temperature wall boundary conditions, respectively. From this, we finally obtain the equivalent thermal conductivity values ​​for three different directions.

[0084] Through simulation calculations Figure 2 The equivalent thermal conductivity in the thickness (y) direction in the model is 22.68 W / (m·K). Table 1 shows a comparison between the predicted and experimentally measured equivalent thermal conductivity in the thickness direction of the vertically cross-arranged unidirectional fiber-reinforced CMC material.

[0085] Table 1

[0086]

[0087] As can be seen from the table, the prediction results of this method match the experimental results very well, with a prediction accuracy of 3%. During the experiment, the testing equipment was a Netzsch LFA 467HT (Germany), and the testing method was the flash method (GB / T22588-2008). The equipment's measurement range was 0.1-2000 W / (m·K), and the testable temperature range was 298-1523 K. The test sample was a unidirectional fiber-reinforced SiCf / SiC CMC material, with a block size of 10×10×3 mm.

[0088] This invention first employs parametric Relational Evolution (RVE) modeling of structures such as fibers, matrix, interface phases, and pores. On one hand, this considers more microstructural information; on the other hand, it allows engineers and designers to directly and quickly modify the overall model and the dimensions of the microstructures such as fibers, pores, and interface phases by adjusting parameters such as porosity and fiber volume fraction. In subsequent research, such as in the analysis of the responsiveness of material thermal conductivity dispersion and microstructure geometry to the equivalent thermal conductivity solution, this invention can quickly obtain the overall equivalent thermal conductivity of the material under specified microstructure and corresponding thermal conductivity conditions, and discuss the impact on the equivalent thermal conductivity solution. Secondly, the parametric modeling of the double-layer arrangement model provides input / output interfaces, enabling the method to be quickly integrated into other analysis tools, such as using machine learning and other artificial intelligence techniques for anisotropic thermal conductivity-based thermal analysis, laying an important foundation for further scientific research and engineering applications.

[0089] Furthermore, the application scenario of this invention is the double-layer vertical cross-arrangement of CMC materials under the condition of aero-engine turbine blades. In the current aero-engine field, the processing method for unidirectional fiber-toughened CMC materials for turbine blades is a vertical cross-arrangement. Traditional single-layer structures and modeling methods that only consider fibers and matrix are not suitable for current engineering application requirements. However, the double-layer vertical cross-arrangement RVE model constructed in this invention is more representative in application and can more effectively reflect material properties and processing characteristics. Specifically, the double-layer vertical cross-arrangement model is adopted in RVE modeling, and the equivalent thermal conductivity is solved based on this. Moreover, the final equivalent thermal conductivity solution is corrected by experimental data. This step can quickly correct the accuracy of microstructure modeling and the assignment of thermal conductivity values ​​for specific internal structures. At the same time, parametric modeling has better visualization features.

[0090] Example 2

[0091] The present invention also provides a CMC material equivalent thermal conductivity prediction system based on parametric modeling. The CMC material equivalent thermal conductivity prediction system based on parametric modeling can be implemented by executing the process steps of the CMC material equivalent thermal conductivity prediction method based on parametric modeling. That is, those skilled in the art can understand the CMC material equivalent thermal conductivity prediction method based on parametric modeling as a preferred embodiment of the CMC material equivalent thermal conductivity prediction system based on parametric modeling.

[0092] The present invention provides a CMC material equivalent thermal conductivity prediction system based on parametric modeling, comprising:

[0093] Module M1: Constructs a single-layer RVE model for unidirectional fiber-toughened CMC materials. The single-layer RVE model described in Module M1 includes CMC material fibers, matrix, pores, and interface phases. The model is a three-dimensional model with a corresponding thickness in the X-direction. The shape of the three-dimensional model includes a cube, and the number of fibers in the model is periodically and uniformly distributed. The pores are through-holes, and there is an interface phase of a specific thickness between the fibers and the matrix.

[0094] Module M2: Based on the single-layer RVE model, construct a vertically intersecting unidirectional fiber-toughened CMC material RVE model and define its parameters to obtain the final model. Module M2 includes: Module M2.1: Vertically intersecting the single-layer RVE model constructed in Module M1 to form a vertically intersecting unidirectional fiber-toughened CMC material RVE initialization model. Module M2.2: Constructing geometric associations and generating a parameterized template through parameterized expressions, as shown in the following formula:

[0095]

[0096] Among them, D p R is the pore diameter. f R is the fiber radius, a is the side length of the RVE model, b is the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 is the distance between the fiber center in the boundary region and the model boundary, and R i Rt is the outer radius of the interfacial phase, P is the ratio of fiber radius to interfacial phase thickness, and V is the porosity. f n is the volume fraction of the fiber. p and n f These represent the number of pores and the number of fibers, respectively. Step 2.3: Parametrically define the geometric parameters of the two-layer model, inputting parameters P and V. f and R t Perform final parameterization to generate the final model.

[0097] Module M3: Predicts the equivalent thermal conductivity based on the final model. Module M3 includes: Module M3.1: Performs unstructured mesh generation on the RVE model obtained from Module M2. Module M3.2: Obtains and defines the thermal conductivity of each part of the microstructure, including fiber anisotropic thermal conductivity, matrix thermal conductivity, pore thermal conductivity, and interface phase thermal conductivity. Module M3.3: Solves for the equivalent thermal conductivity values ​​in different directions through numerical simulation. Module M3.3 includes: setting the two outer wall surfaces perpendicular to the y-axis as high-temperature and low-temperature wall boundary conditions respectively, and setting other planes as adiabatic wall surfaces, and numerically solving the thermal conductivity equation, as shown in the following formula:

[0098]

[0099] In the formula, T is the temperature at the calculation point, and for the matrix κ...xx , κ yy and κ zz Both are equal to the thermal conductivity of the matrix. For fiber κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the thermal conductivity in two secondary directions. Then, based on the relationship between heat flow and temperature gradient in Fourier's law, the equivalent thermal conductivity in the y-direction is calculated using the following formula:

[0100]

[0101] In the formula, q i and T i Let i = x, y, and z be the total heat flux density in direction i and the temperature difference between the high and low temperature wall boundary conditions, respectively. After solving for the y direction, the equivalent thermal conductivity in the x and z directions is solved similarly, finally yielding the equivalent thermal conductivity values ​​in three different directions.

[0102] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0103] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling, characterized in that, include: Step S1: Construct a single-layer RVE model of unidirectional fiber-toughened CMC material; Step S2: Based on the single-layer RVE model, construct the RVE model of the vertically cross-arranged unidirectional fiber-toughened CMC material, and perform parameterization to obtain the final model; Step S3: Predict the equivalent thermal conductivity based on the final model; Step S2 includes: Step S2.1: Arrange the single-layer RVE model constructed in step S1 in a vertically intersecting pattern to form a vertically intersecting unidirectional fiber-toughened CMC material RVE initialization model; Step S2.2: Construct geometric associations and generate parameterized templates using parametric expressions, as shown in the following formula: （1） （2） （3） （4） Among them, D p R is the pore diameter. f R is the fiber radius, a is the side length of the RVE model, b is the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 is the distance between the fiber center in the boundary region and the model boundary, and R i Rt is the outer radius of the interfacial phase, P is the ratio of fiber radius to interfacial phase thickness, and V is the porosity. f This represents the volume fraction of the fiber. and These represent the number of pores and the number of fibers, respectively. Step S2.3: Parametrically define the geometric parameters of the two-layer model, inputting parameters P and V. f and R t Perform final parameterization to generate the final model; Step S3 includes: Step S3.1: Perform unstructured mesh generation on the RVE model obtained in step S2; Step S3.2: Obtain and define the thermal conductivity of each part of the microstructure, including the anisotropic thermal conductivity of the fiber, the thermal conductivity of the matrix, the thermal conductivity of the pores, and the thermal conductivity of the interfacial phase; Step S3.3: Solve for the equivalent thermal conductivity values ​​in different directions through numerical simulation.

2. The method for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling according to claim 1, characterized in that, The single-layer RVE model mentioned in step S1 includes CMC material fibers, matrix, pores and interface phases, and is a three-dimensional model with corresponding thickness in the X direction during modeling. The three-dimensional model has a cube shape, and the number of fibers in the model is arranged periodically and uniformly; the pores are through holes, and there is an interface phase of a specific thickness between the fibers and the matrix.

3. The method for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling according to claim 1, characterized in that, Step S3.3 includes: The two outer wall surfaces perpendicular to the y-axis are set as high-temperature and low-temperature boundary conditions, respectively, and the other planes are set as adiabatic walls. The heat conduction equation is solved numerically, and the formula is as follows: （5） In the formula, T is the temperature at the calculation point, and for the matrix κ... xx κ yy and κ zz All are equal to the thermal conductivity of the matrix; for fibers κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the thermal conductivity in two secondary directions; Then, the equivalent thermal conductivity in the y-direction is calculated based on the relationship between heat flow and temperature gradient in Fourier's law, as shown in the following formula: （6） In the formula, q i and T i Let i be the total heat flux density in the i-direction and the temperature difference between the high and low temperature wall boundary conditions, respectively, where i = x, y, z; After solving for the y-direction, the equivalent thermal conductivity in the x and z directions is solved in the same way, and finally the equivalent thermal conductivity values ​​in three different directions are obtained.

4. A system for predicting the equivalent thermal conductivity of CMC materials based on parametric modeling, characterized in that, include: Module M1: Construct a single-layer RVE model for unidirectional fiber-toughened CMC materials; Module M2: Based on the single-layer RVE model, construct the RVE model of the vertically cross-arranged unidirectional fiber-toughened CMC material, and define the parameters to obtain the final model; Module M3: Predicts the equivalent thermal conductivity based on the final model; The module M2 includes: Module M2.1: Arrange the single-layer RVE model constructed in Module M1 in a vertically intersecting pattern to form a vertically intersecting unidirectional fiber-toughened CMC material RVE initialization model; Module M2.2: Constructs geometric associations and generates parametric templates through parametric expressions, as shown in the following formula: （1） （2） （3） （4） Among them, D p R is the pore diameter. f R is the fiber radius, a is the side length of the RVE model, b is the distance between the centers of the two rows of fibers on the horizontal y-axis and vertical z-axis, b1 is the distance between the fiber center in the boundary region and the model boundary, and R i Rt is the outer radius of the interfacial phase, P is the ratio of fiber radius to interfacial phase thickness, and V is the porosity. f This represents the volume fraction of the fiber. and These represent the number of pores and the number of fibers, respectively. Module M2.3: Parametrically defines the geometric parameters of the two-layer model, with input parameters P and V. f and R t Perform final parameterization to generate the final model; The module M3 includes: Module M3.1: Performs unstructured mesh generation on the RVE model obtained from Module M2; Module M3.2: Obtain and define the thermal conductivity of each part of the microstructure, including the anisotropic thermal conductivity of the fiber, the thermal conductivity of the matrix, the thermal conductivity of the pores, and the thermal conductivity of the interfacial phase; Module M3.3: Solve for the equivalent thermal conductivity in different directions through numerical simulation.

5. The CMC material equivalent thermal conductivity prediction system based on parametric modeling according to claim 4, characterized in that, The single-layer RVE model described in module M1 includes CMC material fibers, matrix, pores and interface phases, and is modeled as a three-dimensional model with corresponding thickness in the X direction. The three-dimensional model has a cube shape, and the number of fibers in the model is arranged periodically and uniformly; the pores are through holes, and there is an interface phase of a specific thickness between the fibers and the matrix.

6. The CMC material equivalent thermal conductivity prediction system based on parametric modeling according to claim 4, characterized in that, The module M3.3 includes: The two outer wall surfaces perpendicular to the y-axis are set as high-temperature and low-temperature boundary conditions, respectively, and the other planes are set as adiabatic walls. The heat conduction equation is solved numerically, and the formula is as follows: （5） In the formula, T is the temperature at the calculation point, and for the matrix κ... xx κ yy and κ zz All are equal to the thermal conductivity of the matrix; for fibers κ xx Thermal conductivity in the main direction, κ yy and κ zz These are the thermal conductivity in two secondary directions; Then, the equivalent thermal conductivity in the y-direction is calculated based on the relationship between heat flow and temperature gradient in Fourier's law, as shown in the following formula: （6） In the formula, q i and T i Let i be the total heat flux density in the i-direction and the temperature difference between the high and low temperature wall boundary conditions, respectively, where i = x, y, z; After solving for the y-direction, the equivalent thermal conductivity in the x and z directions is solved in the same way, and finally the equivalent thermal conductivity values ​​in three different directions are obtained.

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