Method for generating pore structure and predicting permeability of anisotropic fibrous material

Abstract

The present invention provides a method for generating a pore structure and predicting permeability of an anisotropic fibrous material.SOLUTION: A single fiber rod model is established according to structural characteristic parameters such as the zenith angle θ and the circumferential angle φ of the fiber material, the process of establishing the single fiber rod is repeated until the target porosity ε of the material is reached, the allowable minimum gap dgap between the fibers and the maximum number of iterations Nmax are used as constraints in this process, and then a finite volume simulation program created based on the open source fluid dynamics library OpenFOAM is used to simulate and predict the permeability of the generated anisotropic fiber material. In addition to generating the pore scale characterization structure of the fiber material, the present invention can develop a prediction method of the permeability of the fiber material in combination with the finite volume method, quantitatively analyze the influence of structural parameters on the permeability, and provide a reference for the design and manufacture of the fiber material.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention belongs to the technical field of fibrous materials, and more particularly to a method for predicting the formation of pore structures and permeability of anisotropic fibrous materials. [Background technology]

[0002] Fiber materials have advantages such as large specific surface area, low volume density, high impact resistance, and flexible structural design. They are widely used in various fields, including thermal protection for high-speed supersonic aircraft, ultra-low energy consumption and energy-saving buildings, wind power generation, and solar thermal utilization. Permeability, as a key parameter characterizing the flow characteristics within fiber materials, is a core parameter affecting the performance of material processes. Rapid and accurate prediction of permeability is fundamental for the design and application of fiber materials.

[0003] Experimental measurements, calculations using empirical formulas, and simulations are currently the main methods for obtaining the permeability of fibrous materials. Experimental methods are the most direct and accurate, but they are expensive to implement and a single experimental result is only valid for one type of material. Empirical formulas are only applicable to isotropic materials, so their scope of use is limited. In contrast, simulation-based permeability prediction methods have the advantages of short implementation cycles, low implementation costs, and a wide range of applications, and have become more commonly used in recent years.

[0004] Permeability is closely related to material structure characteristics, and accurately establishing a geometric model that characterizes the material structure characteristics is a prerequisite for ensuring the accuracy of permeability simulation results. After the fiber structure modeling is complete, meshing is performed on the geometric model to achieve discretization of the calculation domain, and then simulation methods such as finite element or finite volume can be used to predict the permeability of the fiber material.

[0005] Currently, scanning imaging reconstruction technology is the most accurate material structure modeling method, but the post-processing method for this method is complicated. Another method is to create a program to virtually generate the fiber pore structure based on an understanding of the material structure. This method has advantages such as fast modeling speed and flexible operation, and has developed rapidly in recent years. However, most modeling programs currently can only generate isotropic fiber structures and are not applicable to predicting the permeability of anisotropic fiber materials. Therefore, it is necessary to establish a method for generating the pore structure of anisotropic fiber materials and predict its permeability, investigate the influence of the anisotropic structural characteristics of the material on permeability, and provide guidance for material structural design. Summary of the Invention [Problem to be solved by the invention]

[0006] The objective of the present invention is to provide a method for predicting the generation of pore structure and permeability of anisotropic fibrous materials, which realizes accurate modeling of anisotropic pore structure and rapid and highly accurate prediction of the permeability of materials, shows the influence of the anisotropic structural characteristics of fibrous materials on their permeability performance, and enriches the structural design theory of fibrous materials. [Means for solving the problem]

[0007] A method for predicting the formation of pore structure and permeability of anisotropic fibrous materials is provided, Step 1: setting the size of the calculation domain and the basic parameters of the fiber material; Minimum allowable spacing between fibers d gap and the maximum number of iterations N max Step 2: setting structure generation control parameters including Step 3: Generate the zenith angle θ and fit it to a von Mises distribution; Step 4: generating the inscribed angle φ and fitting it to a uniform random distribution; Step 5: generating a straight line l0 through the system coordinate system origin O, with θ and φ as the zenith angle and the inscribed angle; Within the calculation domain, there is a point P(X p ,Y p ,Z p) and translate the line l0 along a vector OP to generate a new line l; The straight line l is the center line, and d f Generate cylindrical fiber rods with a diameter of , and the minimum distance between the fiber rods is d i Calculate d i and d gap Determine the magnitude relationship between d i ≦d gap And N i <N max If , regenerate the current fiber rod and N i is the current iteration number, and N max is the maximum number of iterations, and d i ≦d gap And N i ≧N max In the case of , clear all fiber rod data and regenerate the structure, and d i >d gap In this case, the currently generated fiber rod is considered valid and its volume V i Calculate and record the total fiber volume within the calculation area.

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[0008] Furthermore, in step 1, the basic parameters of the fiber material are the length L of the calculation domain X , width L Y , height L Z , fiber diameter d f and material porosity ε, and the volume V of the calculation domain c =L X L Y L Z and establish a system coordinate system XYZ along the length, width and height directions at the vertices of the calculation area, and set the origin of the coordinate system as O.

[0009] In step 3, the probability density function of the von Mises distribution is of the form:

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[0010] Furthermore, in step 4, for the inscribed angle φ∈[0,π), an inscribed angle is generated in the XY plane:φ=2πR φ , where R φ is the uniform random distribution function of the inclined angle, and has a value between 0 and 1.

[0011] Furthermore, in step 5, the zenith angle of the line is θ, i.e., the angle between the line and the Z axis, and the circumferential angle is φ, i.e., the angle between the projection of the line onto the XY plane and the X axis. In the XYZ coordinate system, a line equation of the line 10 is established as X / m=Y / n=Z / k. In step 6, the point P(X P ,Y P ,Z P ) is randomly generated and the linear equation is of the form (XX P ) / m=(YY P ) / n=(ZZ P ) / k.

[0012] Furthermore, in step 7, the minimum distance d between the fiber rods in step 7 i is calculated by the following formula:

number

[0013] Furthermore, in step 9, after the structure meets the target porosity requirements, the generated structure is subjected to smoothing post-processing in the open source CAD software FreeCAD, and then self-adaptive mesh generation is performed on the generated structure using the open source mesh generation tool SnappyHexMesh.

[0014] Furthermore, the specific steps of step 10 are as follows: first, the generated mesh file is introduced into the finite volume simulation program; then, a discrete format is selected to set the calculation parameters; the convection term in the momentum equation is discretized in a first-order headwind format; based on the Gaussian theory discrete diffusion term, a central difference interpolation format is adopted to perform mesh non-orthogonal correction; a light systolic solver is adopted to perform momentum prediction; a multi-mesh solver is adopted to solve the pressure Poisson equation; and finally, the inlet pressure and outlet pressure are respectively calculated as p inlet and p outlet Then, the simulation is performed and the material thickness direction, i.e., the velocity U min in the Z-axis direction, is calculated based on the simulation results. Z and obtain the permeability K through the thickness of the material according to Duchy's law. zz =μU Z / (p inlet -p outlet ) where μ is the dynamic viscosity of the fluid.

[0015] Furthermore, in the process of solving the pressure Poisson equation, the solution rate and pressure relaxation factor were both set to 0.7, and the convergence residuals were both set to 1 × 10 -6 Set as.

[0016] Furthermore, the set inlet pressure p inlet is the outlet pressure p outlet is greater than. [Effects of the Invention]

[0017] According to the above technical solution, the present invention creates a virtual generation program, adopts the von Mises distribution to characterize the non-uniform distribution characteristics of fibers, establishes a geometric model of the pore structure of anisotropic fiber materials, and develops a permeability simulation program for fiber materials based on the finite volume method. By comparing the permeability prediction results with those of empirical formulas, the accuracy of the established geometric model and permeability simulation program can be verified. The established geometric model can be used as an input file to obtain permeability data for such materials through the simulation program.

[0018] For anisotropic fibrous materials, the present invention provides a complete solution including pore structure modeling and permeability prediction, which can provide data support for structural design and evaluation in related technical fields.

[0019] The above description is only an outline of the technical solution of the present invention. In order to make the technical solution of the present invention more clearly understood and be able to implement it in accordance with the content of the specification, the preferred embodiments of the present invention will be described in detail below in combination with the drawings. [Brief explanation of the drawings]

[0020] [Figure 1] 1 is a flowchart of a method for generating anisotropic fiber material structures and predicting permeability. [Figure 2] The different characteristic values ​​κ are the corresponding probability density functions of the von Mises distribution. [Figure 3] Pore ​​structures of fibrous materials produced with different property values ​​κ: (a) κ=5, (b) κ=50. [Figure 4] Comparison of the geometric model of the anisotropic fiber material generated by the present invention with SEM images of the actual fiber material. (a) and (c) are the through-thickness fiber arrangements when κ = 0.5 and κ = 50, respectively. (b) and (d) are through-thickness SEM images of ceramic insulation when ρ = 100 kg / m3 and ρ = 200 kg / m3, respectively. [Figure 5]1A and 1B are geometric models of anisotropic fiber materials generated in accordance with the present invention, where (a) κ=1 and (b) κ=100. [Figure 6] This is a comparison of the predicted permeability of fibrous materials and the calculated value using an empirical formula. DETAILED DESCRIPTION OF THE INVENTION

[0021] The present invention will be further described below with reference to the drawings and specific examples, but the scope of protection of the present invention is not limited thereto.

[0022] As shown in FIG. 1, this embodiment provides a method for predicting the generation and permeability of pore structure of anisotropic fibrous materials, Step 1: setting the size of the calculation domain and the basic parameters of the fiber material; Step 2: setting structure generation control parameters; Step 3: Generate the zenith angle θ and fit it to a von Mises distribution; Step 4: generating the inscribed angle φ and fitting it to a uniform random distribution; Step 5: generating a straight line l0 through the system coordinate system origin O, with θ and φ as the zenith angle and the inscribed angle; Within the computational domain, a point P(X P ,Y P ,Z P ) and translate the line l0 along a vector OP to generate a new line l; The line l is the center line, and d f Generate cylindrical fiber rods with a diameter of , and the minimum distance between the fiber rods is d i Step 7: Calculate Porosity ε in the current calculation domain i and a step 8 of determining the magnitude relationship between the target porosity ε; Step 9: post-processing the geometry and dividing the mesh; and step 10 of setting boundary conditions and predicting permeability.

[0023] The present invention provides a method for generating the pore structure and predicting the permeability of anisotropic fibrous materials. Compared with model reconstruction techniques based on scanning imaging, the developed virtual structure generation method offers the advantages of greater flexibility, controllable structural parameters, and simple model post-processing. Compared with experimental testing methods, the developed permeability prediction method offers the advantages of lower implementation costs, lower material costs, and faster prediction speed, as well as a wider range of application than empirical calculation methods.

[0024] The specific steps of this method are steps 1 to 10 below.

[0025] 1. Set the size of the calculation domain and the basic parameters of the fiber material.

[0026] The basic parameters of the fiber material are the length of the calculation domain, L X , width L Y , height L Z , fiber diameter d f and the volume of the computational domain, V, including the material porosity ε. c =L X L Y L Z Record the values ​​and establish a system coordinate system XYZ along the length, width and height directions at the vertices of the calculation domain, and let O be the origin of the coordinate system.

[0027] 2. Set configuration generation control parameters.

[0028] The structural generation control parameter is the minimum allowable spacing between fibers, d gap and the maximum number of iterations N max d gap The function of N is to prevent the distance between fibers from being too small, which will affect the quality of the subsequent mesh system. max The effect of is to prevent the program from going into an endless cycle due to an abnormality.

[0029] 3. Generate the zenith angle θ and fit it to the von Mises distribution. Here, the formula for the zenith angle θ is as follows: θ=arccos(1-2R θ ) where R θ is a uniform random distribution function of the zenith angle, and its value ranges from 0 to 1.

[0030] The von Mises distribution has good mathematical controllability and is often applied to directional statistics. Its probability density function has the form

number

[0031] 4. Generate the inscribed angle φ and match it to a uniform random distribution.

[0032] The above inscribed angle φ∈[0,π). Generate an inscribed angle in the XY plane: φ=2πR φ where R φ is the uniform random distribution function of the inclined angle, and has a value between 0 and 1.

[0033] 5. Generate a straight line l0 through the origin O of the system coordinate system, with θ and φ as the zenith angle and the circular angle.

[0034] The zenith angle of the line (the angle between the line and the Z axis) is θ, and the inscribed angle (the angle between the projection of the line onto the XY plane and the X axis) is φ, establishing the line equation X / m=Y / n=Z / k for the line l0 in the XYZ coordinate system.

[0035] 6. A point P(X P , Y P , Z P ) is randomly generated, and the line l0 is translated along the vector OP to generate a new line l, and the equation of the line l is (XX P ) / m=(YY P ) / n=(ZZ P ) / k.

[0036] A straight line is created based on the zenith angle, and the equation of the line in the system coordinate system is as follows:

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[0037] 7. The line l is the center line, and d f Generate cylindrical fiber rods with a diameter of , and the minimum distance between the fiber rods is d i Calculate.

[0038] If the spacing between non-intersecting fiber rods is too small, it will affect the quality of the subsequent mesh system and make it difficult to generate the mesh. Therefore, after generating one fiber rod, it is necessary to determine the distance between other fiber rods. Based on the fiber diameter and the fiber rod centerline linear equation, the minimum distance d between the generated fiber rods is calculated. i The minimum distance calculation formula is as follows:

number

[0039] d i and d gap Determine the magnitude relationship between d i ≦d gap And Ni <N max and N i If is the current iteration number, regenerate the current fiber rod, and d i ≦d gap And N i ≧N max If so, clear all fiber rod data and regenerate the structure, and i >d gap If i Calculate and record the total volume of all fibers in the calculation area.

number

[0040] 8. Porosity ε in the current calculation domain i and the target porosity ε.

[0041] The generated fiber cylinders are then judged to see if they meet the target porosity requirement. i If > ε, save the current fiber rod data and continue to generate the next fiber rod, and ε i If ≦ε, the current structure is considered to satisfy the requirements, the cylinder surface is divided into triangular elements, and the fiber structure within the calculation domain is output as an STL file.

[0042] 9. Post-process the geometry and split the mesh.

[0043] After the structure meets the target porosity requirements, the generated geometric structure must be smoothed to reduce sharp edges and facilitate subsequent meshing. This post-smoothing process is performed in the open-source CAD software FreeCAD, using a Laplacian smoothing algorithm. Next, the structure is subjected to self-adaptive meshing using the open-source meshing tool SnappyHexMesh.

[0044] Figure 3 shows the pore structure of the fiber material produced for different values ​​of κ, where the calculation domain is a cube with a side length of 500 μm, the target porosity is 95%, and the diameter of the fiber rod is 10 μm.

[0045] Figure 4 shows a comparison of the geometric models of fiber structures generated with different κ values ​​with SEM images of the actual fiber material. By adjusting the κ value, we were able to simulate and construct the pore-scale structure of the fiber material at different densities. As a result, the virtual structure closely resembled the actual structure, enabling us to characterize the pore features of the material in three-dimensional space.

[0046] 10. Set boundary conditions and predict permeability.

[0047] A finite volume simulation program was developed based on the open-source fluid mechanics library OpenFOAM. The SIMPLE algorithm was used to solve the steady-state momentum equation of the fluid. The velocity field within the calculation domain was obtained through iterative calculations, and Darcy's law was used to calculate the permeability. The generated mesh file was first imported into the simulation program. A discrete format was then selected to set the calculation parameters. The convection term in the momentum equation was discretized using a first-order headwind format. Based on Gaussian theory, a central difference interpolation format was used to perform mesh non-orthogonal correction. A light system solver was used to predict the momentum. A multi-mesh solver was used to solve the pressure Poisson equation. The solution velocity and pressure relaxation factors were both set to 0.7, and the convergence residuals were both set to 1×10. -6 Finally, the inlet and outlet pressures are set as p inlet and p outlet The inlet pressure must be greater than the outlet pressure. Run the simulation and calculate the material thickness direction, i.e., the Z-axis direction, as a function of the speed U min. Z and obtain the permeability K through the thickness of the material according to Duchy's law. zz =μU Z / (p inlet -p outlet ) where μ is the dynamic viscosity of the fluid.

[0048] To verify the accuracy of the method in the present invention, we simulated fibrous materials with different porosities and calculated the dimensionless permeability

number

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[0049] The empirical formula proposed by Clague et al. is as follows:

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[0050] Figure 5 shows a geometric model of an anisotropic fiber material. Different κ values ​​represent different degrees of zenith angle concentration. As κ increases, the anisotropic characteristics of the fiber material are strengthened, exhibiting obvious hierarchical stacking characteristics. When κ=1, the material structure approaches isotropy, and when κ=100, the material exhibits obvious anisotropic characteristics. Figure 6 shows the transmittance prediction results for a fiber material with a porosity range of 70% to 90%. The comparison also shows the transmittance simulation results for κ=1 and κ=100. The results show that the material transmittance decreases with increasing κ. Comparing the transmittance simulation results in Figure 6 with the calculation results using the empirical formula of Woudberg and Clague et al. reveals that the error is small and within the acceptable range, verifying the accuracy of the fiber material geometric model and transmittance prediction method of the present invention.

[0051] The present invention creates a virtual generation program, adopts the von Mises distribution to characterize the non-uniform distribution characteristics of fibers, establishes a geometric model of the void structure of anisotropic fiber materials, and develops a fiber material permeability simulation program based on the finite volume method. By comparing the permeability prediction results with those of empirical formulas, the accuracy of the established fiber material geometric model and permeability simulation program can be verified. The established fiber material geometric model can be used as an input file to obtain permeability data of such materials through the simulation program.

[0052] For anisotropic fibrous materials, the present invention provides a complete solution including pore structure modeling and permeability prediction, which can provide data support for structural design and evaluation in related technical fields.

[0053] The above examples are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any improvements, substitutions, or modifications that can be made by those skilled in the art without departing from the gist of the present invention are all within the protection scope of the present invention.

Claims

1. Step 1: setting the size of the calculation domain and basic parameters of the fiber material; Minimum allowable spacing between fibers d ｇａｐ and the maximum number of iterations N ｍａｘ Step 2: setting structure generation control parameters including Step 3: Generate the zenith angle θ and fit it to a von Mises distribution; Step 4: generating the inscribed angle φ and fitting it to a uniform random distribution; A straight line l passes through the origin O of the system coordinate system, and θ and φ are the zenith angle and the circular angle. ０ Step 5 of generating Within the calculation area, there is a point P(X Ｐ , Y Ｐ , Z Ｐ ) is randomly generated, and the line l is drawn along the vector OP. ０ Step 6: translating the line l to generate a new line l; The straight line l is the center line, and d ｆ Generate cylindrical fiber rods with a diameter of , and the minimum distance between the fiber rods is d ｉ Calculate d ｉ and d ｇａｐ Determine the magnitude relationship between ｉ ≦d ｇａｐ And N ｉ <N ｍａｘ If , the current fiber rod is regenerated, and N ｉ is the current iteration number, and N ｍａｘ is the maximum number of iterations, and d ｉ ≦d ｇａｐ And N ｉ ≧N ｍａｘ In the case of , all fiber rod data is cleared and the structure is regenerated. ｉ >d ｇａｐ In this case, the currently generated fiber rod is considered valid, and its volume V ｉ Calculate and record the total fiber volume within the calculation area. [0011] where M is the number of currently generated fibers and ε ｉ = 1 - V ｆ / V ｃ Calculate and store V ｃ is the volume of the computational domain, Step 7; The porosity ε in the current calculation domain ｉ and the target porosity ε, and ｉ If ε > ε, save the current fiber rod data and continue to generate the next fiber rod; ｉ Step 8: if ε≦ε, the current structure is considered to meet the requirements, and the cylindrical surface of the fiber rod is divided into triangular elements, and the fiber structure in the calculation domain is output as an .stl file; Step 9: performing post-smoothing processing on the generated structure in the open source CAD software FreeCAD, and then performing self-adaptive meshing on the generated structure using the open source meshing tool SnappyHexMesh; and step 10 of introducing the generated mesh file into the created finite volume simulation program, setting boundary conditions, and then executing a simulation calculation to predict transmittance. The finite volume simulation program is created based on the open source fluid mechanics library OpenFOAM, solves the steady momentum conservation equation of the fluid using the SIMPLE algorithm, obtains the velocity field within the calculation domain through iterative calculation, and calculates the permeability using Darcy's law. This is a method for predicting the generation of pore structure and permeability of anisotropic fibrous materials, characterized in that

2. In step 1, the basic parameters of the fiber material are the length L of the calculation domain Ｘ , width L Ｙ , height L Ｚ , fiber diameter d ｆ and material porosity ε, and the volume V of the calculation domain ｃ =L Ｘ L Ｙ L Ｚ and establish a system coordinate system XYZ along the length direction, width direction and height direction at the vertices of the calculation domain, and set the origin of the coordinate system as O.

3. In step 3, the probability density function of the von Mises distribution has the form: [0012] where θ∈[0, 2π), λ represents the average value of the zenith angle θ, and I ０ (κ) represents a zero-order modified Bessel function, and κ is a characteristic value for evaluating the degree of concentration at the zenith angle θ. When κ approaches 0, the probability density function approaches a uniform distribution. When κ approaches ∞, the distribution of the probability density function approximates a Gaussian distribution with a mean value of λ and a variance of 1 / κ. The formula for the zenith angle θ is θ = arccos(1-2R θ ), where R θ is a uniform random distribution function of the zenith angle, and its value ranges from 0 to 1.

4. In step 4, for the inscribed angle φ∈[0,π], generate an inscribed angle in the XY plane: φ=2πR φ , where R φ is the uniform random distribution function of the inclined angle, and has a value between 0 and 1.

5. In step 5, the zenith angle of the straight line is θ, i.e., the angle between the straight line and the Z axis, and the circumferential angle is φ, i.e., the angle between the projection of the straight line onto the XY plane and the X axis. In the XYZ coordinate system, the straight line l ０ In step 6, the linear equation X / m=Y / n=Z / k is established, and the point P(X Ｐ , Y Ｐ , Z Ｐ ) is randomly generated, and the linear equation is of the form (X-X Ｐ ) / m=(Y-Y Ｐ ) / n = (Z - Z Ｐ 2. The method for predicting the formation of pore structure and permeability of anisotropic fiber materials according to claim 1, characterized in that the formula is established as follows:

6. The minimum distance d between the fiber rods in step 7 ｉ is calculated by the following formula: [0013] Here, P ｉ P ｊ represents the vector of the line connecting a point on the current fiber centerline and a point on the generated fiber centerline, and D ｉ is the direction vector of the current fiber centerline, and D ｊ The method for predicting the generation of pore structure and permeability of anisotropic fiber materials according to claim 1, characterized in that: is a direction vector of the generated fiber center line.

7. The method for predicting the generation of pore structure and permeability of anisotropic fiber materials according to claim 1, characterized in that the post-smoothing process in step 9 uses a Laplace smoothing algorithm, and the mesh division uses the open source mesh division tool SnappyHexMesh to perform self-adaptive mesh division on the structure.

8. The specific steps of step 10 are as follows: first, the generated mesh file is introduced into the finite volume simulation program; then, a discrete format is selected to set the calculation parameters; the convection term in the momentum equation is discretized in a first-order headwind format; based on the Gaussian theory discrete diffusion term, a central difference interpolation format is used to perform mesh non-orthogonal correction; a light system solver is used to perform momentum prediction; a multi-mesh solver is used to solve the pressure Poisson equation; and finally, the inlet pressure and outlet pressure are calculated as p ｉｎｌｅｔ and p ｏｕｔｌｅｔ and a simulation calculation is performed. Based on the simulation results, the speed U Ｚ and obtain the permeability K in the thickness direction of the material according to Duchy's law. ｚｚ = μU Ｚ / (p ｉｎｌｅｔ -p ｏｕｔｌｅｔ 2. The method for predicting the generation of pore structure and permeability of anisotropic fibrous materials according to claim 1, characterized in that:

9. In the process of solving the pressure Poisson equation, the solution rate and pressure relaxation factor were both set to 0.7, and the convergence residual was set to 1 × 10 －６ 9. The method for predicting the generation of pore structure and permeability of an anisotropic fiber material according to claim 8, wherein the pore structure is set as follows:

10. The set inlet pressure p ｉｎｌｅｔ is the outlet pressure p ｏｕｔｌｅｔ The method for predicting the generation and permeability of pore structure of anisotropic fibrous materials according to claim 8, characterized in that the pore structure generation and permeability are greater than the pore structure generation and permeability of anisotropic fibrous materials according to claim 8.

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