A numerical modeling method and system for sintered metal porous membrane filtration materials

Abstract

The present application relates to the technical field of powder membrane filter element, and particularly relates to a numerical modeling method and system of sintered metal porous membrane filter material, which comprises obtaining powder membrane porosity and particle size distribution; initializing geometric space; generating particle sphere center coordinates and particle size; judging whether newly generated particle spheres overlap with original particle spheres; calculating theoretical total volume; judging the adjacent overlapping relationship between particle spheres, and using an array to record all original particle spheres overlapping with the generated particle spheres; calculating the overlapping volume between the newly generated particle spheres and all original particle spheres; calculating the actual total volume of the total particle spheres and the total porosity; and continuously iterating until the total particle spheres are less than the porosity of the powder membrane, and then stopping iteration. The present application provides a numerical model construction method of real physical microstructure characteristics of the powder membrane, generates an accurate model conforming to the entity structure characteristics of the porous membrane filter material, and is used for simulating the filtering characteristics of the porous material.

Description

Technical Field

[0001] This invention relates to the field of powder membrane filter technology, and in particular to a numerical modeling method and system for sintered metal porous membrane filter materials. Background Technology

[0002] Powder membrane filter elements are porous materials made from metal or alloy powders through pressing and high-temperature sintering. They contain a large number of interconnected or semi-interconnected pores. Their uniform pore structure, porosity, and pore size distribution depend on the powder particle size, forming, and sintering process. They are widely used in filtration and separation, powder fluidized conveying, battery electrodes, and other fields.

[0003] To study the fluid behavior characteristics and filtration properties within the pores of powder membrane filter elements, it is necessary to accurately establish a microscopic geometric model of porous membrane materials. Due to processes such as sintering, the internal particles of metal powder porous materials need to meet both the requirements of internal particle overlap and a certain porosity. Therefore, establishing an efficient, accurate, and practical three-dimensional particle amorphous complex pore model is a key issue in numerical simulation.

[0004] Currently, there are two main methods for constructing models of the microstructure of porous media both domestically and internationally: the computed tomography (CT) reconstruction method used by Huang J et al. (Chemical Engineering Science, 2021) and the densely packed spherical particle algorithm used by A. Elrahmani et al. (Powder Technology, 2022). The CT method obtains a series of two-dimensional cross-sectional slice images from the original three-dimensional computed tomography images, and stacks the two-dimensional cross-sectional images in the vertical direction to reconstruct a three-dimensional model. Although this method can obtain accurate and intuitive existing three-dimensional models of porous media, it is costly and difficult to generalize to general porous media materials. The densely packed particle algorithm uses a set of tangent spheres to construct the porous media model. This method only considers the tangency of the spheres. In the actual sintering process, the geometry of porous media is more complex, with mutual fusion and stacking. Therefore, it is difficult to reflect the microscopic sintering structure existing in real porous media. In addition, the tangent spheres used in this method have a limit to the space occupancy, making it difficult to establish a porous media model with high solid phase (low porosity) and achieve the specified porosity.

[0005] Current research on porous materials of sintered metal powder mainly focuses on experimental studies of their properties. The detailed mechanisms of their filtration and backflushing are still not fully understood. The main difficulty lies in the complex actual working conditions and microstructure. For example, their amorphous and complex pore structure poses a challenge to the establishment of geometric models. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a numerical model construction method for the true physical microstructure characteristics of powder membranes, generating an accurate model that conforms to the physical structural characteristics of porous membrane filtration materials, thereby enabling accurate research on the filtration properties of porous membrane materials.

[0007] The technical solution adopted in this invention is: a numerical modeling method for sintered metal porous membrane filter materials, comprising the following steps:

[0008] Step 1: Obtain scanning electron microscope (SEM) images of the powder film, and perform binarization processing and extract powder particle boundary information;

[0009] Step 2: Obtain the porosity and particle size distribution of the powder film;

[0010] Step 3: Initialize the total number of particles, the initial value of the total volume of space occupied by the particles, and the geometric space to be modeled;

[0011] Step 4: Use a random method to generate the center coordinates and particle size of the spheres in the geometric space to be modeled; and determine the overlap between the newly generated spheres and the original spheres.

[0012] In a preferred embodiment of the present invention, step four specifically includes:

[0013] Step 41: Control the included angle of the tangential surface by controlling the contact depth between the two particles;

[0014] Step 42: Construct a geometric model of the contact depth between the particles;

[0015] In a preferred embodiment of the present invention, the geometric relationship model formula for contact depth is as follows:

[0016]

[0017] Where r1 and r2 are the radii of adjacent overlapping particles, and θ is the tangential angle between the contact points of the two particles.

[0018] Step 43: Limit the contact depth between particles to be greater than the minimum contact depth to obtain a mesh quality that meets the requirements of numerical simulation calculation;

[0019] Step 5: Calculate the theoretical total volume of all the spheres;

[0020] As a preferred embodiment of the present invention, the formula for the theoretical total volume is:

[0021] V l =V i-1 +4 / 3πr 3 (3)

[0022] Where r is the radius of the newly generated particle sphere, V i-1 This represents the volume of space occupied by the original i-1 particles.

[0023] Step 6: Determine the adjacency and overlap relationships between the particles, and use an array to record all the original particles that overlap with the generated particle; use the Monte Carlo method to calculate the overlap volume between the newly generated particle and all the original particles.

[0024] As a preferred embodiment of the present invention, the Monte Carlo method specifically includes:

[0025] Step 61: Based on the diameter and coordinates of the newly generated particle, traverse all the original particles and use an array to record all the original particles that overlap with the newly generated particle.

[0026] Step 62: Generate M uniformly distributed random points in the newly generated particle sphere;

[0027] In a preferred embodiment of the present invention, the coordinates of the random point include:

[0028] Step 621: Randomly sample to generate uniformly distributed random numbers u, v, w;

[0029] Step 622, Calculate w 2 =u 2 +v 2 ;

[0030] Step 633: Calculate the coordinates of the generated random points:

[0031] Step 63: Count the random points in the particles that fall into the array and the newly generated particles, and calculate the overlap volume between the newly generated particles and the original particles.

[0032] In a preferred embodiment of the present invention, the formula for calculating the overlapping volume is:

[0033] v cap =(Mm)v i / M (4)

[0034] Where M is the total number of random points in the newly generated particle sphere and the original particle spheres, m is the total number of random points in all the original particle spheres that overlap with the newly generated particle sphere, and v i Let be the volume of the newly generated i-th particle sphere.

[0035] Step 7: Calculate the total volume and total porosity of the total spheres.

[0036] In a preferred embodiment of the present invention, the formulas for calculating the total volume and total porosity are as follows:

[0037] V i =V l -v cap (5)

[0038] ε i =(VV i ) / V (6)

[0039] Among them, V l v is the theoretical total volume of all the spheres. cap V represents the overlap volume between the newly generated particle sphere and the original particle sphere. i Let be the total volume of space actually occupied by the i original spheres.

[0040] Step 8: Compare the total porosity of all the original spheres with the porosity of the powder film. If the porosity of the original spheres is greater than that of the powder film, repeat steps 4 to 8 until the porosity of all the original spheres is less than that of the powder film, at which point stop the iteration.

[0041] The beneficial effects of this invention are:

[0042] 1. A simple and efficient method is provided for constructing a numerical model of the microstructure of powder membrane filter material;

[0043] 2. Construct a numerical model for filter materials with high solid phase and low porosity, which cannot be achieved by the traditional close-packing model;

[0044] 3. The constructed numerical model can guarantee the generation of high-quality meshes, thereby improving the accuracy of simulation results;

[0045] 4. The constructed numerical model is more consistent with the actual microstructure of sintered metal powder porous media materials. Attached Figure Description

[0046] Figure 1 This is a scanning electron microscope (SEM) image of the metal powder membrane filter material of the present invention;

[0047] Figure 2 This is a flowchart of the method of the present invention;

[0048] Figure 3 This is a schematic diagram illustrating the calculation of the contact depth between the two balls according to the present invention;

[0049] Figure 4 This is a schematic diagram illustrating the calculation of the overlapping volume of the present invention;

[0050] Figure 5 This is a comparison diagram between the actual particle size distribution used in the model constructed in this invention and a given normal distribution;

[0051] Figure 6This is a schematic diagram of the model structure of the present invention;

[0052] Figure 7 This is a schematic diagram illustrating the construction of the entity model of the present invention;

[0053] Figure 8 The figure shows the flow field numerical simulation results of the solid model of the present invention. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0055] like Figure 2 As shown, a numerical modeling method for sintered metal porous membrane filter materials includes the following steps:

[0056] Step 1: Obtain a scanning electron microscope (SEM) image of the powder film; and perform binarization processing on the SEM image to extract powder particle information from the image;

[0057] like Figure 1 The four images shown are the original SEM image, the converted grayscale image, the image after binarization, and the image from which the powder particle boundary information was extracted.

[0058] Step 2: Obtain the porosity ε and particle size distribution n(d) of the powder film, where d is the particle size and n(d) is the particle size distribution function;

[0059] Step 3: Initialize the total number of particles N = 1, and the initial value of the total volume occupied by the particles V. i =0, V i Let V be the total volume of space actually occupied by all i particles, and V be the geometric space to be modeled.

[0060] Step 4, as Figure 3 As shown, the coordinates (x, y) of the center of the i-th (i=N) particle sphere are generated in geometric space V using a random method. i y i , z i and particle size r i Partial overlap between particles is allowed; the overlap between newly generated particles and existing particles is determined to ensure high-quality mesh generation during subsequent numerical simulations; for example... Figure 3 The small red spheres are newly generated particles, and the large blue spheres are existing particles.

[0061] When two spheres are close to being tangent, the angle θ between their tangent surfaces is small, which limits the skewness of the generated mesh due to the topological structure and overall geometry, making it impossible to generate a mesh that meets the computational quality requirements. Therefore, this invention controls the angle θ between the tangent surfaces by limiting the coordinates and particle size of the newly generated spheres.

[0062] Specifically, it includes:

[0063] Step 41: Control the included angle θ of the tangential surface by controlling the contact depth Δx between the two particles;

[0064] Step 42: Based on the geometric relationship between the particles, the tangential angle θ between the contact points of two particles and the contact depth Δx are approximately related as follows:

[0065]

[0066] Where r1 and r2 are the radii of adjacent overlapping particles, and θ is the tangential angle between the contact points of the two particles.

[0067] Step 43: Limit the contact depth between particles to be greater than the minimum contact depth to obtain mesh quality that meets the requirements of numerical simulation calculations; the formula for the minimum contact depth is:

[0068] Δx=αmin(r1,r2) (2)

[0069] In this embodiment, α = 0.01, which is the minimum coefficient to meet the mesh requirements; at this time, θ is approximately 11°, which can meet the mesh requirements of general fluid calculations.

[0070] Step 5: Calculate the theoretical total volume V of all the spheres. l The formula is:

[0071] V l =V i-1 +4 / 3πr 3 (3)

[0072] Among them, V i-1 r is the volume of space occupied by the original i-1 particles, and r is the radius of the newly generated particle.

[0073] Step 6: Determine the adjacency and overlap relationship between the particles, that is, obtain the adjacency and overlap relationship based on the contact depth of two particles; use array S to record all the original particles that overlap with the i-th particle, and use the Monte Carlo method to calculate the overlap volume between the i-th particle and all the original particles.

[0074] The Monte Carlo method includes the following calculations:

[0075] Step 61: Based on the newly generated particle sphere p iGiven the diameter and coordinates of the newly generated particle p, iterate through all existing particles and use array S to record the relationship between the particle p and the newly generated particle p. i All existing particles that have overlapping relationships;

[0076] like Figure 4 In the image, the red sphere represents the newly generated particle sphere p. i There are 3 blue balls, which are the original particles; the total number of red and green random points is M, and the number of green random points is m.

[0077] Step 62, in the newly generated particle sphere p i M uniformly distributed random points are generated within the particle; the calculation process for the coordinates of random points within a single particle is as follows:

[0078] Step 621: Randomly sample to generate uniformly distributed random numbers u, v, w; where u and v are in the range [-1, 1], and w is in the range [0, 1].

[0079] Step 622, Calculate w 2 =u 2 +v 2 If w 2 If the value is greater than 1, then resample until w is satisfied. 2 ≤1;

[0080] Step 633: Calculate the coordinates of the generated random points:

[0081] Step 63: Count the number of particles falling into array S and the number of newly generated particles p. i Random points within, where only those falling on p i If the number of random points is m, then the overlap volume between the newly generated particle sphere and the original particle sphere is calculated using the following formula:

[0082] v cap =(Mm)v i / M (4)

[0083] Where M is the total number of random points in the newly generated particle sphere and the original particle spheres, m is the total number of random points in all the original particle spheres that overlap with the newly generated particle sphere, and v i Let be the volume of the newly generated i-th particle sphere.

[0084] Step 7: Calculate the total actual volume V occupied by all i particles. i The formula is:

[0085] V i =V l -v cap (5)

[0086] And calculate the total porosity after generating i original spheres, using the following formula:

[0087] ε i =(VV i ) / V (6)

[0088] Step 8: Compare the current total porosity ε i The porosity ε of the powder film; if ε i If ε > 1, then the total number of particles N increases by 1: N new =N old +1, and increment the value of i by 1; repeat steps four to eight; otherwise, stop the iteration and complete the establishment of the numerical model of the microstructure of the powder membrane filter material.

[0089] like Figure 5 To use the actual particle size distribution and the given normal distribution n(d) i )contrast;

[0090] like Figure 6 This is a schematic diagram of the model structure, showing actual spheres in different layers. Figure 7 This is a schematic diagram of the solid model of the sintered metal porous membrane filter element.

[0091] like Figure 8 To utilize Figure 7 The model was used to perform numerical simulations to obtain pressure contour maps of the flow field.

[0092] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A numerical modeling method for sintered metal porous membrane filter materials, characterized in that, Includes the following steps: Step 1: Extract powder particle boundary information; Step 2: Obtain the porosity and particle size distribution of the powder film; Step 3: Initialize the total number of particles, the initial value of the total volume of space occupied by the particles, and the geometric space to be modeled; Step 4: Use a random method to generate the center coordinates and particle size of the spheres in the geometric space to be modeled; and determine the overlap between the newly generated spheres and the original spheres. Step 5: Calculate the theoretical total volume of all the spheres; Step 6: Determine the adjacency and overlap relationships between the particles, and use an array to record all the original particles that overlap with the generated particle; use the Monte Carlo method to calculate the overlap volume between the newly generated particle and all the original particles. Step 7: Calculate the total volume and total porosity of the total spheres. Step 8: Compare the total porosity of all the original spheres with the porosity of the powder film. If the porosity of the original spheres is greater than that of the powder film, repeat steps 4 to 8 until the porosity of all the original spheres is less than that of the powder film, at which point stop the iteration.

2. The numerical modeling method for sintered metal porous membrane filter materials according to claim 1, characterized in that, Step four specifically includes: Step 41: Control the angle between the cut surfaces by controlling the contact depth of the two spheres; Step 42: Construct a geometric model of the contact depth between the particles; Step 43: Limit the contact depth between particles to be greater than the minimum contact depth to obtain a mesh quality that meets the requirements of numerical simulation calculation.

3. The numerical modeling method for sintered metal porous membrane filter materials according to claim 2, characterized in that, The geometric relationship model formula for contact depth is: Where r1 and r2 are the radii of adjacent overlapping particles, and θ is the tangential angle between the contact points of the two particles.

4. The numerical modeling method for sintered metal porous membrane filter materials according to claim 1, characterized in that, The formula for the theoretical total volume of all spheres is: V l =V i-1 +4 / 3πr 3 (3) Where r is the radius of the newly generated particle sphere, V i-1 This represents the volume of space occupied by the original i-1 particles.

5. The numerical modeling method for sintered metal porous membrane filter materials according to claim 1, characterized in that, The Monte Carlo method specifically includes: Step 61: Based on the diameter and coordinates of the newly generated particle, traverse all the original particles and use an array to record all the original particles that overlap with the newly generated particle. Step 62: Generate M uniformly distributed random points in the newly generated particle sphere; Step 63: Count the random points in the particles that fall into the array and the newly generated particles, and calculate the overlap volume between the newly generated particles and the original particles.

6. The numerical modeling method for sintered metal porous membrane filter materials according to claim 5, characterized in that, The coordinates of the random point include: Step 621: Randomly sample to generate uniformly distributed random numbers u, v, w; Step 622, Calculate w 2 =u 2 +v 2 ; Step 633: Calculate the coordinates of the generated random points:

7. The numerical modeling method for sintered metal porous membrane filter materials according to claim 5, characterized in that, The formula for calculating the overlapping volume is: in cap =(Mm)v i / M (4) Where M is the total number of random points in the newly generated particle sphere and the original particle spheres, m is the total number of random points in all the original particle spheres that overlap with the newly generated particle sphere, and v i Let be the volume of the newly generated i-th particle.

8. The numerical modeling method for sintered metal porous membrane filter materials according to claim 7, characterized in that, The formulas for calculating total volume and total porosity are as follows: V i =V l -v cap (5) ε i =(VV i ) / V (6) Among them, V l v is the theoretical total volume of all the spheres. cap V represents the overlap volume between the newly generated particle sphere and the original particle sphere. i Let be the total volume of space actually occupied by the i original spheres.

9. A numerical modeling system for sintered metal porous membrane filter materials, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the numerical modeling method for sintered metal porous membrane filter materials as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code, when executed by a processor, implements the numerical modeling method for sintered metal porous membrane filter materials as described in any one of claims 1-8.

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