A method and system for predicting effective thermal conductivity of porous ceramics with regular-irregular complex pore structure

Abstract

This invention provides a method and system for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures. The method includes: preparing porous ceramics to obtain the total porosity of the porous ceramics; performing binarization processing on the pore feature map to obtain an original binary map; performing depth processing on the original binary map to obtain a depth binary map; calculating the porosity of the regular pore structure in the depth binary map and combining it with the total porosity to obtain the equivalent matrix porosity; based on the equivalent matrix porosity, obtaining an equivalent matrix effective thermal conductivity model and an effective thermal conductivity model of the porous ceramics composed of the regular pore structure and the equivalent matrix; fitting the shape factor in the equivalent matrix effective thermal conductivity model to obtain the effective thermal conductivity of the porous ceramics with regular-irregular complex pore structures. This invention not only solves the problems of long prediction time, complex calculations, and cumbersome steps in conventional effective thermal conductivity prediction, but also ensures high accuracy in effective thermal conductivity prediction.

Description

Technical Field

[0001] This invention belongs to the field of heat and mass transfer technology of porous materials, specifically relating to a method and system for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures. Background Technology

[0002] For porous materials, engineering applications typically focus on their macroscopic heat transfer characteristics, neglecting the specific heat transfer processes within their internal microstructure. In this case, the porous material is considered a continuous medium, and its effective properties are a comprehensive result of the hybrid system composed of a solid three-dimensional framework and pores. The effective thermal conductivity of porous materials is usually obtained through experimental measurement. However, conventional thermal conductivity testing devices are only suitable for large-sized samples. With the increasing miniaturization and micro-miniaturization of various devices, accurately obtaining the thermal conductivity of small / micro samples faces significant challenges. For porous materials, pore characteristics (porosity, pore distribution, etc.) are the main factors affecting thermal conductivity; therefore, accurately predicting the effective thermal conductivity of porous materials based on pore characteristics is a current research focus.

[0003] For porous materials with complex pore structures, conventional effective thermal conductivity models are often insufficient in predicting their thermal conductivity performance. Improving existing effective thermal conductivity models is an important measure to enhance their applicability. Improving existing effective thermal conductivity models based on the microstructural characteristics of porous materials is a strategy to improve the accuracy of effective thermal conductivity prediction. For example, by calculating the pore cross-sectional area of ​​porous materials using fractal theory to obtain the tortuosity of the porous material, and then combining series and parallel models with the tortuosity of the porous material, a new expression for effective thermal conductivity is derived.

[0004] Currently, improving the prediction efficiency of effective thermal conductivity and further enhancing the prediction accuracy of improved effective thermal conductivity models remain significant challenges. Furthermore, obtaining the characteristic parameters of some improved effective thermal conductivity models is difficult, greatly limiting their application scope. Therefore, exploring new, flexible, and effective methods for predicting the effective thermal conductivity of porous materials is a pressing issue that needs to be addressed. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures. By extracting and analyzing the microscopic image features of porous ceramics and detecting the total porosity of porous ceramics, the effective thermal conductivity of porous ceramics can be predicted. This not only solves the problems of long prediction time, complex calculations, and cumbersome steps in conventional effective thermal conductivity prediction, but also ensures high accuracy in predicting effective thermal conductivity.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures includes the following steps:

[0008] Porous ceramics were prepared, and the total porosity of the porous ceramics was obtained based on true density testing and measurement of regular porous ceramics.

[0009] The pore feature map of the porous ceramic is collected, and the Cellpose algorithm is used to perform binarization processing on the pore feature map to obtain the original binary map;

[0010] The original binary image is subjected to depth processing to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image;

[0011] The porosity of the regular pore structure in the depth binary image is calculated, and combined with the total porosity, the equivalent matrix porosity is obtained; wherein, the equivalent matrix is ​​composed of the irregular pore structure and the original porous ceramic matrix.

[0012] Based on the equivalent matrix porosity, an effective thermal conductivity model of the equivalent matrix is ​​obtained, and based on the effective thermal conductivity model of the equivalent matrix, an effective thermal conductivity model of porous ceramics composed of regular pore structure and equivalent matrix is ​​obtained.

[0013] Based on the effective thermal conductivity experiment and the effective thermal conductivity model of the porous ceramic, the shape factor in the effective thermal conductivity model of the equivalent matrix is ​​fitted to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, thus completing the prediction of the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures.

[0014] Preferably, the method for obtaining the total porosity of porous ceramics is as follows:

[0015] Based on the mass and volume of the regularly porous ceramic, the bulk density of the regularly porous ceramic is obtained; the expression for the bulk density is as follows:

[0016] Based on the bulk density and the true density of the regular porous ceramic, the total porosity of the porous ceramic is obtained; the expression for total porosity is as follows:

[0017] In the formula, ρ is the bulk density, m1 is the mass of the regular porous ceramic, V is the volume of the regular porous ceramic, and p t ρ is the total porosity, and ρ0 is the true density.

[0018] Preferably, the method for obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map is as follows:

[0019] Based on image processing software, the pore boundaries in the original binary image are obtained, and irregular pores in the porous ceramic original matrix are removed by referring to the pore feature image.

[0020] The region enclosed by the pore boundaries of the binary image after removing irregular pores is filled to obtain a binary image containing only regular pore structures.

[0021] By employing Boolean operations and boundary optimization, the fused pores in the binary image containing only regular pore structures are segmented to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image.

[0022] Preferably, the method for obtaining the equivalent matrix porosity is as follows:

[0023] The porosity of the regular pore structure in the depth binary image is calculated using ImageJ software, and combined with the total porosity, the porosity of the irregular pore structure in the original binary image is obtained; the expression for the porosity of the irregular pore structure is: χ = p t -v s ;

[0024] The equivalent matrix porosity is obtained based on the porosity of the irregular pore structure; the expression for the equivalent matrix porosity is:

[0025] In the formula, p t v represents the total porosity. s The porosity is for a near-spherical regular pore structure.

[0026] Preferably, the expression for obtaining the equivalent matrix effective thermal conductivity model is as follows:

[0027]

[0028] In the formula, k1 and k2 are the thermal conductivity of the original matrix and the air in the pores, respectively, and n is the shape factor related to the sphericity of the porosity in the original matrix.

[0029] The expression for the effective thermal conductivity model of porous ceramics is as follows:

[0030]

[0031] This invention also provides a system for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, used to implement the effective thermal conductivity prediction method, comprising:

[0032] The total porosity calculation module is used to prepare porous ceramics and obtain the total porosity of porous ceramics based on true density testing and regular porous ceramic measurement.

[0033] The binary processing module is used to acquire the pore feature map of porous ceramics and perform binarization processing on the pore feature map using the Cellpose algorithm to obtain the original binary map.

[0034] The depth processing module is used to perform depth processing on the original binary image to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image.

[0035] The equivalent matrix porosity calculation module is used to calculate the porosity of the regular pore structure in the depth binary map and combine it with the total porosity to obtain the equivalent matrix porosity; wherein, the equivalent matrix is ​​composed of the irregular pore structure and the original porous ceramic matrix.

[0036] The model acquisition module is used to obtain the effective thermal conductivity model of the equivalent matrix based on the porosity of the equivalent matrix, and to obtain the effective thermal conductivity model of the porous ceramic composed of the regular pore structure and the equivalent matrix based on the effective thermal conductivity model of the equivalent matrix.

[0037] The shape factor fitting module is used to fit the shape factor in the effective thermal conductivity model of the equivalent matrix based on the effective thermal conductivity experiment and the effective thermal conductivity model of the porous ceramic, to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, and to complete the prediction of the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures.

[0038] Preferably, the total porosity calculation module includes:

[0039] The bulk density calculation unit is used to obtain the bulk density of a regular porous ceramic based on its mass and volume; the expression for bulk density is as follows:

[0040] The total porosity calculation unit is used to obtain the total porosity of the porous ceramic based on the bulk density and the true density of the regular porous ceramic; the expression for total porosity is as follows:

[0041] In the formula, ρ is the bulk density, m1 is the mass of the regular porous ceramic, V is the volume of the regular porous ceramic, and p t ρ is the total porosity, and ρ0 is the true density.

[0042] Preferably, the depth processing module includes:

[0043] The irregular pore removal unit is used to obtain the pore boundaries in the original binary image based on image processing software, and remove irregular pores in the porous ceramic original matrix by referring to the pore feature map.

[0044] Filling cells are used to fill the area enclosed by the pore boundaries of the binary image after removing irregular pores, so as to obtain a binary image with only regular pore structures.

[0045] The segmentation unit is used to segment the fused pores in the binary map containing only regular pore structures using Boolean operations and boundary optimization, thereby obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map.

[0046] Compared with existing technologies, the advantages of this invention are as follows: This invention, combined with image depth processing, can accurately extract the pore features of porous ceramics, precisely analyze the pore structure of porous materials, and comprehensively consider the influence of irregular pores in porous ceramics on the effective thermal conductivity. Furthermore, it optimizes the effective thermal conductivity model by combining an equivalent matrix model, resulting in high operability and accuracy. Simultaneously, it eliminates the need for complex finite element construction and calculations; only a microscopic image of the porous ceramic and its total porosity are required to predict the effective thermal conductivity, thus improving the prediction efficiency. Moreover, this method is simple, flexible, and low-cost, making it suitable for industrial application and promotion. Attached Figure Description

[0047] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is an equivalent schematic diagram of the internal pore structure of porous ceramics with regular-irregular complex pore structures in this invention;

[0049] Figure 2 The diagram illustrates the identification and processing of pore structures in microscopic images of porous ceramics; (a) is the identification bounding box selection; (b) is the identification filling; (c) is the binarization processing; (d) is the pore boundary identification; (e) is the pore filling; and (f) is the fused pore segmentation.

[0050] Figure 3 SEM images and corresponding binary images of mullite-based porous ceramics with different hollow sphere sizes are shown; (a) and (d) are 150–200 μm, (b) and (e) are 97–150 μm; (c) and (f) are 54–97 μm.

[0051] Figure 4 SEM images and their corresponding binary images of mullite-based porous ceramics with different hollow sphere contents: (a) and (e) are 30 wt%; (b) and (f) are 40 wt%; (c) and (g) are 50 wt%; (d) and (h) are 60 wt%.

[0052] Figure 5SEM images and their corresponding binary images of mullite-based porous ceramics with different hollow sphere contents: (a, e) 30wt%; (b, f) 40wt%; (c, g) 50wt%; (d, h) 60wt%;

[0053] Figure 6 The figures show a comparison of the prediction results of the method of the present invention with other effective thermal conductivity models in Examples 2, 3, and 4.

[0054] Figure 7 This is a flowchart of the method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures according to the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] Example 1

[0058] like Figure 7 As shown, a method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures includes the following steps:

[0059] S1: Prepare porous ceramics, and obtain the total porosity of the porous ceramics based on true density testing and regular porous ceramic measurement; a further embodiment, the method for obtaining the total porosity of porous ceramics is as follows:

[0060] Based on the mass and volume of the regularly porous ceramic, the bulk density of the regularly porous ceramic is obtained; the expression for the bulk density is as follows:

[0061] Based on the bulk density and the true density of the regular porous ceramic, the total porosity of the porous ceramic is obtained; the expression for total porosity is as follows:

[0062] In the formula, ρ is the bulk density, m1 is the mass of the regular porous ceramic, V is the volume of the regular porous ceramic, and p t ρ is the total porosity, and ρ0 is the true density.

[0063] S2: Collect pore feature images of porous ceramics and use the Cellpose algorithm to binarize the pore feature images to obtain the original binary images; specifically, observe the microscopic morphology of the fracture surface of porous ceramics using a scanning electron microscope or a high-magnification optical microscope to obtain the corresponding pore feature images, and use functions or algorithms to binarize the images to extract the pore features of porous ceramics in the images; before observing the fracture morphology, the fracture surface of porous ceramics must be polished flat, and the field of view should include multiple pore structures; use the built-in "imbinarize" function in Matlab or call the open-source Cellpose algorithm on the Github platform (see www.github.com / mouseland / cellpose) to binarize the images to facilitate the automatic identification of pore features of porous ceramics. Figure 2 As shown, (a) is the recognition box selection; (b) is the recognition filling; and (c) is the binarization process.

[0064] S3: Perform depth processing on the original binary image to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image; for example... Figure 2 As shown, (d) represents pore boundary identification; (e) represents pore filling; and (f) represents fused pore segmentation. In a further embodiment, the method for obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map is as follows:

[0065] Based on image processing software, the pore boundaries in the original binary image are obtained, and irregular pores in the original porous ceramic matrix are removed by referring to the pore feature map.

[0066] The region enclosed by the pore boundaries of the binary image after removing irregular pores is filled to obtain a binary image containing only regular pore structures.

[0067] By using the Boolean operations and boundary optimization methods built into ImageJ software, the fused pores in the binary image containing only regular pore structures are segmented to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image.

[0068] S4: Calculate the porosity of the regular pore structure in the depth binary image and combine it with the total porosity to obtain the equivalent matrix porosity; whereby the equivalent matrix is ​​composed of both the irregular pore structure and the original porous ceramic matrix; for example... Figure 1 As shown. In a further embodiment, the method for obtaining the equivalent matrix porosity is as follows:

[0069] The porosity of regular pore structures in the depth binary image was calculated using ImageJ software, and combined with the total porosity to obtain the porosity of irregular pore structures in the original binary image. The expression for the porosity of irregular pore structures is: χ = p t -v s ;

[0070] Based on the porosity of the irregular pore structure, the equivalent matrix porosity is obtained; the expression for the equivalent matrix porosity is:

[0071] In the formula, p t v represents the total porosity. s The porosity is for a near-spherical regular pore structure.

[0072] S5: Based on the equivalent matrix porosity, obtain the effective thermal conductivity model of the equivalent matrix, and based on the effective thermal conductivity model of the equivalent matrix, obtain the effective thermal conductivity model of the porous ceramic composed of the regular pore structure and the equivalent matrix. Specifically, the regular and irregular pore structures are evenly distributed in the binary graph, which conforms to the classic Maxwell-Eucken model. Thus, the equivalent matrix composed of the irregular pore structure and the original matrix, as well as the effective thermal conductivity model form of the porous ceramic composed of the regular pore structure and the equivalent matrix, are determined.

[0073] In a further implementation, the expression for the equivalent matrix effective thermal conductivity model is obtained as follows:

[0074]

[0075] In the formula, k1 and k2 are the thermal conductivity of the original matrix and the air in the pores, respectively, and n is the shape factor related to the sphericity of the porosity in the original matrix.

[0076] The expression for the effective thermal conductivity model of porous ceramics is as follows:

[0077]

[0078] S6: Based on the effective thermal conductivity experiment and the effective thermal conductivity model of porous ceramics, the shape factor in the effective thermal conductivity model of the equivalent matrix is ​​fitted to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, and the effective thermal conductivity prediction of porous ceramics with regular-irregular complex pore structures is completed.

[0079] On the other hand, the present invention also provides an effective thermal conductivity prediction system for porous ceramics with regular-irregular complex pore structures, for realizing an effective thermal conductivity prediction method, including: a total porosity calculation module, a binary processing module, a depth processing module, an equivalent matrix porosity calculation module, a model acquisition module, and a shape factor fitting module.

[0080] A total porosity calculation module is used to prepare porous ceramics and obtain the total porosity of the porous ceramics based on true density testing and measurements of regular porous ceramics; in a further embodiment, the total porosity calculation module includes:

[0081] The bulk density calculation unit is used to obtain the bulk density of a regular porous ceramic based on its mass and volume; the expression for bulk density is as follows:

[0082] The total porosity calculation unit is used to obtain the total porosity of porous ceramics based on the bulk density and the true density of regular porous ceramics; the expression for total porosity is as follows:

[0083] In the formula, ρ is the bulk density, m1 is the mass of the regular porous ceramic, V is the volume of the regular porous ceramic, and p t ρ is the total porosity, and ρ0 is the true density.

[0084] The binary processing module is used to acquire the pore feature map of porous ceramics and use the Cellpose algorithm to perform binarization processing on the pore feature map to obtain the original binary map.

[0085] A depth processing module is used to perform depth processing on the original binary image to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image; in a further embodiment, the depth processing module includes:

[0086] The irregular pore removal unit is used to obtain the pore boundaries in the original binary image based on image processing software, and remove irregular pores in the original porous ceramic matrix by referring to the pore feature map.

[0087] Filling cells are used to fill the area enclosed by the pore boundaries of the binary image after removing irregular pores, so as to obtain a binary image with only regular pore structures.

[0088] The segmentation unit is used to segment the fused pores in the binary map containing only regular pore structures using Boolean operations and boundary optimization, thereby obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map.

[0089] The equivalent matrix porosity calculation module is used to calculate the porosity of regular pore structures in the depth binary map and combine it with the total porosity to obtain the equivalent matrix porosity; wherein, the equivalent matrix is ​​composed of irregular pore structures and porous ceramic original matrix.

[0090] The equivalent matrix porosity calculation module includes:

[0091] The irregular pore structure porosity calculation unit is used to calculate the porosity of regular pore structures in the depth binary image based on ImageJ software, and combine it with the total porosity to obtain the porosity of irregular pore structures in the original binary image; the porosity expression for irregular pore structures is: χ = p t -v s ;

[0092] The equivalent matrix porosity calculation unit is used to obtain the equivalent matrix porosity based on the porosity of irregular pore structures; the expression for equivalent matrix porosity is:

[0093] In the formula, p t v represents the total porosity. s The porosity is for a near-spherical regular pore structure.

[0094] The model acquisition module is used to obtain the effective thermal conductivity model of the equivalent matrix based on the equivalent matrix porosity, and to obtain the effective thermal conductivity model of the porous ceramic composed of the regular pore structure and the equivalent matrix based on the effective thermal conductivity model of the equivalent matrix. The model acquisition module includes:

[0095] The expression for the effective thermal conductivity model of the equivalent matrix is ​​as follows:

[0096]

[0097] In the formula, k1 and k2 are the thermal conductivity of the original matrix and the air in the pores, respectively, and n is the shape factor related to the sphericity of the porosity in the original matrix.

[0098] The expression for the effective thermal conductivity model of porous ceramics is as follows:

[0099]

[0100] The shape factor fitting module is used to fit the shape factor in the effective thermal conductivity model of the equivalent matrix based on the effective thermal conductivity experiment and the effective thermal conductivity model of porous ceramics, to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, and to complete the prediction of the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures.

[0101] Example 2

[0102] In this embodiment, using aluminosilicate powder as the matrix and fly ash hollow spheres of different particle sizes as inorganic pore-forming agents, mullite-based porous ceramics with a hollow sphere content of 50 wt% and a complex pore structure were prepared by protein gel casting method. The total porosity of the porous ceramics was calculated based on true density testing and measurements of regular porous ceramics, as shown in the following formula. The thermal conductivity of the mullite-based porous ceramics with different hollow sphere particle sizes was tested using a thermal conductivity meter.

[0103]

[0104] Where ρ is the bulk density, m1 is the mass of the regular porous material, V is the volume of the regular porous material, and p t ρ is the total porosity, and ρ0 is the true density.

[0105] Porous ceramics with different hollow sphere sizes were selected, and the fracture surfaces were polished smooth. The fracture morphology of each porous ceramic was observed using a scanning electron microscope. Figure 3 (a)- Figure 3 (c) Next, the microscopic images of the porous ceramics are subjected to depth processing ( Figure 3 (d)- Figure 3 (f) The Cellpose algorithm is used to binarize the image to facilitate automatic identification of pore features in porous ceramics. ImageJ image processing software is used to automatically identify pore boundaries in the original binary image, and irregular pores in the matrix are removed by referring to the actual fracture surface image. Then, the area enclosed by the boundary is automatically filled to display a binary image containing only regular pore structures. Furthermore, Boolean operations and boundary optimization are used to segment the fused pores in the binary image to obtain a binary image that matches the regular pore structure features in the actual fracture surface image. Based on this, ImageJ software is used to calculate the porosity corresponding to the regular pore structures in the binary image. Combined with the total porosity of the porous ceramic obtained from testing, the porosity χ = p corresponding to the irregular pore structures in the binary image is calculated. t -v s And the equivalent matrix porosity, as shown in the following formula.

[0106]

[0107] Where χ' is the volume fraction of irregular pores in the matrix (i.e., equivalent matrix porosity), v s The porosity represents the porosity of the near-spherical regular pore structure. The regular and irregular pore structures are evenly distributed in the binary graph, which conforms to the classic Maxwell-Eucken model. This allows us to determine the equivalent matrix formed by the irregular pore structure and the original matrix, as well as the effective thermal conductivity model form corresponding to the porous ceramic formed by the regular pore structure and the equivalent matrix.

[0108]

[0109] in, and k e denoted by k1 and k2, respectively, represent the effective thermal conductivity of the equivalent matrix and the porous material. k1 and k2 represent the thermal conductivity of the original matrix and the air in the pores, respectively. The parameter n is a shape factor related to the sphericity of the impurities in the original matrix; the shape factor n is 1.26 obtained by fitting experimental data. Substituting the effective thermal conductivity of the equivalent matrix into the effective thermal conductivity expression of the porous ceramic composed of the regular pore structure and the equivalent matrix, the effective thermal conductivity expression of the porous ceramic is obtained, thus enabling the prediction of the thermal conductivity of the porous ceramic. The results are shown in Table 1. Further comparison of the prediction results with other effective thermal conductivity models is also performed. Figure 6 It can be found that the prediction accuracy of this method is significantly higher.

[0110] Table 1

[0111]

[0112] Example 3

[0113] Using aluminosilicate powder as the matrix and hollow fly ash spheres of varying contents (particle size 97–150 μm) as inorganic pore-forming agents, mullite-based porous ceramics with complex pore structures were prepared using a protein gel casting method. The total porosity of the porous ceramics was calculated based on true density testing and measurements of regular porous ceramics. The thermal conductivity of the mullite-based porous ceramics with different hollow sphere sizes was also tested using a thermal conductivity meter.

[0114] Porous ceramics with different hollow sphere sizes were selected, and the fracture surfaces were polished smooth. The fracture morphology of each porous ceramic was observed using a scanning electron microscope. Figure 4 (a)- Figure 4 (d) Next, the microscopic images of the porous ceramics are subjected to depth processing ( Figure 4 (e)- Figure 4 (h) The Cellpose algorithm is used to binarize the image to facilitate automatic identification of pore features in porous ceramics. ImageJ image processing software is used to automatically identify pore boundaries in the original binary image, and irregular pores in the matrix are removed by referring to the actual fracture image. Then, the boundary-enclosed areas are automatically filled to display a binary image containing only regular pore structures. Furthermore, Boolean operations and boundary optimization are used to segment the fused pores in the binary image to obtain a binary image that matches the regular pore structure features in the actual fracture image. Based on this, ImageJ software is used to calculate the porosity corresponding to the regular pore structures in the binary image. Combined with the total porosity of the porous ceramic obtained from testing, the porosity corresponding to the irregular pore structures in the binary image and the equivalent matrix porosity are calculated.

[0115] The binary image shows a uniform distribution of regular and irregular pore structures, conforming to the classic Maxwell-Eucken model. This allows us to determine the equivalent matrix formed by the irregular pore structure and the original matrix, as well as the effective thermal conductivity model for the porous ceramic formed by the regular pore structure and the equivalent matrix. Fitting experimental data yields a shape factor n of 1.26. The expression for the effective thermal conductivity of the porous ceramic is thus obtained, enabling the prediction of its thermal conductivity. The results are shown in Table 2. Further comparison of the prediction results with other effective thermal conductivity models is also presented. Figure 6 It can be found that the prediction accuracy of this method is significantly higher.

[0116] Table 2 Calculation results of effective thermal conductivity

[0117]

[0118] Example 4:

[0119] Using aluminosilicate powder as the matrix and hollow fly ash spheres of varying contents (particle size 97–150 μm) as inorganic pore-forming agents, mullite-based porous ceramics with complex pore structures were prepared via a foaming method. The total porosity of the porous ceramics was calculated based on true density testing and measurements of regular porous ceramics. The thermal conductivity of the mullite-based porous ceramics with different hollow sphere sizes was then tested using a thermal conductivity meter.

[0120] Porous ceramics with different hollow sphere sizes were selected, and the fracture surfaces were polished smooth. The fracture morphology of each porous ceramic was observed using a scanning electron microscope. Figure 5 (a)- Figure 5 (d) Next, the microscopic images of the porous ceramics are subjected to depth processing ( Figure 5 (e)- Figure 5 (h) The Cellpose algorithm is used to binarize the image to facilitate automatic identification of pore features in porous ceramics. ImageJ image processing software is used to automatically identify pore boundaries in the original binary image, and irregular pores in the matrix are removed by referring to the actual fracture image. Then, the boundary-enclosed areas are automatically filled to display a binary image containing only regular pore structures. Furthermore, Boolean operations and boundary optimization are used to segment the fused pores in the binary image to obtain a binary image that matches the regular pore structure features in the actual fracture image. Based on this, ImageJ software is used to calculate the porosity corresponding to the regular pore structures in the binary image. Combined with the total porosity of the porous ceramic obtained from testing, the porosity corresponding to the irregular pore structures in the binary image and the equivalent matrix porosity are calculated.

[0121] The binary image shows a uniform distribution of regular and irregular pore structures, conforming to the classic Maxwell-Eucken model. This allows us to determine the equivalent matrix formed by the irregular pore structure and the original matrix, as well as the effective thermal conductivity model for the porous ceramic formed by the regular pore structure and the equivalent matrix. Fitting experimental data yields a shape factor n of 1.23. The expression for the effective thermal conductivity of the porous ceramic is thus obtained, enabling the prediction of its thermal conductivity. The results are shown in Table 3. Further comparison of the prediction results with other effective thermal conductivity models is also presented. Figure 6 It can be found that the prediction accuracy of this method is significantly higher.

[0122] Table 3 Calculation results of effective thermal conductivity

[0123]

[0124]

[0125] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, characterized in that, Includes the following steps: Porous ceramics were prepared, and the total porosity of the porous ceramics was obtained based on true density testing and measurement of regular porous ceramics. The pore feature map of the porous ceramic is collected, and the Cellpose algorithm is used to perform binarization processing on the pore feature map to obtain the original binary map; The original binary image is subjected to depth processing to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image; The porosity of the regular pore structure in the depth binary image is calculated, and combined with the total porosity, the equivalent matrix porosity is obtained; wherein, the equivalent matrix is ​​composed of the irregular pore structure and the original porous ceramic matrix. Based on the equivalent matrix porosity, an effective thermal conductivity model of the equivalent matrix is ​​obtained, and based on the effective thermal conductivity model of the equivalent matrix, an effective thermal conductivity model of porous ceramics composed of regular pore structure and equivalent matrix is ​​obtained. Based on the effective thermal conductivity experiment and the effective thermal conductivity model of the porous ceramic, the shape factor in the effective thermal conductivity model of the equivalent matrix is ​​fitted to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, thus completing the prediction of the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures. The method for obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map is as follows: Based on image processing software, the pore boundaries in the original binary image are obtained, and irregular pores in the porous ceramic original matrix are removed by referring to the pore feature image. The region enclosed by the pore boundaries of the binary image after removing irregular pores is filled to obtain a binary image containing only regular pore structures. Boolean operations and boundary optimization are used to segment the fused pores in the binary image where only regular pore structures exist, and a depth binary image that matches the actual regular pore structure features in the pore feature image is obtained. The expression for the equivalent matrix effective thermal conductivity model is as follows: ， In the formula, k 1 and k 2 represents the thermal conductivity of the original matrix and the air in the pores, respectively. n It is a shape factor related to the sphericity of porosity in the original matrix. p t Total porosity v s The porosity of a near-spherical regular pore structure; The expression for the effective thermal conductivity model of porous ceramics is as follows: 。 2. The method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures according to claim 1, characterized in that, The method for obtaining the total porosity of porous ceramics is as follows: Based on the mass and volume of the regularly porous ceramic, the bulk density of the regularly porous ceramic is obtained; the expression for the bulk density is as follows: ; Based on the bulk density and the true density of the regular porous ceramic, the total porosity of the porous ceramic is obtained; the expression for total porosity is as follows: ; In the formula, ρ For bulk density, m 1 represents the quality of regular porous ceramics. V For regular porous ceramic volume, p t Total porosity ρ 0 represents true density.

3. The method for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures according to claim 1, characterized in that, The method for obtaining the equivalent matrix porosity is as follows: The porosity of the regular pore structure in the depth binary image is calculated using ImageJ software, and combined with the total porosity, the porosity of the irregular pore structure in the original binary image is obtained; the expression for the porosity of the irregular pore structure is: χ = p t - v s ; The equivalent matrix porosity is obtained based on the porosity of the irregular pore structure. The equivalent matrix porosity expression is: ; In the formula, p t Total porosity v s The porosity is for a near-spherical, regular pore structure.

4. A system for predicting the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, used to implement the effective thermal conductivity prediction method according to any one of claims 1-3, characterized in that, include: The total porosity calculation module is used to prepare porous ceramics and obtain the total porosity of porous ceramics based on true density testing and regular porous ceramic measurement. The binary processing module is used to acquire the pore feature map of porous ceramics and perform binarization processing on the pore feature map using the Cellpose algorithm to obtain the original binary map. The depth processing module is used to perform depth processing on the original binary image to obtain a depth binary image that matches the actual regular pore structure features in the pore feature image. The equivalent matrix porosity calculation module is used to calculate the porosity of the regular pore structure in the depth binary map and combine it with the total porosity to obtain the equivalent matrix porosity; wherein, the equivalent matrix is ​​composed of the irregular pore structure and the original porous ceramic matrix. The model acquisition module is used to obtain the effective thermal conductivity model of the equivalent matrix based on the porosity of the equivalent matrix, and to obtain the effective thermal conductivity model of the porous ceramic composed of the regular pore structure and the equivalent matrix based on the effective thermal conductivity model of the equivalent matrix. The shape factor fitting module is used to fit the shape factor in the effective thermal conductivity model of the equivalent matrix based on the effective thermal conductivity experiment and the effective thermal conductivity model of the porous ceramic, to obtain the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures, and to complete the prediction of the effective thermal conductivity of porous ceramics with regular-irregular complex pore structures.

5. The effective thermal conductivity prediction system for porous ceramics with regular-irregular complex pore structures according to claim 4, characterized in that, The total porosity calculation module includes: The bulk density calculation unit is used to obtain the bulk density of a regular porous ceramic based on its mass and volume; the expression for bulk density is as follows: ; The total porosity calculation unit is used to obtain the total porosity of the porous ceramic based on the bulk density and the true density of the regular porous ceramic; the expression for total porosity is as follows: ; In the formula, ρ For bulk density, m 1 represents the quality of regular porous ceramics. V For regular porous ceramic volume, p t Total porosity ρ 0 represents true density.

6. The effective thermal conductivity prediction system for porous ceramics with regular-irregular complex pore structures according to claim 4, characterized in that, The depth processing module includes: The irregular pore removal unit is used to obtain the pore boundaries in the original binary image based on image processing software, and remove irregular pores in the porous ceramic original matrix by referring to the pore feature map. Filling cells are used to fill the area enclosed by the pore boundaries of the binary image after removing irregular pores, so as to obtain a binary image with only regular pore structures. The segmentation unit is used to segment the fused pores in the binary map containing only regular pore structures using Boolean operations and boundary optimization, thereby obtaining a depth binary map that matches the actual regular pore structure features in the pore feature map.

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