A method for generating a porous structure and a flow simulation method thereof

Abstract

The present invention discloses a method for generating a porous structure and a streamer simulation method thereof, and relates to the technical field of generating and simulating a porous structure. The method for generating a porous structure comprises: defining and determining the phase parameters of the porous structure; selecting a preset proportion of nodes from all nodes in a set area and setting them as pore seed nodes, simulating the growth process of pores based on the initial values ​​of the phase parameters of the set nodes and using the results of numerical iterative solution processing; and constructing a porous structure model. The method for simulating streamers of a porous structure comprises: removing pores that are not connected to the surface of the porous structure to obtain a porous solid medium model; setting gas parameters to perform transient solution on a discrete electron diffusion model of streamer development; and analyzing and obtaining the influence of the pore structure on the streamer development characteristics according to the transient development process of the streamer. By applying the method provided by the present invention, the density of the grid division in the simulation of the porous structure model is reduced, and the efficiency of the streamer simulation is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of porous structure generation and simulation, and more specifically, to a porous structure generation method and a flow simulation method thereof. Background Art

[0002] Porous materials are materials rich in through or closed pores. Rocks, wood, bones, etc. are natural porous materials. They are used together with many artificial porous materials in the fields of adsorption, separation, catalysis, sound absorption, heat insulation, low dielectric materials and improving insulation performance. Numerical simulation is an important means to study the properties of porous materials. For example, it can simulate physical processes such as solid mechanics, acoustics, electricity, fluid mechanics and fluid-solid coupling. The porous structure models generated by computer programs are widely used in earth sciences, petroleum engineering, electrical engineering, heat transfer and other fields. The use of numerical methods to generate porous media models similar to actual pore structures is of great significance for studying the properties of porous materials.

[0003] Physical experimental modeling and numerical reconstruction are the main methods for constructing porous structure models (such as Chinese patent application CN111696211A). The physical experimental modeling method first uses a microscope or computer tomography (CT) to observe the pore distribution of the cross section of the porous material, and then constructs a porous structure model through numerical methods, but the relevant experimental measurement methods are costly and inefficient. The numerical reconstruction method generates a porous structure model that simulates the actual pore structure through computer programming. Among them, the four-parameter random growth method is the most commonly used method, but this method does not consider the physical process of pore growth, and the resulting pores are relatively discrete, which is quite different from the structure of actual porous materials, which are mostly connected pores; in addition, the pore edges generated by this method are sharper, which increases the difficulty of meshing in the simulation of porous model characteristics. Therefore, it is of great significance to develop new methods for generating porous structures.

[0004] Porous materials are used to regulate the discharge characteristics of gas insulating media under high voltage. For example, porous structures can effectively improve the bulk breakdown and surface flashover strength of the gas, and porous materials can improve the uniformity of dielectric barrier discharge plasma. However, there is a lack of research on the discharge characteristics of porous materials, resulting in a lack of understanding of their discharge phenomena and mechanisms. Streamer simulation is an important means to study the discharge mechanism, so it is of great significance to use porous structure models to carry out dynamic simulation of streamer development.

[0005] In summary, it is necessary to introduce a new method. On the one hand, the diffusion equation can be used to simulate the pore growth process to generate a porous structure model with connected pores and smooth edges, so as to solve the technical problems of pore discreteness, sharp edges, high cost and low efficiency of the porous structure model in the prior art. On the other hand, a discrete electron diffusion model and an adaptive mesh are used to perform streamer simulation on the porous structure based on the porous structure model to solve the technical problems of the lack of research on the discharge characteristics of porous materials in the prior art and the limitation of the simulation time step by the mesh size, thereby reducing the density of mesh division in the simulation of the porous structure model and improving the efficiency of streamer simulation. Summary of the invention

[0006] In view of the technical problems mentioned above, in order to improve the accuracy and computational efficiency of the simulation of the physical properties of porous materials, the present invention provides a method for generating a porous structure and a streamer simulation method thereof, which iteratively solves the diffusion equation by a numerical method to describe the pore growth process and optimizes the simulation process of streamer development, so that the simulation results are closer to the actual situation and the numerical calculation efficiency is improved.

[0007] The present invention provides a method for producing a porous structure, the method comprising:

[0008] S11, parameter definition: according to the pore distribution characteristics of the porous structure of the porous material, define and determine the phase parameters of the porous structure, wherein the phase parameters include: porosity, spatial dimension, number of subdivided grids, potential barrier parameters, simulation step length and anisotropy generation coefficient;

[0009] S12, parameter initialization: select a preset proportion of nodes from all nodes in the set area and set the selected nodes as pore seed nodes, set the initial values ​​of the phase parameters of the pore seed nodes to 1, and set the initial values ​​of the phase parameters of other nodes that are not selected from all nodes to 0, wherein the preset proportion is 5%, and the other nodes are the remaining nodes after the pore seed nodes are selected from all nodes;

[0010] S13, pore growth simulation: based on the initial values ​​of the phase parameters of the nodes set in step S12, a numerical method is used to iteratively solve the diffusion equation to perform a numerical iterative solution process, and the result of the numerical iterative solution process is used to simulate the pore growth process;

[0011] S14, porous structure model construction: After the pore growth is completed, the phase parameters are plotted as an image to obtain a porous structure model.

[0012] Preferably, the numerical method iteratively solves the diffusion equation as follows: , where p is the phase parameter, t For time, αis the barrier parameter, c x , c y , c z They are x , y , z The anisotropy generation coefficient of the axis, ∂ is the mathematical symbol representing the partial derivative;

[0013] The iterative solution of the diffusion equation by the numerical method is obtained according to the result of the iterative solution of the numerical method, and the numerical method is Fourier spectral method, finite difference time domain method or finite element method.

[0014] Preferably, in step S13, the step of performing numerical iterative solution processing by iteratively solving the diffusion equation using a numerical method based on the initial value of the phase parameter of the node set in step S12 further includes:

[0015] S13-1, based on the initial value of the phase parameter of the pore seed node and the initial value of the phase parameter of other nodes, the diffusion equation is iteratively solved using the numerical method to obtain updated phase parameters corresponding to all nodes;

[0016] S13-2, normalizing the updated phase parameter to a range of 0 to 1 to obtain a normalized phase parameter;

[0017] S13-3, setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are greater than 0.5 to 1, and setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are less than or equal to 0.5 to 0, to obtain the binary phase parameters of all nodes;

[0018] S13-4, performing a morphological opening operation on the binary phase parameters to remove burr points at the edges of pores in the porous structure model, and obtaining post-processing phase parameters of all nodes;

[0019] S13-5, calculating the porosity of the porous structure based on the post-processing phase parameter and the porosity calculation formula to obtain the porosity of the porous structure; if the porosity of the porous structure is less than the set porosity, using the normalized phase parameter as the iteration initial value, repeating steps S13-1 to S13-5; if the porosity of the porous structure is greater than or equal to the set porosity, outputting the post-processing phase parameter;

[0020] The set porosity is set according to the pore distribution characteristics of the porous structure of the porous material.

[0021] Preferably, the porosity calculation formula is: ,in, Por is the porosity of the porous structure,N p is the number of nodes greater than 0.5 in the post-processing phase parameter, N a is the total number of nodes.

[0022] Accordingly, the present invention also provides a porous structure flow simulation method, the porous structure flow simulation method comprising:

[0023] S51, preprocessing the porous structure model obtained in step S14, removing pores that are not connected to the surface of the porous structure, and obtaining a porous solid medium model;

[0024] S52, based on the porous solid medium model, establishing a geometric model containing the porous solid medium, wherein the geometric model includes the porous solid medium, the gas medium and the rod electrode;

[0025] S53, setting simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, setting the relative dielectric constant of the gas medium to 1, setting the relative dielectric constant of the porous solid medium according to the material type, and setting the boundary conditions of the rod electrode,

[0026] The simulation parameters of the gas medium include charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, reaction coefficient, and gas dielectric constant; the simulation parameters of the porous solid medium include solid dielectric constant and secondary electron emission coefficient; the boundary conditions of the geometric model include electric potential, zero charge flux, and gas-solid interface charge accumulation; and the simulation control parameters of the geometric model include meshing parameters and result output step size;

[0027] S54, adding the simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, the relative dielectric constant of the gas medium, the relative dielectric constant of the porous solid medium, the boundary conditions of the rod electrode, and the reaction equation to the simulation software input file, using an adaptive refined grid to divide the calculation area, and performing a transient solution to the discrete electron diffusion model of streamer development;

[0028] S55, the electron and ion density, electric field strength, and ionization source term obtained by transient solution are plotted as images to obtain the transient development process of the streamer, and the influence of the pore structure on the streamer development characteristics is analyzed and obtained.

[0029] Preferably, in step S54, the discrete electron diffusion model includes:

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, X(t) is the position vector of the electron, dt is the simulation step length, dX is the electron displacement within the time dt, V is the electron migration velocity vector, N is the standard normal distribution vector, is the density of positive or negative ions during the simulation, Indicates the polarity of the ion, , , are the migration velocity, diffusion coefficient and source term of positive or negative ions, respectively; D is the diffusion coefficient of positive or negative ions; σ is the surface charge density of the solid medium; Jσ is the charge flux on the surface of the porous solid medium; is the dielectric constant, is the electric potential, is the space charge density, is the mathematical symbol for partial derivatives, is the mathematical symbol for total differential.

[0035] Preferably, the source terms of the electrons, the positive ions and the negative ions are obtained by calculating the source terms through electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction using a random reaction simulation algorithm.

[0036] Preferably, the specific steps of using the random reaction simulation algorithm to calculate the source term are:

[0037] S81, convert the density of electrons, positive ions and negative ions into quantity, and convert the reaction coefficients of electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction into reaction probability;

[0038] S82, based on the number of electrons, positive ions, and negative ions, a statistical method is used to determine the changes in the electrons, positive ions, and negative ions, which are then converted into particle density to obtain the source terms of electrons, positive ions, and negative ions.

[0039] Preferably, the charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient and reaction coefficient of the gas are calculated based on a collision cross section data set of the gas.

[0040] Preferably, in step S54, the adaptive refinement grid adopts a Cartesian coordinate system vertical cross grid, when ( α - η )∆ x >1 condition, the mesh is refined, and when ( α - η )∆x <0.1, the mesh is coarsened, where α and η are the electron impact ionization coefficient and the electron attachment coefficient, ∆ x is the mesh size.

[0041] By applying the above technical solution, the present invention produces the following beneficial technical effects:

[0042] 1. The present invention uses the diffusion equation to simulate the pore growth process, and can generate a porous structure model with connected pores and smooth edges, which is closer to the actual pore structure and effectively solves the problem of discrete pores and sharp edges generated by the existing method. The pore structure with smooth edges reduces the density of mesh division in subsequent simulations and improves the simulation efficiency of the pore structure.

[0043] 2. The porous structure model generation method of the present invention has the advantages of simple program, high calculation efficiency, low programming difficulty, and porous structure models with various pore distribution characteristics can be obtained by adjusting input parameters.

[0044] 3. The streamer simulation method of the present invention adopts a discrete electron diffusion model, which solves the problem that the simulation time step is limited by the size of the subdivision grid; in addition, an adaptive refined grid is adopted to automatically adopt a finer subdivision grid at the streamer head, avoiding the problem of using a refined grid for the entire geometric model, and improving the computational efficiency of the streamer simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 A schematic flow chart of a method for producing a porous structure according to an embodiment of the present invention is shown.

[0047] Figure 2 A schematic flow chart of a porous structure flow simulation method according to an embodiment of the present invention is shown.

[0048] Figure 3 A streamer simulation model diagram of an embodiment of the present invention is shown.

[0049] Figure 4 A grid division diagram of a streamer simulation according to an embodiment of the present invention is shown.

[0050] Figure 5 The phase parameter distribution evolution diagram of the porous structure generation method and the stream injection simulation method thereof according to the first embodiment of the present invention is shown.

[0051] Figure 6 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the first embodiment of the present invention is shown.

[0052] Figure 7 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the second embodiment of the present invention is shown.

[0053] Figure 8 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the third embodiment of the present invention is shown.

[0054] Fig. 9 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the fourth embodiment of the present invention is shown.

[0055] Fig.10 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the fifth embodiment of the present invention is shown.

[0056] Fig.11 A porous structure model diagram obtained by the porous structure generation method and the flow simulation method according to the sixth embodiment of the present invention is shown.

[0057] Fig.12 The electron density evolution diagram obtained by simulation in the porous structure generation method and streamer simulation method according to the seventh embodiment of the present invention is shown.

[0058] Fig.13 The graph of electron density evolution obtained by simulation in the porous structure generation method and streamer simulation method according to the eighth embodiment of the present invention is shown.

[0059] Fig.14 The porous structure model diagram obtained by the four-parameter random growth method of comparative example 1 is shown.

[0060] Fig.15 The porous structure model diagram obtained by the four-parameter random growth method of comparative example 2 is shown.

[0061] Fig.16 The porous structure model diagram obtained by the four-parameter random growth method of comparative example three is shown. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0063] The present invention provides a method for producing a porous structure, such as Figure 1 As shown, the method for producing the porous structure comprises:

[0064] S11, parameter definition: define and determine the phase parameters of the porous structure according to the pore distribution characteristics of the porous material, wherein the phase parameters include: porosity, spatial dimension, number of subdivision grids, potential barrier parameters, simulation step size and anisotropy generation coefficient.

[0065] In a specific embodiment, the porosity range can be set between 5% and 90%, and the spatial dimension can be selected as 2D or 3D according to the needs. The number of subdivided grids in different spatial dimensions can be selected according to the needs. When the Fourier spectrum method is used to solve the diffusion equation, the number of subdivided grids is usually selected as one of 128, 256, and 512. The barrier parameter is 10 -8 ~10 -3 When the parameter is selected within this range, a porous structure model with continuity and porosity that meet the requirements can usually be obtained. If the barrier parameter is too large, it is difficult to obtain continuous pores. The simulation step size is preferably between 0.01 and 0.1. The larger the simulation step size, the shorter the program running time, but the accuracy of solving the diffusion equation is slightly reduced. The anisotropic generation coefficient is used to control the growth rate of pores in different spatial dimensions. Its value range is 0.01~1. If the anisotropic generation coefficient in a certain dimension is smaller, the pore growth rate in that direction is slower.

[0066] S12, parameter initialization: select a preset proportion of nodes from all nodes in the set area and set the selected nodes as pore seed nodes, set the initial values ​​of the phase parameters of the pore seed nodes to 1, and set the initial values ​​of the phase parameters of other nodes that are not selected from all nodes to 0, wherein the preset proportion is 5%, and the other nodes are the remaining nodes after the pore seed nodes are selected from all nodes.

[0067] Specifically, nodes in a set area are randomly selected by generating random numbers, and the selected nodes are set as pore seed nodes until the number of selected pore seed nodes accounts for 5% of the total number of nodes.

[0068] S13, pore growth simulation: based on the initial values ​​of the phase parameters of the nodes set in step S12, a numerical method is used to iteratively solve the diffusion equation for numerical iterative solution processing, and the result of the numerical iterative solution processing is used to simulate the pore growth process.

[0069] S14, porous structure model construction: After the pore growth is completed, the phase parameters are plotted as an image to obtain a porous structure model.

[0070] In this embodiment, the numerical method iteratively solves the diffusion equation as follows: , where p is the phase parameter, t For time, α is the barrier parameter, c x , c y , c z They are x , y , z The anisotropy generation coefficient of the axis, ∂ is the mathematical symbol representing the partial derivative;

[0071] The iterative solution of the diffusion equation by the numerical method is obtained according to the result of the iterative solution of the numerical method, and the numerical method is Fourier spectral method, finite difference time domain method or finite element method.

[0072] It should be noted that the numerical method is one of Fourier spectrum method, finite difference time domain method or finite element method.

[0073] As an embodiment, a finite difference time domain method is used to iteratively solve the diffusion equation using a numerical method. Taking two-dimensional space as an example, the diffusion equation can be rewritten as:

[0074]

[0075]

[0076]

[0077]

[0078] Where p(t) is the phase parameter at time t, and the subscripts i and j represent the node numbers on the x and y axes, respectively.

[0079] By iteratively solving , which can simulate the pore growth process.

[0080] As an embodiment, the diffusion equation is solved by iterative numerical method using Fourier spectral method. Taking two-dimensional space as an example, the diffusion equation can be rewritten as follows:

[0081]

[0082] Transformed to the Fourier domain, the iterative formula for the phase parameter is:

[0083]

[0084] In the formula, P (t ) is the Fourier transform of the phase parameter, k x , k y , k z They are x , y , z The iterative formula of the phase parameter can be used to implement the rapid iteration of the numerical method to iteratively solve the diffusion equation, and the updated phase parameter can be obtained through the inverse transformation.

[0085] In this embodiment, in step S13, the step of performing numerical iterative solution processing by iteratively solving the diffusion equation using a numerical method based on the initial value of the phase parameter of the node set in step S12 further includes:

[0086] S13-1, based on the initial value of the phase parameter of the pore seed node and the initial value of the phase parameter of other nodes, the diffusion equation is iteratively solved using the numerical method to obtain updated phase parameters corresponding to all nodes;

[0087] S13-2, normalizing the updated phase parameter to a range of 0 to 1 to obtain a normalized phase parameter;

[0088] Specifically, the phase parameter normalization is obtained by dividing the updated phase parameter by the maximum value of the phase parameters of all nodes.

[0089] S13-3, setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are greater than 0.5 to 1, and setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are less than or equal to 0.5 to 0, to obtain the binary phase parameters of all nodes;

[0090] S13-4, performing a morphological opening operation on the binary phase parameters to remove burr points at the edges of pores in the porous structure model, and obtaining post-processing phase parameters of all nodes;

[0091] Specifically, the morphological opening operation is performed using a matrix of size 3 by 3 with all elements equal to 1, which can smooth the pore boundaries. If there are sharp burr areas on the pore boundaries, a very high mesh density is required to segment the burr areas during subsequent physical property simulation, which increases the simulation burden. Therefore, the morphological opening operation is used to remove the burr points on the pore edges in the porous structure model.

[0092] S13-5, calculating the porosity of the porous structure based on the post-processing phase parameter and the porosity calculation formula to obtain the porosity of the porous structure; if the porosity of the porous structure is less than the set porosity, using the normalized phase parameter as the iteration initial value, repeating steps S13-1 to S13-5; if the porosity of the porous structure is greater than or equal to the set porosity, outputting the post-processing phase parameter;

[0093] The set porosity is set according to the pore distribution characteristics of the porous structure of the porous material.

[0094] In this embodiment, the porosity calculation formula is: ,in, Por is the porosity of the porous structure, N p is the number of nodes greater than 0.5 in the post-processing phase parameter, N a is the total number of nodes.

[0095] By applying the above technical solution provided by the present invention and simulating the pore growth process using the diffusion equation, a porous structure model with interconnected pores and smooth edges can be generated, which is closer to the actual pore structure and effectively solves the problem of discrete pores and sharp edges generated by the existing method. The pore structure with smooth edges reduces the density of mesh division in subsequent simulations and improves the simulation efficiency of the pore structure.

[0096] Accordingly, the present invention also provides a porous structure flow simulation method, such as Figure 2 As shown, the porous structure flow simulation method includes:

[0097] S51, preprocessing the porous structure model obtained in step S14, removing pores that are not connected to the surface of the porous structure, and obtaining a porous solid medium model;

[0098] It should be noted that the model assumes that the streamer develops only in the gas medium, so the streamer cannot enter the pores that are not connected to the surface. If the pores that are not connected to the surface are still retained in the model, the software automatically uses a dense mesh at the pores, which increases the calculation burden but does not affect the calculation results. Therefore, the pores that are not connected to the surface are artificially removed.

[0099] S52, based on the porous solid medium model, establishing a geometric model containing the porous solid medium, wherein the geometric model includes the porous solid medium, the gas medium and the rod electrode;

[0100] Wherein, the rod electrode is located on the gas side close to the gas-solid interface;

[0101] Specifically, the geometric model containing porous solid media is as follows Figure 3As shown, the size of the simulation area is 10mmX10mm, the length and width of the porous solid medium (1) are 10mm and 5mm respectively, the gas medium (2) in the upper part of the model is air, and the medium in the air gap inside the porous solid medium (1) is also air. The rod electrode (3) is 1mm long and 0.2mm in diameter, and the distance from the surface of the porous solid medium is 2mm.

[0102] S53, setting simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, setting the relative dielectric constant of the gas medium to 1, setting the relative dielectric constant of the porous solid medium according to the material type, and setting the boundary conditions of the rod electrode,

[0103] The simulation parameters of the gas medium include charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, reaction coefficient, and gas dielectric constant; the simulation parameters of the porous solid medium include solid dielectric constant and secondary electron emission coefficient; the boundary conditions of the geometric model include electric potential, zero charge flux, and gas-solid interface charge accumulation; and the simulation control parameters of the geometric model include meshing parameters and result output step size;

[0104] S54, adding the simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, the relative dielectric constant of the gas medium, the relative dielectric constant of the porous solid medium, the boundary conditions of the rod electrode, and the reaction equation to the simulation software input file, using an adaptive refined grid to divide the calculation area, and performing a transient solution to the discrete electron diffusion model of streamer development;

[0105] S55, the electron and ion density, electric field strength, and ionization source term obtained by transient solution are plotted as images to obtain the transient development process of the streamer, and the influence of the pore structure on the streamer development characteristics is analyzed and obtained.

[0106] In this embodiment, in step S54, the discrete electron diffusion model includes:

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, X(t) is the position vector of the electron, dt is the simulation step length, dX is the electron displacement within the time dt, V is the electron migration velocity vector, N is the standard normal distribution vector, is the density of positive or negative ions during the simulation, Indicates the polarity of the ion, , , are the migration velocity, diffusion coefficient and source term of positive or negative ions, respectively; D is the diffusion coefficient of positive or negative ions; σ is the surface charge density of the solid medium; Jσ is the charge flux on the surface of the porous solid medium; is the dielectric constant, is the electric potential, is the space charge density, is the mathematical symbol for partial derivatives, is the mathematical symbol for total differential.

[0112] In this embodiment, the source terms of the electrons, the positive ions and the negative ions are obtained by electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction, and the source terms are calculated using a random reaction simulation algorithm.

[0113] In this embodiment, the specific steps of using the random reaction simulation algorithm to calculate the source term are:

[0114] S81, convert the density of electrons, positive ions and negative ions into quantity, and convert the reaction coefficients of electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction into reaction probability;

[0115] S82, based on the number of electrons, positive ions, and negative ions, a statistical method is used to determine the changes in the electrons, positive ions, and negative ions, which are then converted into particle density to obtain the source terms of electrons, positive ions, and negative ions.

[0116] In actual examples, the densities of electrons, positive ions, and negative ions are first converted into quantities, and the reaction coefficients of electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction, and photoionization reaction are converted into reaction probabilities. Based on the number of electrons, positive ions, and negative ions, statistical methods are used to determine the changes in the amounts of electrons, positive ions, and negative ions, which are then converted into particle densities, thereby obtaining the source terms of electrons, positive ions, and negative ions.

[0117] In this embodiment, the charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient and reaction coefficient of the gas are calculated based on the collision cross section data set of the gas.

[0118] Specifically, the charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, and reaction coefficient of the gas are calculated using the Phelps collision cross section data set using the BOLSIG+ software. The relative dielectric constants of the gas and solid medium are set to 1 and 4, respectively. Figure 3 As shown, the boundary conditions of the rod electrode and the left boundary are set to 30 kV potential, the right boundary condition is set to grounding, and the upper and lower boundary conditions are set to Neumann boundary conditions.

[0119] In this embodiment, in step S54, the adaptive fine grid adopts a Cartesian coordinate system vertical cross grid. When ( α - η )∆ x >1 condition, the mesh is refined, and when ( α - η )∆ x <0.1, the mesh is coarsened, where α and η are the electron impact ionization coefficient and the electron attachment coefficient, ∆ x is the mesh size.

[0120] In order to enable those skilled in the art to have a deeper understanding of the technical solution of this step, reference is made to Figure 4 , Figure 4 The grid division during the streamer simulation process shows that the simulation uses a non-uniform Cartesian coordinate system vertical cross grid. The grid density is higher near the streamer head and the edge of the pore, and the grid density is lower in other areas. This grid division method ensures the accuracy of the streamer simulation on the one hand, while avoiding the problem of large simulation memory and long running time caused by the use of dense grids in the entire simulation area. The grid division is adjusted as the streamer develops, and a dense grid is always guaranteed at the streamer head to ensure the accuracy of the simulation.

[0121] By applying the above technical solutions and using numerical methods to iteratively solve the diffusion equation to simulate the pore growth process, a porous structure model with interconnected pores and smooth edges can be generated, which is closer to the actual pore structure and effectively solves the problem of discrete pores and sharp edges generated by existing methods. The pore structure with smooth edges reduces the density of mesh division in subsequent simulations and improves the simulation efficiency of the pore structure. The method for generating the porous structure model has the advantages of simple program, high computational efficiency, low programming difficulty, and porous structure models with various pore distribution characteristics can be obtained by adjusting the input parameters.

[0122] In addition, the streamer simulation method of the present invention adopts a discrete electron diffusion model, which solves the problem that the simulation time step is limited by the size of the subdivision grid; in addition, an adaptive refined grid is adopted to automatically adopt a finer subdivision grid at the streamer head, avoiding the problem of using a refined grid for the entire geometric model, thereby improving the computational efficiency of the streamer simulation.

[0123] In order to enable those skilled in the art to more clearly understand the method provided by the present invention, reference is made to Figures 1 to 16, the porous structure generation method and the flow simulation method thereof provided by the present invention are supplemented by examples.

[0124] Embodiment 1:

[0125] The spatial dimension is set to 2D, the number of grids is selected to be 256X256, and the porosity is 40%. The barrier parameter is set to 10 -6 , the simulation step is set to 0.02s, and the anisotropy generation coefficients of the two spatial dimensions are set to 1. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0. The diffusion equation is iteratively solved using the time-domain finite difference method to simulate the pore growth process, and the phase parameter distribution under different simulation times is obtained as follows Figure 5 As shown. It can be seen that at the beginning of the iteration, the pore seed nodes are randomly distributed in the set area; when the simulation time is 3s, the phase parameters of the area with relatively dense pore seed nodes gradually increase, but the areas are relatively independent; as the simulation time increases, the area with larger phase parameters gradually expands, and some areas are gradually connected, simulating the growth process of the pores. When the simulation time is 12s, the proportion of nodes with phase parameters greater than 0.5 in the total nodes reaches the set porosity, and the nodes with phase parameters greater than 0.5 are set as pores, and the nodes with phase parameters less than or equal to 0.5 are set as continuous phases, and the required porous structure model is obtained, as shown in Figure 6 As shown in the figure, the blue area is the continuous solid phase, and the dark red area is the pore; it can be seen that the obtained pores have good connectivity and the pore edges are relatively smooth, which meets the needs of subsequent physical property simulation.

[0126] Embodiment 2:

[0127] The spatial dimension is set to 2D, the number of grids is selected to be 256X256, and the porosity is 20%. The barrier parameter is set to 10 -6 , the simulation step is set to 0.02s, and the anisotropy generation coefficients of the two spatial dimensions are set to 1. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0; the diffusion equation is iteratively solved using the Fourier spectrum method to simulate the pore growth process and obtain the required porous structure model, such as Figure 7 As shown in the figure. The blue area is the continuous solid phase, and the dark red area is the pores; it can be seen that due to the low porosity setting, the pore area accounts for a small proportion in the generated porous structure model, and the pore distribution is relatively discrete, which meets the generation requirements under low porosity.

[0128] Embodiment 3:

[0129] The spatial dimension is set to 2D, the number of grids is selected to be 256X256, and the porosity is 60%. The barrier parameter is set to 10 -6 , the simulation step is set to 0.02s, and the anisotropy generation coefficients of the two spatial dimensions are set to 1. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0; the diffusion equation is iteratively solved using the time-domain finite difference method to simulate the pore growth process and obtain the required porous structure model, such as Figure 8 As shown in the figure. The blue area is the continuous solid phase, and the dark red area is the pores; it can be seen that due to the high porosity setting, the area of ​​the pore region in the generated porous structure model exceeds the area of ​​the continuous solid phase, and the pores are mostly connected structures, which is consistent with the parameter setting requirements.

[0130] Embodiment 4:

[0131] The spatial dimension is set to 2D, the number of grids is selected to be 512X512, and the porosity is 40%. The barrier parameter is set to 10 -6 , the simulation step is set to 0.02s, and the anisotropy generation coefficients of the two spatial dimensions are set to 1. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0; the diffusion equation is iteratively solved using the Fourier spectrum method to simulate the pore growth process and obtain the required porous structure model, such as Fig. 9 As shown. Figure 4 By comparison, it can be seen that although the porosity set in the two embodiments is 40%, the number of subdivision grids in Embodiment 1 is selected as 256X256, and the pore size of the porous structure model generated in Embodiment 4 is significantly smaller. Therefore, the pore size of the porous structure model can be adjusted by changing the number of subdivision grids.

[0132] Embodiment 5:

[0133] The spatial dimension is set to 2D, the number of grids is selected to be 256X256, and the porosity is 40%. The barrier parameter is set to 10 -6 , the simulation step size is set to 0.02s, x Axis and y The anisotropic generation coefficients of the axes are set to 0.1 and 1 respectively. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0. The diffusion equation is iteratively solved using the Fourier spectrum method to simulate the pore growth process and obtain the required porous structure model, such as Fig.10 As shown in the figure. The blue area is the continuous solid phase, and the dark red area is the pores; it can be seen that the porous structure model is along yThe axis has good connectivity, indicating that the pore distribution has the characteristics of heterogeneous distribution. This is due to y The anisotropy generation coefficient of the axis is high, making the pores along y The axis has a higher growth rate, so the growth direction of the pores can be controlled by changing the anisotropy generation coefficient.

[0134] Embodiment 6:

[0135] The spatial dimension is set to 3D, the number of grids is selected to be 256X256X256, and the porosity is 30%. The barrier parameter is set to 10 -6 , the simulation step is set to 0.02s, and the anisotropic generation coefficients of the three spatial dimensions are all set to 1. Nodes accounting for 5% of the total number of nodes are randomly selected in the set area and set as pore seed nodes. The phase parameters of the pore seed nodes are set to 1, and the phase parameters of other nodes are set to 0; the diffusion equation is iteratively solved using the time-domain finite difference method to simulate the pore growth process and obtain the required porous structure model, such as Fig.11 As shown in the figure, the blue area is a continuous solid phase, and the white area is a pore; it can be seen that the generated three-dimensional pores also have good connectivity, and the pore edges are relatively smooth, indicating that the method of the present invention is suitable for the generation of a three-dimensional porous structure model.

[0136] Embodiment 7:

[0137] The spatial dimension is set to 2D, the number of grids is selected to be 256X128, and the porosity is 40%. The barrier parameter is set to 10 -6 The simulation step size is set to 0.02s, and the anisotropy generation coefficients of the two spatial dimensions are set to 1. The diffusion equation is iteratively solved using the finite difference time domain method to simulate the pore growth process and obtain the porous structure model.

[0138] The generated porous structure model is used to carry out flow simulation. Figure 3 As shown. The size of the simulation area is 10mmX10mm, the length and width of the porous solid medium are 10mm and 5mm respectively, the gas medium in the upper half of the model is air, and the medium in the air gap inside the porous solid medium is also air. The rod electrode is 1mm long and 0.2mm in diameter, and the distance from the surface of the porous solid medium is 2mm. The electron mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, and reaction coefficient are calculated using the BOLSIG+ software using the Phelps collision cross section data set; the ion mobility is set to 2X10 -4 m 2 (Vs) -1, the diffusion coefficient is set to 0. The relative dielectric constants of the gas and solid medium are set to 1 and 4 respectively, and the secondary electron emission coefficient of the solid medium is 0.1. The boundary conditions of the rod electrode and the left boundary are set to 30kV potential, the right boundary condition is set to ground, and the upper and lower boundary conditions are set to Neumann boundary conditions. In the entire simulation area, the initial number of electrons is set to 100.

[0139] Using the above conditions, the streamer development process is simulated and analyzed, and the electron density distribution at different simulation times is obtained as follows: Fig.12 As shown. It can be seen that since the electric field intensity at the rod electrode head is the highest and the collision ionization reaction in this area is intense, the streamer starts to develop from the rod electrode. After that, the streamer develops through the pores to the surface of the solid medium, indicating that the solid medium has a certain attraction to the streamer. This is because the dielectric constant of the solid medium is higher than that of the gas medium, which enhances the electric field intensity between the streamer head and the solid medium, making the streamer tend to develop toward the solid medium. In addition, since the pore size of the generated pore is large, about 1 mm, which is much larger than the Debye length of the plasma in the air, the streamer can be injected into the pore and develop inside the pore. There are two modes of streamer development in the porous structure: pore micro-discharge and pore wall surface discharge. The streamer develops in the gas medium in the form of micro-discharge in the initial stage, but after encountering the solid medium, it accumulates charges on the surface of the solid medium and transforms into a surface discharge development mode. In addition, the streamer is blocked by the pore wall during the development process, so the pore wall plays a role in blocking the development of the streamer, reducing the average development speed of the streamer.

[0140] Embodiment 8:

[0141] The spatial dimension is set to 2D, the number of grids is selected to be 256X128, and the porosity is 40%. The barrier parameter is set to 10 -6 The simulation step size is set to 0.02s, and the anisotropic generation coefficients of the two spatial dimensions are set to 1. The diffusion equation is iteratively solved using the finite difference time domain method to simulate the pore growth process and obtain the porous structure model. The obtained porous structure model is shown in Fig.13 As shown, since the selection of pore seed nodes is random, the pore distribution obtained under the same parameters is also different. The porous structure model obtained in this embodiment has a higher number of pores at the surface.

[0142] The generated porous structure model is used to carry out flow simulation. Figure 3As shown. The size of the simulation area is 10mmX10mm, the length and width of the porous solid medium are 10mm and 5mm respectively, the gas medium in the upper half of the model is air, and the medium in the air gap inside the porous solid medium is also air. The rod electrode is 1mm long and 0.2mm in diameter, and the distance from the surface of the porous solid medium is 2mm. The electron mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, and reaction coefficient are calculated using the BOLSIG+ software using the Phelps collision cross section data set; the ion mobility is set to 2X10 -4 m 2 (Vs) -1 , the diffusion coefficient is set to 0. The relative dielectric constants of the gas and solid medium are set to 1 and 4 respectively, and the secondary electron emission coefficient of the solid medium is 0.1. The boundary conditions of the rod electrode and the left boundary are set to 30kV potential, the right boundary condition is set to ground, and the upper and lower boundary conditions are set to Neumann boundary conditions. In the entire simulation area, the initial number of electrons is set to 500.

[0143] Using the above conditions, the streamer development process is simulated and analyzed, and the electron density distribution at different simulation times is obtained as follows: Fig.13 As shown. It can be seen that since the electric field intensity is the highest near the rod electrode, the streamer first starts from the rod electrode, and then is attracted by the solid medium and develops toward the surface of the solid medium. While the streamer starts to develop at the rod electrode, gas micro-discharge is generated at the position with higher electric field intensity in the pore. As shown in the electron density distribution at 17.0ns, there may be multiple micro-discharges in the air gap; when the gas micro-discharge develops to the opposite pore wall, it is blocked by the pore wall and transformed into surface discharge, and develops to both sides along the pore wall. Afterwards, the surface discharge current streamer formed by the pore micro-discharge merges with the surface streamer started by the rod electrode and develops toward the ground electrode synchronously. It should be pointed out that after the second pore generates micro-discharge, the micro-discharge forms a surface negative streamer that develops toward the high-voltage electrode, and meets the surface positive streamer started by the rod electrode at 21.2ns, and finally causes surface flashover breakdown together.

[0144] Comparative Example 1:

[0145] The porous structure model was generated using the four-parameter random growth method. The number of grids was selected as 256X256, the porosity was 40%, the distribution probability was set to 0.005, the axial growth probability was 0.1, and the diagonal growth probability was 0.05. The porous structure model is as follows: Fig.14 As shown in the figure, the blue area is a continuous solid phase, and the dark red area is a pore. It can be seen that the obtained pore distribution is relatively discrete, there are solid phase areas in some pore areas, and many isolated pore areas are generated, which is different from the porous structure of the actual material. In addition, there are many burrs on the edges of the pores, which greatly increases the difficulty of meshing when used for physical property simulation.

[0146] Comparative Example 2:

[0147] The porous structure model was generated using the four-parameter random growth method. The number of grids was selected as 256X256, the porosity was 40%, the distribution probability was set to 0.05, the axial growth probability was 0.1, and the diagonal growth probability was 0.05. The porous structure model is as follows: Fig.15 As shown in the figure, the blue area is the continuous solid phase, and the dark red area is the pore. It can be seen that the obtained pore distribution is very discrete, and many isolated pore areas are produced, which is different from the porous structure of the actual material. In addition, there are many burrs on the edges of the pores, which greatly increases the difficulty of meshing when used for physical property simulation.

[0148] Comparative Example 3:

[0149] The porous structure model was generated using the four-parameter random growth method. The number of grids was selected as 256X256, the porosity was 60%, the distribution probability was set to 0.005, the axial growth probability was 0.1, and the diagonal growth probability was 0.05. The porous structure model is as follows: Fig.16 As shown in the figure, the blue area is the continuous solid phase, and the dark red area is the pore. It can be seen that due to the high porosity setting, the resulting pore connectivity is high, but the distribution of the solid phase and the pores is relatively discrete, which is somewhat different from the porous structure of the actual material; in addition, there are many burrs on the edges of the pores, which greatly increases the difficulty of meshing when used for physical property simulation.

[0150] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0151] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for producing a porous structure, characterized in that: The method for producing the porous structure comprises: S11, parameter definition: according to the pore distribution characteristics of the porous structure of the porous material, define and determine the phase parameters of the porous structure, wherein the phase parameters include: porosity, spatial dimension, number of subdivided grids, potential barrier parameters, simulation step length and anisotropy generation coefficient; S12, parameter initialization: select a preset proportion of nodes from all nodes in the set area and set the selected nodes as pore seed nodes, set the initial values ​​of the phase parameters of the pore seed nodes to 1, and set the initial values ​​of the phase parameters of other nodes that are not selected from all nodes to 0, wherein the preset proportion is 5%, and the other nodes are the remaining nodes after the pore seed nodes are selected from all nodes; S13, pore growth simulation: based on the initial values ​​of the phase parameters of the nodes set in step S12, a numerical method is used to iteratively solve the diffusion equation to perform a numerical iterative solution process, and the result of the numerical iterative solution process is used to simulate the pore growth process; S14, porous structure model construction: After the pore growth is completed, the phase parameters are plotted as an image to obtain a porous structure model.

2. The method according to claim 1, characterized in that The numerical method iteratively solves the diffusion equation as: , where p is the phase parameter, t For time, α is the barrier parameter, c x , c y , c z They are x , y , z The anisotropy generation coefficient of the axis, is the mathematical symbol for partial derivatives; The iterative solution of the diffusion equation by the numerical method is obtained according to the result of the iterative solution of the numerical method, and the numerical method is Fourier spectral method, finite difference time domain method or finite element method.

3. The method according to claim 1, characterized in that In step S13, the step of performing numerical iterative solution processing by using a numerical method to iteratively solve the diffusion equation based on the initial value of the phase parameter of the node set in step S12 further includes: S13-1, based on the initial value of the phase parameter of the pore seed node and the initial value of the phase parameter of other nodes, the diffusion equation is iteratively solved using the numerical method to obtain updated phase parameters corresponding to all nodes; S13-2, normalizing the updated phase parameter to a range of 0 to 1 to obtain a normalized phase parameter; S13-3, setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are greater than 0.5 to 1, and setting the phase parameters of the nodes corresponding to the normalized phase parameters whose values ​​are less than or equal to 0.5 to 0, to obtain the binary phase parameters of all nodes; S13-4, performing a morphological opening operation on the binary phase parameters to remove burr points at the edges of pores in the porous structure model, and obtaining post-processing phase parameters of all nodes; S13-5, calculating the porosity of the porous structure based on the post-processing phase parameter and the porosity calculation formula to obtain the porosity of the porous structure; if the porosity of the porous structure is less than the set porosity, using the normalized phase parameter as the iteration initial value, repeating steps S13-1 to S13-5; if the porosity of the porous structure is greater than or equal to the set porosity, outputting the post-processing phase parameter; The set porosity is set according to the pore distribution characteristics of the porous structure of the porous material.

4. The method according to claim 3, characterized in that The porosity calculation formula is: ,in, Por is the porosity of the porous structure, N p is the number of nodes greater than 0.5 in the post-processing phase parameter, N a is the total number of nodes.

5. A porous structure flow simulation method, characterized in that: The porous structure stream injection simulation method comprises: S51, preprocessing the porous structure model obtained in claim 1, removing pores that are not connected to the surface of the porous structure, and obtaining a porous solid medium model; S52, based on the porous solid medium model, establishing a geometric model containing the porous solid medium, wherein the geometric model includes the porous solid medium, the gas medium and the rod electrode; S53, setting simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, setting the relative dielectric constant of the gas medium to 1, setting the relative dielectric constant of the porous solid medium according to the material type, and setting the boundary conditions of the rod electrode, The simulation parameters of the gas medium include charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient, reaction coefficient, and gas dielectric constant; the simulation parameters of the porous solid medium include solid dielectric constant and secondary electron emission coefficient; the boundary conditions of the geometric model include electric potential, zero charge flux, and gas-solid interface charge accumulation; and the simulation control parameters of the geometric model include meshing parameters and result output step size; S54, adding the simulation parameters, boundary conditions, initial charge quantity and simulation control parameters of the geometric model, the relative dielectric constant of the gas medium, the relative dielectric constant of the porous solid medium, the boundary conditions of the rod electrode, and the reaction equation to the simulation software input file, using an adaptive refined grid to divide the calculation area, and performing a transient solution to the discrete electron diffusion model of streamer development; S55, the electron and ion density, electric field strength, and ionization source term obtained by transient solution are plotted as images to obtain the transient development process of the streamer, and the influence of the pore structure on the streamer development characteristics is analyzed and obtained.

6. The method according to claim 5, characterized in that In step S54, the discrete electron diffusion model includes: In the formula, X(t) is the position vector of the electron, dt is the simulation step length, dX is the electron displacement within the time dt, V is the electron migration velocity vector, N is the standard normal distribution vector, is the density of positive or negative ions during the simulation, Indicates the polarity of the ion, , , are the migration velocity, diffusion coefficient and source term of positive or negative ions, respectively; D is the diffusion coefficient of positive or negative ions; σ is the surface charge density of the solid medium; Jσ is the charge flux on the surface of the porous solid medium; is the dielectric constant, is the electric potential, is the space charge density, is the mathematical symbol for partial derivatives, is the mathematical symbol for total differential.

7. The method according to claim 6, characterized in that The source terms of the electrons, the positive ions and the negative ions are obtained by calculating the source terms through electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction using a random reaction simulation algorithm.

8. The method according to claim 7, characterized in that The specific steps of using the random reaction simulation algorithm to calculate the source term are: S81, convert the density of electrons, positive ions and negative ions into quantity, and convert the reaction coefficients of electron impact ionization reaction, electron attachment reaction, electron-ion recombination reaction, ion-ion recombination reaction and photoionization reaction into reaction probability; S82, based on the number of electrons, positive ions, and negative ions, a statistical method is used to determine the changes in the electrons, positive ions, and negative ions, which are then converted into particle density to obtain the source terms of electrons, positive ions, and negative ions.

9. The method according to claim 5, characterized in that The charge mobility, diffusion coefficient, electron impact ionization coefficient, electron attachment coefficient and reaction coefficient of the gas are calculated based on a collision cross section data set of the gas.

10. The method according to claim 5, characterized in that In step S54, the adaptive fine grid adopts a Cartesian coordinate system vertical cross grid, when ( α - η )∆ x >1 condition, the mesh is refined, and when ( α - η )∆ x <0.1, the mesh is coarsened, where α and η are the electron impact ionization coefficient and the electron attachment coefficient, ∆ x is the mesh size.

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