Method for modeling and heat transfer performance analysis of multiphase composites based on voxel grid

Abstract

This invention relates to the field of thermal protection materials technology, and in particular to a method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes. By establishing a voxelized representative volume element model to characterize the microstructure of multiphase composite materials, and dividing the representative volume element into a uniformly structured voxel mesh, the method directly assigns material properties to the mesh elements based on random numbers and volume fraction interval matching. This allows for the rapid generation of multiphase composite material finite element models without the need for pre-constructing complex geometric models, effectively solving the problems of difficult modeling, difficult mesh generation, and large computational load in traditional methods. Furthermore, by combining standardized periodic temperature boundary conditions with finite element solutions, the equivalent heat transfer performance of the material can be accurately obtained, realizing an integrated process of modeling and heat transfer performance analysis. This method boasts significant advantages such as high modeling efficiency, precise volume fraction control, stable and reliable calculation, wide applicability, and ease of automation.

Description

Technical Field

[0001] This invention relates to the field of thermal protection materials technology, and in particular to a method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel grids. Background Technology

[0002] Multiphase composite materials have complementary components, possessing superior properties not found in traditional materials, such as light weight, high specific strength, high specific modulus, and strong designability. Therefore, they are widely used in aerospace and other fields. For example, gas-solid two-phase materials such as foam materials are widely used in thermal protection due to their excellent heat insulation capabilities.

[0003] The macroscopic properties of materials depend on their microstructural characteristics, such as the size of the microstructure, the properties of the base material, and the distribution and proportion of each phase in the microstructure. The quantitative relationship between the macroscopic properties and microstructure of materials has always been an important topic of interest for many researchers. Establishing a microstructural model of the phase distribution of multiphase composite materials and performing numerical calculations based on this model is a crucial method for linking the macroscopic properties and microstructure of materials. Traditional microstructural modeling methods require first establishing a geometric model of the microstructure and then meshing it. When the microstructure is very complex, not only is modeling difficult, but meshing may also fail. Even if a mesh is generated by reducing the mesh size, the number of meshes becomes enormous, increasing the computational burden.

[0004] Existing modeling techniques for the random microstructure of heterogeneous materials mostly rely on probability distribution functions and pseudo-random numbers to assign element properties. While these techniques can construct randomly distributed microstructure models, they lack a standardized workflow that directly integrates with voxel meshes and do not provide a corresponding system for periodic temperature boundary loading and equivalent thermal conductivity calculation for heat transfer performance analysis. Additionally, there are matrix sequence-based finite element modeling methods for composite materials. These methods achieve phase separation by matching template models with matrix sequences and are primarily used for modeling reinforced structures such as particles, fibers, and lattices. However, they do not offer a complete solution for the integrated analysis of the random microstructure and heat transfer performance of multiphase composite materials.

[0005] Therefore, there is an urgent need for an integrated analysis method that does not require pre-built geometric models, has controllable mesh rules, can achieve rapid modeling by directly assigning voxel mesh attributes, and can complete the solution of periodic temperature boundary loading and heat transfer performance. This method can overcome the shortcomings of traditional methods, such as difficult modeling, difficult mesh generation, and large computational load, and meet the needs of efficient design and accurate thermal performance characterization of multiphase composite materials.

[0006] In view of this, the present invention is proposed. Summary of the Invention

[0007] The purpose of this invention is to provide a method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes. This method solves the problem of complex microstructure modeling and mesh generation of multiphase composite materials in the prior art. At the same time, by combining standardized periodic temperature boundary conditions and finite element solution, the equivalent heat transfer performance of the material can be accurately obtained.

[0008] In a first aspect, the present invention provides a method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes, comprising the following steps: Establish a voxelized representative volumetric unit model for characterizing the microstructure of multiphase composite materials; A representative volume element is divided into a uniformly structured voxel mesh to obtain multiple mesh elements of the same size. Count the total number of grid cells and store the grid cells in an array in ascending order of their numbers; For each grid cell, a random number between 0 and 1 is matched, and the random number is stored in the corresponding array position; Based on the preset volume fractions of each phase in the multiphase composite material, a1, a2, ..., a... n Within the range of random numbers 0 to 1, sequentially divide the data into continuous non-overlapping intervals: (0, a1), (a1, a1+a2), ..., (a1+a2+...+a1). n-1 a1+a2+…+a n By assigning material properties of the corresponding phase to mesh elements whose random numbers fall within the corresponding interval, a multiphase composite material finite element model is constructed. Through a strict matching method between 0 and 1 random numbers and the volume fraction interval, precise assignment of material properties for each phase is achieved, allowing for strict control of a1, a2…a… n The volume fraction of each phase ensures both the randomness of the microstructure and the homogeneity of the macrostructure, resulting in high modeling accuracy and strong repeatability. Periodic temperature boundary conditions are applied to the finite element model, and the temperature field and heat flux density are obtained through finite element solution, thereby calculating the equivalent heat transfer performance of the multiphase composite material.

[0009] This invention eliminates the need for pre-constructing complex geometric models, directly achieving multiphase composite material modeling based on uniformly structured voxel meshes. The meshes are regular, of high quality, and free from distortion, eliminating the need for repeated adjustments to mesh parameters. Furthermore, the mesh size is controllable, significantly reducing the modeling difficulty of complex microstructures such as randomly distributed pores and multiphase mixtures, thereby significantly improving modeling efficiency and success rate. It also avoids mesh generation failures due to structural complexity and prevents a surge in computational load caused by excessive mesh refinement, thus balancing computational accuracy and efficiency.

[0010] As a preferred embodiment of this technical solution, the representative volumetric unit model of the voxelization is a cube model.

[0011] As a preferred embodiment of this technical solution, the size of the mesh unit is no greater than 1 / 100 of the size of the representative volume unit model.

[0012] In a preferred embodiment of this technical solution, the total number of grid cells is calculated as e_total, and the grid cells are sorted in ascending order of their numbers.

[0013] As a preferred embodiment of this technical solution, a two-dimensional array with dimension e_total×2 is established. e_num Store the grid numbers in order into the first column of the array, that is... e_num (n) i ,1)= e i n i For the grid cell order, n i =1,2,...,e_total e i For the nth i The grid number.

[0014] In a preferred embodiment of this technical solution, a random number within the range of 0 to 1 is matched for each grid cell and stored in the second column of the array, i.e. e_num (n) i ,2)=rand(0,1),rand(0,1) means to generate a random number between 0 and 1, then each grid e_ num (n) i ,1) with a random number e_num (n) i ,2) Matching.

[0015] In a preferred embodiment of this technical solution, for the n-phase composite material, the volume fraction of each phase is a1, a2…a… n ,but e_num (n) i ,2) (0,0+a1) mesh element e_num (n) i 1) The material property is the first phase. e_num (n) i ,2) Mesh element of (a1, a1+a2) e_num (n) i 1) The material property is the second phase, ... e_num (n) i ,2) (a1+a2+…a) n-1 ,a1+a2+…a n ) grid cells e_num (n) i ,1) The material property is the nth phase.

[0016] As a preferred embodiment of this technical solution, the periodic temperature boundary conditions include: applying periodic temperature constraints to the nodes in the relative planes in the x, y, and z directions and the corresponding edge nodes, and applying constant temperature constraints to the vertices of the model.

[0017] This invention employs strict periodic temperature constraints and constant vertex temperature loading to ensure consistent boundary conditions of the unit cell model. It can accurately solve for the equivalent thermal conductivity, temperature field, and heat flux density in the x, y, and z dimensions, meeting the requirements for accurate characterization of aerospace thermal protection materials.

[0018] As a preferred embodiment of this technical solution, the total heat flux, cross-sectional area, and unit cell length in the x, y, and z directions are extracted by finite element calculation, and the equivalent thermal conductivity in the corresponding directions is obtained by solving.

[0019] As a preferred embodiment of this technical solution, the formula for calculating the equivalent thermal conductivity is: k i = ( i = x, y, z ) q i for i Average heat flux density at the directional heat flow output surface , S i for i Directional unit cell cross-sectional area, Q i for i The sum of the heat flux output from all nodes of the directional heat flux output surface can be extracted from the finite element analysis results. l i for i Directional unit cell length 。

[0020] As a preferred embodiment of this technical solution, the multiphase composite material includes any n-phase random uniformly mixed composite material such as gas-solid two-phase foam material.

[0021] Secondly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0022] This invention is based on a clear and standardized logic of grid numbering, two-dimensional arrays, and random number matching. It is easy to write computer programs to achieve fully automated modeling and calculation, which greatly reduces the cost of manual operation and is suitable for engineering batch applications.

[0023] The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes of the present invention has at least the following beneficial effects: This invention establishes a voxelized representative volume element model for characterizing the microstructure of multiphase composite materials, and divides the representative volume element into a uniformly structured voxel mesh. Material property assignment to the mesh elements is achieved directly based on random numbers and volume fraction interval matching. This allows for the rapid generation of multiphase composite material finite element models without the need for pre-constructing complex geometric models, effectively solving the problems of difficult modeling of complex microstructures, easy mesh distortion and failure in mesh generation, and high computational costs due to excessive mesh numbers in traditional methods. Furthermore, by combining standardized periodic temperature boundary conditions with finite element solutions, the equivalent heat transfer performance of materials can be accurately obtained, realizing an integrated process of modeling and heat transfer performance analysis. This invention boasts significant advantages such as high modeling efficiency, precise volume fraction control, stable and reliable calculation, wide applicability, and ease of automation, meeting the needs of efficient design and accurate performance characterization of multiphase thermal protection materials in aerospace and other fields. Attached Figure Description

[0024] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating the steps of the method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes in this embodiment of the invention. Figure 2 This is a schematic diagram of the structure of the foam material in an embodiment of the present invention; Figure 3 This is a two-dimensional finite element model diagram from an embodiment of the present invention; Figure 4 This is a schematic diagram of the periodic temperature boundary conditions in an embodiment of the present invention. Figure 1 ; Figure 5 This is a schematic diagram of the periodic temperature boundary conditions in an embodiment of the present invention. Figure 2 ; Figure 6 This is a temperature distribution cloud map of the foam material in an embodiment of the present invention; Figure 7 This illustrates the relationship between the thermal conductivity of the foam material and its porosity in an embodiment of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. 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.

[0027] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0028] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0029] Example 1 like Figure 1-7 As shown in the figure, the method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes in this embodiment specifically includes the following steps: Step 1: Establish a voxelized representative volumetric unit model to characterize the microstructure of multiphase composite materials. The model is generally a cube with a sufficiently large size. Taking foam materials as an example, foam materials are gas-solid two-phase materials with pores randomly distributed in the matrix, exhibiting macroscopic homogeneity. The matrix material is silicon carbide with a porosity of α, and its structure is as follows: Figure 2 As shown.

[0030] The representative volumetric unit model of foam material is a two-dimensional model with both length and width L. Step 2: Perform uniform structured voxel meshing on the representative volume unit to obtain multiple mesh units of the same size. The size of each mesh unit is no larger than 1 / 100 of the size of the representative volume model to ensure the accuracy of microstructure characterization. Step 3: Count the total number of grid cells e_total, sort the grid cells in ascending order of their numbers and store them in an array; Step 4: Create a two-dimensional array e_num with dimension e_total×2, and store the grid numbers in order in the first column of the array, i.e., e_num(n i ,1)=e i n i For the grid cell order, n i =1,2,...,e_total,e i For the nth i The grid number; For each grid cell, a random number between 0 and 1 is matched and stored in the second column of the array, namely e_num(n). i ,2)=rand(0,1), rand(0,1) means to generate a random number between 0 and 1, then each grid e_num(n i ,1) and a random number e_num(n) i ,2) Matching; Step 5: Based on the preset volume fractions of each phase in the multiphase composite material, a1, a2…a… n Within the range of random numbers 0 to 1, sequentially divide the data into continuous non-overlapping intervals: (0, a1), (a1, a1+a2), ..., (a1+a2+...+a1). n-1 a1+a2+…+a n ), assigning the material properties of the corresponding phase to the mesh elements whose random numbers fall into the corresponding interval, and constructing a finite element model of multiphase composite materials; In this embodiment, the foam material is a two-phase composite material. The solid phase volume fraction is set as a1, and the gas phase volume fraction as a2, satisfying a1 + a2 = 1. Mesh elements with random numbers falling within the interval (0, a1) are assigned silicon carbide solid phase properties, and mesh elements with random numbers falling within the interval (a1, 1) are assigned air gas phase properties, thus completing the construction of the two-phase finite element model. Figure 3 As shown; Step 6: Apply periodic temperature boundary conditions to the finite element model, obtain the temperature field and heat flux density through finite element solution, and then calculate the equivalent heat transfer performance of the multiphase composite material. The periodic temperature boundary conditions include: applying periodic temperature constraints to the nodes in the relative planes in the x, y, and z directions and the corresponding edge nodes, and applying constant temperature constraints to the vertices of the model to complete the boundary loading; The temperature field and heat flux density are obtained through finite element analysis. The total heat flux, cross-sectional area and unit cell length in each direction are extracted. The equivalent thermal conductivity in the corresponding direction is obtained by solving the equivalent thermal conductivity formula.

[0031] The application of periodic temperature boundary conditions in this embodiment is illustrated as follows: Figure 4-5 As shown, its loading equation is:

[0032] In the above formula, T i express i Temperature at point x 1 、x 2 is x The nodes corresponding to the inner faces of both sides of the plane (excluding points on the sides), y 1 、y 2 is y The nodes corresponding to the inner faces of both sides of the plane (excluding points on the sides), z 1 、z 2 is z The nodes corresponding to the two sides of the face (excluding points on the sides); x d 、x c These are the nodes corresponding to edges 34 and 78 (excluding vertices 3, 4, 7, and 8). x a 、x b These are the nodes corresponding to edges 12 and 56 (excluding vertices 1, 2, 5, and 6); y d 、y c These are the nodes corresponding to edges 48 and 37 (excluding vertices 3, 4, 7, and 8). y a 、y b These are the nodes corresponding to edges 15 and 26 (excluding vertices 1, 2, 5, and 6); z d 、z c For the nodes corresponding to edges 58 and 67 (excluding vertices 5, 6, 7, and 8), z a 、z b These are the nodes corresponding to edges 14 and 23 (excluding vertices 1, 2, 3, and 4); By applying the above set of equations to the finite element model, and given the temperature values ​​of the four vertices at positions 1, 2, 5, and 4, boundary conditions with different temperature loading modes can be applied. This can be achieved by determining the boundary conditions along the surface of the unit cell. x, y, zTemperature difference Δ in three directions T x 、 Δ T y 、 Δ T z It is possible to solve for the surface of the unit cell along... x, y, z Thermal conductivity in three directions k x 、k y 、k z The formula for calculating thermal conductivity is: k i = ( i = x, y, z ) In the formula, q i for i Average heat flux density at the directional heat flow output surface , S i for i Directional unit cell cross-sectional area, Q i for i The sum of the heat flux output from all nodes of the directional heat flux output surface can be extracted from the finite element analysis results. l i for i Directional unit cell length.

[0033] In this embodiment, the periodic temperature boundary condition of the foam material is two-dimensional, and the periodic temperature boundary loading equation can be simplified as follows:

[0034] In the above formula, T i express i Temperature at point x a 、x b These are the nodes corresponding to edges 12 and 56 (excluding vertices 1, 2, 5, and 6); y a 、y b These are the nodes corresponding to edges 15 and 26 (excluding vertices 1, 2, 5, and 6); By loading the above equations onto the unit cell model, and given the temperature values ​​of the three vertices at positions 1, 2, and 5, boundary conditions can be applied under different temperature loading modes. This can be achieved by determining the boundary conditions along the unit cell surface. x, y Temperature difference Δ in directionT x 、 Δ T y It is possible to solve for the surface of the unit cell along... x, y Thermal conductivity in the direction k x 、k y The formula for calculating thermal conductivity is: k i =- ( i = x, y ) In the formula, Q i for i The sum of the heat flux output from all nodes of the directional heat flux output surface can be extracted from the finite element calculation results.

[0035] Figure 6 and Figure 7 The temperature distribution cloud map and the relationship between thermal conductivity and porosity of the foam material were obtained in this embodiment.

[0036] Example 2 This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method of Embodiment 1.

[0037] In summary, based on the modeling and numerical calculation requirements of multiphase composite materials, and addressing the difficulties in modeling and meshing complex microstructures of multiphase composite materials, this invention proposes a voxel-mesh-based method for modeling and analyzing the heat transfer performance of multiphase composite materials. By establishing a representative volumetric model, dividing the structured mesh, and directly modifying the material properties of corresponding phase mesh elements, a microstructure model of the multiphase composite material is obtained. Periodic temperature boundary conditions are then applied, and the heat transfer performance of the composite material is solved. This method solves the difficulties in modeling complex microstructures and meshing of multiphase composite materials in existing technologies.

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes, characterized in that, Includes the following steps: Establish a voxelized representative volumetric unit model for characterizing the microstructure of multiphase composite materials; A representative volume element is divided into a uniformly structured voxel mesh to obtain multiple mesh elements of the same size. Count the total number of grid cells and store the grid cells in an array in ascending order of their numbers; For each grid cell, a random number between 0 and 1 is matched, and the random number is stored in the corresponding array position; According to the preset volume fractions a1, a2, …, a n , the continuous non-overlapping intervals (0, a1), (a1, a1+a2), …, (a1+a2+…+a n-1 , a1+a2+…+a n ) are sequentially divided in the range of 0-1 random number, the grid cells falling into the corresponding interval are assigned with the material properties of the corresponding phase, and a finite element model of the multi-phase composite material is constructed. Periodic temperature boundary conditions are applied to the finite element model, and the temperature field and heat flux density are obtained through finite element solution, thereby calculating the equivalent heat transfer performance of the multiphase composite material.

2. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 1, characterized in that, The representative volumetric unit model for voxelization is a cube model.

3. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 1, characterized in that, The size of the mesh cell is no greater than 1 / 100 of the size of the representative volume cell model.

4. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 1, characterized in that, The total number of grid cells is calculated to be e_total, and the grid cells are sorted in ascending order of their numbers.

5. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 4, characterized in that, Create a two-dimensional array with dimension e_total×2. e_num Store the grid numbers in order into the first column of the array, that is... e_num (n) i ,1)= e i n i For the grid cell order, n i =1,2,...,e_total e i For the nth i The grid number.

6. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 5, characterized in that, For each grid cell, a random number between 0 and 1 is matched and stored in the second column of the array. e_num (n) i ,2)=rand(0,1),rand(0,1) means to generate a random number between 0 and 1, then each grid e_num (n) i ,1) with a random number e_num (n) i ,2) Matching.

7. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 6, characterized in that, For an n-phase composite material, the volume fraction of each phase is a1, a2…a… n ,but e_num (n) i ,2) (0,0+a1) mesh element e_num (n) i 1) The material property is the first phase. e_num (n) i ,2) Mesh element of (a1, a1+a2) e_ num (n) i 1) The material property is the second phase, ... e_num (n) i ,2) (a1+a2+…a) n-1 , a1+a2+…a n ) grid cells e_num (n) i ,1) The material property is the nth phase.

8. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 1, characterized in that, The periodic temperature boundary conditions include: applying periodic temperature constraints to the nodes in the relative planes in the x, y, and z directions and the corresponding edge nodes, and applying constant temperature constraints to the vertices of the model.

9. The method for modeling and analyzing the heat transfer performance of multiphase composite materials based on voxel meshes according to claim 8, characterized in that, The total heat flux, cross-sectional area, and unit cell length in the x, y, and z directions are extracted by finite element method, and the equivalent thermal conductivity in the corresponding directions is obtained by solving.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-9.

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