CN110987749A - Method for researching equivalent permeability coefficient microscopic scale of multiphase composite material - Google Patents
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Abstract
The invention relates to a microscopic and scale research method for equivalent permeability coefficient of a multiphase composite material. Aiming at the heterogeneous characteristics of the composite material, a numerical model is established based on a finite element method from the viewpoint of microscopic scale so as to estimate the equivalent permeability coefficient of the composite material. The established numerical model is simulated by a Monte Carlo algorithm to obtain a multiphase material structure with space randomness under a microscopic scale, and the equivalent permeability coefficient of the composite material is evaluated by combining a finite element calculation method and a Darcy law. The invention provides a method for simulating the heterogeneity of the internal structure of the multiphase composite material based on the microscopic scale, provides a new idea for analyzing the permeability characteristic of the multiphase composite material, and is simple, feasible, rapid and convenient.
Description
Technical Field
The invention belongs to the field of research on characteristics of multiphase composite materials, and particularly relates to a microscopic scale research method for equivalent permeability coefficient of a multiphase composite material.
Background
The seepage characteristic is the capacity of the material to allow liquid to pass through interconnected pores, and the same strength and deformation characteristics are important physical and mechanical parameters of the rock-soil material. Seepage characteristics can cause seepage problems such as reservoir dam instability and the like, and engineering benefits are influenced; on the other hand, it can cause problems of infiltration and stability, such as water gushes and soil runoff, which can lead to landslides or foundation pit collapse. In general, permeability performance can be characterized by a permeability coefficient, also referred to as hydraulic characteristics.
At present, the determination of the permeability coefficient of a material is mainly realized by two methods, namely direct measurement and indirect acquisition of a test method. The experimental measurement method of the permeability coefficient can be divided into two types, wherein the first type is based on Darcy's law, a water head is applied to two sides of a sample at the same time, and the permeability coefficient is calculated by measuring the seepage flow. This method is also known as a penetration test and includes constant head and variable head tests. The second method is based on the sand-based consolidation theory and works by finding the permeability coefficient of the sample back from the consolidation coefficient, which is obtained by measuring the development of the deformation of the sample over time. In fact, due to the influence of many factors such as test conditions, sample size, sample defects, and the like, permeability coefficients measured by different test methods often have large differences, and it is difficult to achieve high precision. Meanwhile, because the soil sample cannot be influenced by disturbance during sampling, a representative original sample is difficult to obtain, and therefore, tests such as field well point water pumping and the like are often required to measure the permeability. However, no matter what method is adopted, the permeability coefficient is measured through tests or field tests, and the method is tedious and time-consuming and has high capital and labor cost.
Besides the permeability coefficient measured by direct methods such as test or field measurement, the permeability coefficient can also be obtained by indirect methods. If a fractal model is used for evaluating the permeability coefficient, the method cannot reflect the flowing condition of the fluid in the material and the seepage mechanism; the real internal structure of the material is reconstructed by the CT scanning technology, the method can simulate the internal composition of the material more truly, but is only suitable for a certain specific material and cannot obtain the general law of seepage; the scholars determine the permeability coefficient according to the matrix suction value of the SWCC experiment; or an empirical formula suitable for a certain soil body is provided, such as a classical Terzaghi formula, a Hazen formula, a Kozeny-Carman formula and the like, but the methods are not suitable for multiphase composite materials with strong heterogeneity and large difference of permeability coefficients of all phases. The permeability coefficient of the multiphase composite is not a simple combination of components and is determined by the coupling of high and low permeability media.
Therefore, determining the permeability coefficient of a multiphase composite material remains a difficult problem in geotechnical engineering. For heterogeneous multi-phase composites, the permeability coefficient is compounded from different permeable media materials. Because the permeability of different phases may be obviously different, the microscopic internal seepage field distribution of the multiphase composite material has extreme non-uniformity and is influenced by the content, form, spatial distribution and other microscopic structural characteristics of each phase. The inhomogeneity of the seepage field on a microscopic scale influences the overall macroscopic seepage characteristics to a certain extent. Therefore, an effective method is found for evaluating the permeability coefficient of the multiphase composite material, and the properties and equivalent permeability coefficients of the internal components of the soil-stone mixture are researched on a microscopic scale, so that the method has important theoretical significance and engineering application value.
Disclosure of Invention
The invention aims to provide a method for researching the mesoscale of the equivalent permeability coefficient of a multiphase composite material. The mesoscale research method provided by the invention is based on finite element method modeling, realizes heterogeneity of an internal structure of the multiphase composite material through a Monte Carlo algorithm, and evaluates the equivalent permeability coefficient of the composite material by combining Darcy's law.
The research method for researching the equivalent permeability coefficient of the multiphase composite material from the microscopic scale based on the finite element method has the following four remarkable characteristics. Firstly, the method establishes a numerical simulation model by a finite element method from the viewpoint of microscopic dimension. Compared with the conventional test method and empirical formula method, the calculation method is simple, and the heterogeneity of the multiphase composite material can be well simulated. The second remarkable characteristic is that the method has simple calculation principle, applies corresponding water head difference on the upper surface and the lower surface of the material based on Darcy's law, and can obtain the seepage flow and seepage pressure distribution condition of each node of the material through finite element calculation. And substituting the finite element node calculation result into a Darcy formula to obtain the equivalent permeability coefficient of the multiphase material under a certain distribution condition. Thirdly, the method realizes heterogeneity in the material by means of a Monte Carlo algorithm, can realize a multiphase structure with different spatial arrangements in each simulation, and obtains a statistical rule of the equivalent permeability coefficient by calculating a Monte Carlo result. Compared with a test method or a traditional empirical formula, the method can change a single factor, study the influence of the single factor on the permeability coefficient and is beneficial to researching the most main factor influencing the permeability coefficient. In summary, the microscopic research method for the equivalent permeability coefficient of the multiphase composite material provided by the invention has the following advantages: compared with the traditional method, the calculation principle is simple and clear, the operability is strong, and time and labor are saved; modeling by a finite element method can construct heterogeneity inside the multiphase material; through Monte Carlo simulation, a statistical rule of the equivalent permeability coefficient can be obtained; the method can realize single variable control and explore the influence of various factors on the integral equivalent permeability coefficient.
The invention provides a microscopic scale research method for equivalent permeability coefficient of a multiphase composite material, which comprises the following steps:
(1) the study object attributes are determined. Including the input parameters such as the simulated sample size of the multiphase composite material to be researched, the geometric size and material parameters of each component, the volume content of each component and the like.
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (disperse phase) is round and randomly distributed in the matrix, and a random simulation sample is formed by means of a Monte Carlo method. When simulating with the Monte Carlo method, random variables that satisfy random uniform distributions must first be generated.
The positions of any dispersed phase particles in the dispensing domain are randomly distributed, and in a Cartesian coordinate system XOY, the coordinate of a reference point O of any dispersed phase particle can be expressed as
In the formula: f. of11(x，y)、f12(x，y)、f21(x，y)、f22(x, y) are the boundary curve functions of the dispersed phase throwing area (matrix phase).
For a rectangular cross-section, the coordinates of any reference point O are:
in the formula: xmax、Xmin、Ymax、YminRespectively the maximum value and the minimum value of the horizontal coordinate and the vertical coordinate on the boundary of the dispersed phase throwing area.
Considering that the dispersed phase of the simulated composite is circular, there are:
wherein Range (1, 1), Range (1, 2), Range (2, 1) and Range (2, 2) are respectively the minimum value and the maximum value of the horizontal and vertical coordinates of the edge position of the simulation sample η1、η2Is [0, 1 ]]A random number.
In the actual process of constructing the mesoscopic model, the most complicated and difficult solution is coincidence judgment. Because the disperse phases are not mutually contacted in the simulation process, an influence area can be set around each disperse phase particle, other disperse phases cannot enter the influence area in the range, namely, the throwing condition is met, and the influence area can be judged by the center distance of the adjacent disperse phase particles, namely:
in the formula: x is the number ofO、yOThe coordinate of the reference point of the impurity particles generated this time; xO、YONumbering reference point coordinates of the generated and put dispersed particles, wherein i belongs to R; r is1、r2The radius of the dispersed phase generated this time and the radius of the dispersed phase that has been put in are respectively given.
It should be noted that the above method for determining coincidence, also called "taking and putting", is to first take a dispersed phase particle and try to put it into a model. Once the dispersed phase particles are found to coincide with a certain dispersed phase already present in the model, they are removed and then a second attempt is made to place them in the model, the process continuing until a suitable dispersed phase position is found. The specific operation process can refer to the attached figure 1.
According to the introduction of the basic principle, the modeling of the multiphase composite material with the dispersed phases distributed randomly can be realized.
(3) And (3) carrying out mesh generation on the established finite element model by adopting a free mesh generation method, and automatically realizing the mesh generation of the numerical simulation model by means of finite element commercial software. Compared with the background mesh generation method, the method can automatically fit the shape of a geometric body, has strong applicability, can automatically complete mesh generation, and cannot cause distortion of the shape of dispersed phase particles due to the problems of mesh mapping and the like. The mesh generation result is shown in detail in fig. 3.
(4) A boundary condition is applied. Corresponding water head difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are water-impermeable boundaries. The boundary condition diagram is shown in fig. 2.
(5) Finite element calculation and post-processing. And (4) carrying out constant head simulation, obtaining distribution conditions such as seepage pressure distribution, seepage flow and the like of the final model through a finite element post-processing module, and extracting seepage flow values of all nodes at the top of the model. See figures 4 and 5 for details.
(6) And (4) calculating an equivalent permeability coefficient, and substituting the seepage flow of the top node of the simulated sample obtained in the fifth step into a Darcy formula to obtain the equivalent permeability coefficient. The specific expression is as follows:
ΔQ/Δt＝νA＝kiA；
wherein, Δ Q/Δ t is the seepage flow passing in unit time, k represents the permeability coefficient, A is the cross-sectional area orthogonal to the water flow direction, and i represents the hydraulic gradient. Considering the imposed boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiThe seepage flow (mm/s) of each node at the top of the sample; n is the number of nodes, HtopAnd HbottomThe water head values of the upper and lower surfaces, respectively, L is the length of the sample in the direction of the water flow, keffIs the equivalent permeability coefficient (mm/s) of the final heterogeneous material.
In summary, compared with the prior art, the method has the following remarkable effects:
1. the method is different from the traditional test method and empirical formula method, and a numerical model is established based on a finite element method from the aspect of microscopic dimension so as to evaluate the equivalent permeability coefficient of the multiphase composite material. The method provides a brand new idea for solving the equivalent permeability coefficient of the multiphase composite material, is simple, has strong operability, saves the cost of time, equipment and the like;
2. according to the method, the heterogeneity of the internal structure of the multi-phase composite material is realized through Monte Carlo simulation, the dispersed phases are randomly distributed in the matrix and are not overlapped with each other, the spatial random arrangement of each component in the composite material can be simulated more truly, and a new way is provided for researching the material attribute of the multi-phase composite material;
3. the method is based on Darcy's law, corresponding water head difference is applied to the upper surface and the lower surface of the material, the equivalent permeability coefficient of the multi-phase composite material can be determined through finite element calculation, and the algorithm is simple and clear and is easy to popularize;
4. the method can make up the defect that the factors are mutually influenced in test measurement, can change a single factor, researches the influence of the single factor on the permeability coefficient, and is favorable for researching the main factors influencing the permeability coefficient.
Drawings
FIG. 1 is a flow chart for solving for the equivalent permeability coefficient of a multiphase composite.
It can be seen from the figure that the solving process is mainlyIncluding finite element modeling, mesh generation, finite element solving analysis and infiltration
And (5) calculating a transmittance coefficient.
Fig. 2 is a schematic diagram of boundary conditions.
It can be seen from the figure that the upper and lower surfaces of the model are applied with corresponding head differences, and the left and right boundaries are watertight boundaries.
Fig. 3 is a finite element mesh subdivision.
As can be seen from the figure, in the two-dimensional finite element model of 100mm x 100mm, the dispersed phase is randomly distributed in the matrix
In phase, they are not overlapped and have different sizes.
Fig. 4 is a head distribution cloud.
Fig. 5 is a cloud of density distribution of seepage.
It can be seen from the figure that the permeation rate of the component with large permeability coefficient is larger.
FIG. 6 is a calculation of a multiphase composite with 60% dispersed phase over 200 Monte Carlo simulations.
FIG. 7 is a 600 Monte Carlo simulation calculation result, which was explored for the effect of different permeability coefficient ratios of each component on the equivalent permeability coefficient of the multiphase composite material.
Fig. 8 is a calculation result of exploring the influence of the particle size distribution type of the dispersed phase on the equivalent permeability coefficient of the multiphase composite.
Wherein the content of the first and second substances,(a) three different types of particle size distribution curves, and (b) three different particle size distribution curvesThe results of the Monte Carlo simulation of (1) 600 times.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the process of parameter sensitivity analysis, the method for researching the microscopic scale of the equivalent permeability coefficient of the multiphase composite material provided by the invention is used, so that the specific example described herein is the research on the influence of different influencing factors on the equivalent permeability coefficient. Note that when conducting sensitivity analysis of a single variable, other variables should remain consistent.
Example 1
In this example, the influence of the spatial arrangement of the dispersed phase on the permeability coefficient of the multiphase composite material is studied according to the microscopic research method of the equivalent permeability coefficient of the multiphase composite material provided by the present invention. The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 5-20mm and do not touch each other.
② the volume fraction of each phase was determined to be 60% for the dispersed phase and 40% for the matrix phase.
③ determining the material parameters of each phase
The permeability coefficients of the phases are respectively: the permeability coefficient of the dispersed phase was 5X 10-3m/s, permeability coefficient of matrix phase of 1X 10-9m/s。
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (disperse phase) is round and randomly distributed in the matrix, and a random simulation sample is formed by means of a Monte Carlo method. When simulating with the Monte Carlo method, random variables that satisfy random uniform distributions must first be generated.
The positions of any dispersed phase particles in the throwing domain are randomly distributed, and in a Cartesian coordinate system XOY, for a square section, the coordinate of any reference point O is as follows:
in the formula: xmax、Xmin、Ymax、YminRespectively the maximum value and the minimum value of the horizontal coordinate and the vertical coordinate on the boundary of the dispersed phase throwing area.
Considering that the dispersed phase of the simulated composite is circular, there are:
wherein Range (1, 1), Range (1, 2), Range (2, 1) and Range (2, 2) are respectively the minimum value and the maximum value of the horizontal and vertical coordinates of the edge position of the simulation sample η1、η2Is [0, 1 ]]A random number.
In the actual process of constructing the mesoscopic model, the most complicated and difficult solution is coincidence judgment. This part can be implemented by a "pick and place" algorithm. Because the disperse phases are not mutually contacted in the simulation process, an influence area can be set around each disperse phase particle, other disperse phases cannot enter the influence area in the range, namely, the throwing condition is met, and the influence area can be judged by the center distance of the adjacent disperse phase particles, namely:
in the formula: x is the number ofO、yOThe coordinate of the reference point of the impurity particles generated this time; xO、YONumbering reference point coordinates of the generated and put dispersed particles, wherein i belongs to R; r is1、r2The radius of the dispersed phase generated this time and the radius of the dispersed phase that has been put in are respectively given.
(3) And (3) carrying out mesh generation on the established finite element model by adopting a free mesh generation method, and automatically realizing the mesh generation of the numerical simulation model by means of finite element commercial software. Compared with the background mesh generation method, the method can automatically fit the shape of a geometric body, has strong applicability, can automatically complete mesh generation, and cannot cause distortion of the shape of dispersed phase particles due to the problems of mesh mapping and the like.
(4) A boundary condition is applied. Corresponding water head difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are water-impermeable boundaries.
(5) Finite element calculation and post-processing. And (4) performing constant head simulation, obtaining distribution conditions such as water head distribution, seepage density and the like of the final model through a finite element post-processing module, and extracting seepage density values of all nodes at the top of the model.
(6) And (4) calculating an equivalent permeability coefficient, and substituting the seepage density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent permeability coefficient. The specific expression is as follows:
wherein Δ Q/Δ t is the heat flux passing per unit time, k represents the permeability coefficient, A is the material area orthogonal to the heat transfer direction,
indicating a temperature gradient. Considering the imposed boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiThe seepage density of each node at the top, n is the total number of nodes at the top, TtopAnd TbottomRespectively the temperature values of the upper and lower surfaces, L the length of the sample in the heat flow transfer direction, keffIs the equivalent permeability coefficient of the final heterogeneous material.
(6) And repeating the steps, and carrying out 200 times of Monte Carlo simulation to obtain a calculation result. The results show that the permeability coefficient is not sensitive to the random position distribution of the dispersed phase. As can be seen from fig. 6, for the multiphase composite material with different random spatial position arrangements, although each component has different permeability characteristics, the permeability coefficient obtained by solving each simulation is slightly different, but the cumulative average permeability coefficient gradually becomes stable as the simulation times increase.
Example 2
In this example, the method for investigating the microscopic scale of the equivalent permeability coefficient of the multiphase composite material according to the present invention was investigated for the influence of the different permeability coefficient ratios of the components on the permeability coefficient of the multiphase composite material.
The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 5-20mm and do not touch each other.
② the volume fraction of each phase is determined, the volume fraction of the dispersed phase is in the range of 0-65%.
③ determining the material parameters of each phase
The permeability coefficients of the phases are respectively: the matrix phase is soil body, and the permeability coefficient takes five typical values into consideration, namely 1 multiplied by 10-10m/s、1×10-8m/s、1×10-7m/s、1×10-6m/s、1×10-4m/s, the matrix phase is blocky stone with a permeability coefficient of 1X 10-9m/s。
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (disperse phase) is round and randomly distributed in the matrix, and a random simulation sample is formed by means of a Monte Carlo method. When simulating with the Monte Carlo method, random variables that satisfy random uniform distributions must first be generated.
The positions of any dispersed phase particles in the throwing domain are randomly distributed, and in a Cartesian coordinate system XOY, for a square section, the coordinate of any reference point O is as follows:
in the formula: xmax、Xmin、Ymax、YminRespectively horizontal and vertical at the boundary of the dispersed phase throwing areaMaximum and minimum values of coordinates.
Considering that the dispersed phase of the simulated composite is circular, there are:
wherein Range (1, 1), Range (1, 2), Range (2, 1) and Range (2, 2) are respectively the minimum value and the maximum value of the horizontal and vertical coordinates of the edge position of the simulation sample η1、η2Is [0, 1 ]]A random number.
In the actual process of constructing the mesoscopic model, the most complicated and difficult solution is coincidence judgment. This part can be implemented by a "pick and place" algorithm. Because the disperse phases are not mutually contacted in the simulation process, an influence area can be set around each disperse phase particle, other disperse phases cannot enter the influence area in the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of the adjacent disperse phase particles, namely, the center distance of the adjacent disperse phase particles is judged
In the formula: x is the number ofO、yOThe coordinate of the reference point of the impurity particles generated this time; xO、YONumbering reference point coordinates of the generated and put dispersed particles, wherein i belongs to R; r is1、r2The radius of the dispersed phase generated this time and the radius of the dispersed phase that has been put in are respectively given.
(3) And (3) carrying out mesh generation on the established finite element model by adopting a free mesh generation method, and automatically realizing the mesh generation of the numerical simulation model by means of finite element commercial software. Compared with the background mesh generation method, the method can automatically fit the shape of a geometric body, has strong applicability, can automatically complete mesh generation, and cannot cause distortion of the shape of dispersed phase particles due to the problems of mesh mapping and the like.
(4) A boundary condition is applied. Corresponding water head difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are water-impermeable boundaries.
(5) Finite element calculation and post-processing. And (4) performing constant head simulation, obtaining distribution conditions such as water head distribution, seepage density and the like of the final model through a finite element post-processing module, and extracting seepage density values of all nodes at the top of the model.
(6) And (4) calculating an equivalent permeability coefficient, and substituting the seepage density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent permeability coefficient. The specific expression is as follows:
wherein Δ Q/Δ t is the heat flux passing per unit time, k represents the permeability coefficient, A is the material area orthogonal to the heat transfer direction,
indicating a temperature gradient. Considering the imposed boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiThe seepage density of each node at the top, n is the total number of nodes at the top, TtopAnd TbottomRespectively the temperature values of the upper and lower surfaces, L the length of the sample in the heat flow transfer direction, keffIs the equivalent permeability coefficient of the final heterogeneous material.
(6) The above steps were repeated, 600 Monte Carlo simulations were performed, and the calculation results are shown in FIG. 7. To eliminate the effect of dimension, the relative permeability (k) was investigatedm/kiI.e. byRatio of matrix phase to dispersed phase) introduces a normalized permeability (k)n＝keff/ki) The concept of (1). As shown in the figure, the influence of the different permeability coefficients of the components of the composite material on the normalized permeability is obvious, and as the content of the dispersed phase (trabecite) increases, when the permeability coefficient of the dispersed phase is smaller than that of the matrix phase, the normalized permeability k of the multi-phase composite material isnGradually decrease and conversely increase. This observation is consistent with the actual situation, since in a practical multiphase composite sample, an increase in the volume content of the dispersed phase (rock) is beneficial to increase the equivalent permeability coefficient when it is greater than the matrix phase (soil). Therefore, the internal structure of the multiphase composite material can be correspondingly adjusted in engineering so as to meet the requirement of the equivalent permeability coefficient of the multiphase composite material.
Example 3
This example was conducted by a microscopic examination method of the equivalent permeability coefficient of the multiphase composite material proposed in the present invention, and the influence of the particle size distribution type of the dispersed phase on the permeability coefficient of the multiphase composite material was examined.
The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 5-20mm and do not touch each other.
② the volume fraction of each phase is determined, the volume fraction of the dispersed phase is in the range of 0-65%.
③ determining the material parameters of each phase
The permeability coefficients of the phases are respectively: the permeability coefficient of the matrix phase is 1X 10-4m/s, permeability coefficient of matrix phase of 1X 10-9m/s。
④, the particle distribution curve was determined, taking into account three cases, i.e. a curve with large particles as the main, homogeneous distribution and large particles as the main (see fig. 8 a).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (disperse phase) is round and randomly distributed in the matrix, and a random simulation sample is formed by means of a Monte Carlo method. When simulating with the Monte Carlo method, random variables that satisfy random uniform distributions must first be generated.
The positions of any dispersed phase particles in the throwing domain are randomly distributed, and in a Cartesian coordinate system XOY, for a square section, the coordinate of any reference point O is as follows:
in the formula: xmax、Xmin、Ymax、YminRespectively the maximum value and the minimum value of the horizontal coordinate and the vertical coordinate on the boundary of the dispersed phase throwing area.
Considering that the dispersed phase of the simulated composite is circular, there are:
wherein Range (1, 1), Range (1, 2), Range (2, 1) and Range (2, 2) are respectively the minimum value and the maximum value of the horizontal and vertical coordinates of the edge position of the simulation sample η1、η2Is [0, 1 ]]A random number.
In the actual process of constructing the mesoscopic model, the most complicated and difficult solution is coincidence judgment. This part can be implemented by a "pick and place" algorithm. Because the disperse phases are not mutually contacted in the simulation process, an influence area can be set around each disperse phase particle, other disperse phases cannot enter the influence area in the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of the adjacent disperse phase particles, namely, the center distance of the adjacent disperse phase particles is judged
In the formula: x is the number ofO、yOThe coordinate of the reference point of the impurity particles generated this time; xO、YOFor dispersed particles already formed and dosedReference point coordinates are numbered, i belongs to R; r is1、r2The radius of the dispersed phase generated this time and the radius of the dispersed phase that has been put in are respectively given.
(3) And (3) carrying out mesh generation on the established finite element model by adopting a free mesh generation method, and automatically realizing the mesh generation of the numerical simulation model by means of finite element commercial software. Compared with the background mesh generation method, the method can automatically fit the shape of a geometric body, has strong applicability, can automatically complete mesh generation, and cannot cause distortion of the shape of dispersed phase particles due to the problems of mesh mapping and the like.
(4) A boundary condition is applied. Corresponding water head difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are water-impermeable boundaries.
(5) Finite element calculation and post-processing. And (4) performing constant head simulation, obtaining distribution conditions such as water head distribution, seepage density and the like of the final model through a finite element post-processing module, and extracting seepage density values of all nodes at the top of the model.
(6) And (4) calculating an equivalent permeability coefficient, and substituting the seepage density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent permeability coefficient. The specific expression is as follows:
wherein Δ Q/Δ t is the heat flux passing per unit time, k represents the permeability coefficient, A is the material area orthogonal to the heat transfer direction,
indicating a temperature gradient. Considering the imposed boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiThe seepage density of each node at the top, n is the total number of nodes at the top, TtopAnd TbottomRespectively the temperature values of the upper and lower surfaces, L the length of the sample in the heat flow transfer direction, keffIs the equivalent permeability coefficient of the final heterogeneous material.
(6) The above steps were repeated, 600 Monte Carlo simulations were performed, and the calculation results are shown in FIG. 8 b. To eliminate the effect of the dimensions, a normalized permeability (k) is introducedn＝keff/ki) The concept of (1). The results show that the type of particle size distribution curve of the dispersed phase does not have a significant effect on the normalized permeability. The particle size distribution curve of the dispersed phase is changed mainly by increasing or decreasing the number of particles of each particle size of the lump stone, and the voids between the large particles are filled with the smaller particles (matrix phase). The change in the type of particle size distribution of the dispersed phase does not affect the permeability coefficient of the matrix phase, while the matrix phase with greater permeability primarily controls the permeability properties of the multiphase material. Therefore, in practical engineering, the purpose of obviously improving the permeability coefficient of the multiphase composite material cannot be achieved by adjusting the grading distribution type of the dispersed phase particles.
Claims (1)
1. A method for researching the mesoscale of the equivalent permeability coefficient of a multiphase composite material is characterized by comprising the following steps:
1) establishing a numerical simulation model, and realizing the space distribution randomness of the internal structure of the multi-phase composite material through a Monte Carlo algorithm:
the method specifically comprises the following steps: the following parameters were entered: simulating the size, the geometric size and the permeability coefficient of a sample; realizing the space distribution randomness of the internal structure of the multi-phase composite material through a MonteCarlo algorithm, and establishing a finite element model; the heterogeneity of the internal structure of the multi-phase composite material is realized through a MonteCarlo algorithm, the dispersed phases are randomly distributed in the matrix and are not overlapped with each other, and the method is mainly realized through a 'taking and placing' method;
2) and aiming at the established numerical simulation model, carrying out finite element meshing:
importing the established numerical simulation model into finite element calculation software to realize free mesh subdivision; the finite element software automatically completes mesh subdivision according to the appearance of the geometric body;
3) applying boundary conditions to the simulated sample:
predicting the permeability coefficient by combining Darcy's law; applying corresponding water head difference on the upper surface and the lower surface of the simulation sample, wherein the left surface and the right surface are watertight boundaries;
4) carrying out finite element solving calculation under a given boundary condition, and substituting the seepage density at the top of the sample obtained by the finite element calculation into a Darcy formula to obtain an equivalent permeability coefficient;
after the seepage calculation is carried out by finite element software, the seepage quantity of a top node of the simulation sample can be obtained and is brought into the Darcy formula, and the equivalent permeability coefficient can be obtained; the specific expression is as follows:
ΔQ/Δt＝vA＝kiA；
wherein, Δ Q/Δ t is the seepage flow passing in unit time, k represents the permeability coefficient, A is the cross-sectional area orthogonal to the water flow direction, and i represents the hydraulic gradient; considering the imposed boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiThe seepage flow of each node at the top of the sample is mm/s; n is the number of nodes, HtopAnd HbottomThe water head values of the upper and lower surfaces, respectively, and L is the sample along the water flow directionLength, keffIs the equivalent permeability coefficient mm/s of the final heterogeneous material.
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