CN111027236A - Microscopic scale research method for equivalent thermal conductivity coefficient of multiphase composite material - Google Patents
Microscopic scale research method for equivalent thermal conductivity coefficient of multiphase composite material Download PDFInfo
- Publication number
- CN111027236A CN111027236A CN201911043580.1A CN201911043580A CN111027236A CN 111027236 A CN111027236 A CN 111027236A CN 201911043580 A CN201911043580 A CN 201911043580A CN 111027236 A CN111027236 A CN 111027236A
- Authority
- CN
- China
- Prior art keywords
- phase
- thermal conductivity
- soil
- composite material
- heat
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
Landscapes
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Abstract
The invention relates to a microscopic scale research method for equivalent thermal conductivity of a multiphase composite material. The invention aims at the heterogeneous characteristic of the composite material, aims at the most common material in geotechnical engineering, namely the soil body from the aspect of microscopic scale, and establishes a numerical model based on a finite element method so as to estimate the equivalent thermal conductivity coefficient of the composite material. The established numerical model is simulated by a Monte Carlo algorithm to obtain a soil body structure with space randomness, the equivalent heat conductivity coefficients under three conditions of the soil body are contrastively analyzed by combining a finite element calculation method and a Fourier formula based on steady-state analysis, and the influence of factors such as soil body type, porosity, saturation, space distribution of disperse phases and the like on the equivalent heat conductivity coefficients of the soil body is explored. The invention provides a method capable of simulating the heterogeneity of the internal structure of the multiphase composite material based on the microscopic scale, provides a new idea for analyzing the heat conduction 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 thermal conductivity of a multiphase composite material.
Background
Many materials in geotechnical engineering are considered to be multiphase composite materials, for example, earth is generally considered to be a multiphase system consisting of a soil skeleton, air, water and ice. Geotechnical materials play an important role in environmental and engineering applications, and the thermal performance thereof is one of the most critical parameters of the geotechnical materials. The heat conductivity coefficient, the convective heat transfer coefficient and the specific heat capacity are main factors influencing the thermal behavior of the soil body, wherein the heat conductivity coefficient is the most key parameter reflecting the heat transfer capacity, and the heat transfer coefficient has important application in geothermal energy development and underground engineering construction.
With the drastic reduction of fossil energy fuels, and the resulting greenhouse effect, there is an increasing trend towards the development and use of environmentally friendly, sustainable renewable energy sources, such as wind, solar, tidal, biological, geothermal, etc. Among these green energy sources, geothermal energy is developed at a high speed with great rapidity in recent years due to the advantages of wide distribution, easy development and mature technology, and underground engineering construction such as urban subways, tunnels and the like is not favored, but due to the lack of unified national and industrial standards, the testing method is respectively very difficult to accurately calculate, evaluate and evaluate the heat conductivity coefficient. Therefore, the accurate measurement of the heat conductivity coefficient has important significance for saving investment and reasonable development.
In the process of underground engineering construction, the heat conductivity coefficient is one of the most main thermophysical parameters for calculating a temperature field, and is also an important parameter for determining a frozen curtain during the construction design of a thermotechnical ground freezing technology. In the design and construction of artificial freezing method in underground engineering (such as subway tunnel and deep mine), it is also very important to accurately select thermal physical parameters of unfrozen soil and frozen soil. In actual engineering, the measurement of all soil bodies in a construction area is unrealistic, and reasonable evaluation of thermal conductivity has important theoretical significance and engineering practical value for geotechnical engineering construction.
The thermal conductivity is affected by many factors including the mineral composition, particle size, grading, particle size, dry density, porosity, water content, temperature, pore size, pore shape, pore orientation, pore space arrangement, etc. of the soil mass. The method for determining the thermal conductivity coefficient mainly comprises two methods of experimental test and empirical model prediction.
The test measurement method is generally divided into a probe method and a field drilling measurement method. The probe method can directly measure the heat conductivity coefficient of the soil body through equipment, has the characteristics of short test period, high precision, relatively low requirement on test environment, good equipment portability and the like, and is limited by the limitation that the probe size can only measure the heat conductivity coefficient of the soil body in a shallow layer. The comprehensive heat conductivity coefficient can be measured by a field drilling test, but the operation is complicated, the cost is high, and the result is only a local small-range soil mass value. The thermal conductivity measured by the experimental method has high precision, but compared with the calculation method by an empirical formula, the method is relatively time-consuming and expensive.
The second type of determination is empirical formula calculation, which provides a relatively coarse estimate. The method can obtain equivalent thermal conductivity coefficients only by determining input parameters of a formula, which is beneficial to the estimation of the performance of various materials, but the prediction method is greatly influenced by a physical model and can only be used as a simple method for predicting before actual engineering.
The multiphase material has strong heterogeneity and is influenced by various factors, so that the determination of the heat conductivity coefficient of the multiphase composite material is complex. However, the above methods cannot independently explore the influence of a single factor on the equivalent thermal conductivity of the multi-phase composite material. Therefore, how to accurately measure the equivalent thermal conductivity of the multiphase composite material and simultaneously explore the influence of different factors on the thermal conductivity is always a hot point of attention.
Disclosure of Invention
The invention aims to provide a microscopic scale research method for equivalent thermal conductivity of a multiphase composite material. The microscopic scale research method provided by the invention is based on finite element method modeling, realizes heterogeneity of the internal structure of the multiphase composite material through Monte Carlo algorithm, and evaluates the influence of various factors such as porosity, saturation, soil type, soil state and the like on the equivalent heat conductivity coefficient.
The research method for researching the multiphase composite material from the microscopic scale based on the finite element method has the following four remarkable characteristics. Firstly, the method is based on the microscopic scale, and a numerical simulation model is established by taking a soil body in geotechnical engineering as an example through a finite element method. Compared with the conventional test method and empirical formula method, the calculation is simpler, and the heterogeneity of the multiphase composite material can be better simulated. The second remarkable characteristic is that the method has a simple calculation principle, a certain temperature difference is applied to the upper surface and the lower surface of the material based on the principle of steady-state thermal analysis, and the heat flow density and the temperature field distribution condition of each node of the material can be obtained through finite element calculation. And substituting the finite element node calculation result into a Fourier formula to obtain the equivalent heat conductivity 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, a multiphase soil body structure with different spatial arrangements can be obtained through each simulation, and a statistical rule of equivalent heat conductivity coefficients is obtained through Monte Carlo result calculation. Compared with a test method or a traditional empirical formula, the method can change a single factor to study the influence of the single factor on the thermal conductivity, and is favorable for researching the most main factor influencing the thermal conductivity. In summary, the microscopic method for studying the equivalent thermal conductivity 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 equivalent heat conductivity coefficients can be obtained; the method can realize single variable control and explore the influence of various factors on the overall equivalent thermal conductivity.
The microscopic scale research method of the equivalent thermal conductivity coefficient of the multiphase composite material provided by the invention comprises the following steps:
(1) the study object attributes are determined. Including input parameters such as simulated sample size of the multiphase composite material to be studied, geometric dimensions and material parameters of each component, and percentages of each component. The volume fraction of each phase can be expressed in terms of porosity (n) which is the percentage of the dispersed phase in the total volume and saturation (Sr) which represents the percentage of the aqueous phase in the pore volume, and the other phases can be transformed according to the two parameters: the volume content of the soil skeleton is 1-n, the volume content of the pore phase is n, the volume content of the water phase is n.Sr, and the volume content of the air phase is n (1-Sr).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (inclusion phase) is circular 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 inclusion phase of the simulated composite material 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 dispersed phases are not mutually contacted in the simulation process, an influence area can be set around each dispersed phase particle, other inclusion phases cannot enter the influence area within the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of adjacent inclusion 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 inclusion phase already put in are respectively.
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 dispersion already present in the mould, they are removed and a second attempt is made to place them in the mould, the process continuing until a suitable dispersed phase location 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 results are shown in detail in fig. 3.
(4) A boundary condition is applied. A certain temperature difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are heat insulation boundaries. The boundary condition diagram is shown in fig. 2.
(5) Finite element calculation and post-processing. And performing steady-state thermal analysis, obtaining the distribution conditions such as the temperature field, the heat flow density and the like of the final model through a finite element post-processing module, and extracting the heat flow density value of each node at the top of the model. Specific temperature field distribution cloud charts and heat flow density distribution diagrams are shown in fig. 4 and 5.
(6) And (4) calculating the equivalent thermal conductivity, and substituting the heat flow density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent thermal conductivity. The specific expression is as follows:
where Δ Q/Δ T is the heat flux passing per unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient.
Wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffIs the equivalent thermal conductivity of the final heterogeneous material.
(7) Parameter sensitivity analysis
The influence of porosity, saturation, dispersed phase space position, soil type and soil state on the equivalent heat conductivity coefficient is mainly researched. The method specifically comprises the following steps:
① porosity, saturation, can be achieved by changing the input parameters n and Sr of the model;
②, the distribution of the spatial positions of the dispersed phases can be realized by researching the influence of Monte Carlo simulation on the equivalent heat conductivity coefficient through multiple solving;
③ soil type, because the soil material is composed of different mineral compositions, the heat conductivity is different, the soil type is different, which is expressed as the difference of heat conductivity value, therefore, the influence of the soil material on the equivalent heat conductivity can be explored by changing the heat conductivity value of the matrix phase in the multi-phase material;
④ the state of soil body can be divided into saturated soil and unsaturated soil according to whether water is full of the pores in the soil, frozen soil and non-frozen soil according to whether ice phase is contained, different states can be determined by saturation and ice content, and the soil body can be divided into three states according to the ice content, namely natural state soil (no ice phase), partially frozen soil (water and ice are contained, but the specific ice content is difficult to determine in the actual engineering), and completely frozen soil (no water phase).
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, a numerical model is established based on a finite element method from the viewpoint of microscopic dimension, and the equivalent thermal conductivity can be obtained through a Fourier formula based on steady-state analysis. The method provides a brand new idea for solving the equivalent heat conductivity coefficient of the multiphase composite material, is simple, has strong operability, and 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, each inclusion phase is randomly distributed in the matrix and is not overlapped with each other, the spatial random arrangement of each component in the composite material can be simulated more truly, a new way is provided for researching the attribute of the multi-phase composite material, the algorithm is simple and clear, and the popularization is easy;
3. the Monte Carlo algorithm can simulate the soil body under a certain porosity or saturation condition, is favorable for researching the statistical rule of the soil body through multiple calculations, and analyzes the thermal mechanism influencing the heat conductivity coefficient of the multiphase material from a microscopic scale;
4. the method simultaneously considers the influence of a plurality of factors on the equivalent heat conductivity coefficient, and relates to a plurality of factors such as porosity, saturation, dispersed phase space arrangement, soil state, soil type and the like.
Drawings
FIG. 1 is a flow chart for solving for the equivalent thermal conductivity of a multiphase composite.
It can be seen from the figure that the solving process mainly comprises finite element modeling, mesh subdivision, finite element solving and heat conductivity coefficient
And calculating, influence factor analyzing and the like.
Fig. 2 is a schematic diagram of boundary conditions.
As can be seen from the figure, a certain temperature difference is only applied to the upper and lower surfaces of the model, and the left and right boundaries are completely heat-insulating
State.
Fig. 3 is a finite element mesh subdivision.
Taking partially frozen unsaturated soil as an example, the soil is a four-phase system and is respectively a soil framework, water, gas and ice phases. From the figure
It can be seen that in the two-dimensional finite element model of 100mm × 100mm, the dispersed phases (water phase, gas phase, ice phase) are randomly distributed
In the matrix phase (soil skeleton), the dispersed phases are not overlapped with each other and have different sizes.
Fig. 4 is a temperature field distribution cloud.
As can be seen from the figure, under a certain temperature load, the overall temperature field distribution is relatively uniform and layered.
FIG. 5 is a cloud of heat flux density distributions.
It can be seen that the heat flux density through which the component with the higher thermal conductivity passes is also greater.
FIG. 6 is a result of Monte Carlo simulation calculations performed on three sets of 600 times to investigate the effect of the spatial arrangement of the dispersed phase on the thermal conductivity of the multi-phase composite material.
Wherein (a) is group a cumulative average thermal conductivity; (b) cumulative average thermal conductivity for group B; (c) cumulated for group C
Average thermal conductivity; (d) three sets of cumulative average thermal conductivity coefficients; (e) three sets of cumulative standard deviations.
FIG. 7 is a simulation result of an investigation of the effect of soil mass type on the thermal conductivity of a multi-phase composite.
Fig. 8 is a soil sample finite element mesh split view in different states.
Wherein (a) represents a natural state; (b) indicating a partially frozen soil state; (c) indicating a completely frozen state.
Fig. 9 is a graph of the thermal conductivity versus porosity and saturation for various states, which is a study of the effect of porosity and saturation on the thermal conductivity of a multiphase composite.
Wherein (a) represents a natural state; (b) indicating a partially frozen soil state; (c) indicating a completely frozen state.
FIG. 10 is a graph of thermal conductivity versus porosity for different saturation levels.
Wherein, (a) 20% (b) 40% (c) 60% (d) 80% (e) 100% (e) Sr
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 finite element method-based microscopic research method for the equivalent thermal conductivity of the multiphase composite material is adopted, so that the specific example described herein is the research on the influence of different influencing factors on the equivalent thermal conductivity. Note that when conducting sensitivity analysis of a single variable, other variables should remain consistent.
Example 1
In this example, according to the research method for performing mesoscale on the equivalent thermal conductivity of the multiphase composite material based on the finite element method, the influence of the spatial arrangement of the dispersed phase on the thermal conductivity of the multiphase composite material is researched. The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining input parameters (porosity and saturation)
The simulation of the soil body in the natural state shows that the water content of the soil body in the natural state is 13-105%, and the average value is 29%. Selecting a typical value: the porosity (n) was 50% and the saturation (Sr) was 78.3%. The volume fraction of each phase is determined according to the porosity (n) and the saturation (Sr), the percentage of the dispersed phase in the total volume is 50% of the porosity, the saturation represents the percentage of the water phase in the pore volume, and other phases can be obtained by conversion according to the two parameters: the volume content of the soil skeleton is 50%, the volume content of the pore phase is 50%, the volume content of the water phase is 39.15% and the volume content of the air phase is 10.85%.
② determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The individual dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 1-5mm and do not touch each other.
③ determining the material parameters of each phase
The thermal conductivity of each phase is: the thermal conductivity of the soil skeleton is 2W/(m.K), the thermal conductivity of ice is 2.25W/(m.K), the thermal conductivity of the water phase is 0.5W/(m.K), and the thermal conductivity of air is 0.02W/(m.K).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (inclusion phase) is circular 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、YminMaximum and minimum values of the upper and lower horizontal coordinates of the boundary of the dispersion phase throwing area, where Xmax-Xmin＝Ymax-Ymin＝100。
Considering that the inclusion phase of the simulated composite material 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 "take and put" algorithm. Because the dispersed phases are not mutually contacted in the simulation process, an influence area can be set around each dispersed phase particle, other inclusion phases cannot enter the influence area within the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of adjacent inclusion 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 inclusion phase already put in are respectively.
(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. A certain temperature difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are heat insulation boundaries.
(5) Finite element calculation and post-processing. And performing steady-state thermal analysis, obtaining the distribution conditions such as the temperature field, the heat flow density and the like of the final model through a finite element post-processing module, and extracting the heat flow density value of each node at the top of the model.
(6) And (4) calculating the equivalent thermal conductivity, and substituting the heat flow density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent thermal conductivity. The specific expression is as follows:
where Δ Q/Δ T is the heat flux passing per unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient.
Wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffIs the equivalent thermal conductivity of the final heterogeneous material.
(6) The above steps are repeated, three groups of 600 Monte Carlo simulations are carried out, and a statistical distribution result is obtained. The results show that the thermal conductivity is not sensitive to the random position distribution of the dispersed phase. The cumulative average thermal conductivity of the 600 Monte Carlo simulations was between the maximum and minimum values, as shown in fig. 6. The offset (difference between the maximum value and the minimum value) is close to 1W/(m.K), and the calculated equivalent thermal conductivity gradually becomes stable along with the increase of the simulation times. As can be seen from FIG. 6, 90% of the simulation results were all within the region of 1.05. + -. 0.05W/(m.K). Therefore, the spatially random arrangement of the dispersed phase does not significantly affect the equivalent thermal conductivity of the multiphase composite.
Example 2
In the embodiment, according to the research method for carrying out the mesoscale on the equivalent thermal conductivity of the multiphase composite material based on the finite element method, the influence of the soil body type on the thermal conductivity of the multiphase composite material is researched.
The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining input parameters (porosity and saturation)
The examples mainly study the influence of soil type on equivalent thermal conductivity, and therefore do not specifically limit porosity and saturation. The volume fraction of each phase is determined according to the porosity (n) and the saturation (Sr), wherein the porosity is the percentage of the dispersed phase in the total volume, the saturation represents the percentage of the water phase in the pore volume, and the other phases can be obtained by conversion according to the two parameters: the volume content of the soil skeleton is 1-n, the volume content of the pore phase is n, the volume content of the water phase is n.Sr, and the volume content of the air phase is n (1-Sr).
② determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The individual dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 1-5mm and do not touch each other.
③ determining the material parameters of each phase
The research shows that the mineral components are different, the thermal conductivity of the soil particles is slightly different, and the thermal conductivity of the soil particles is 1.2-7.5W/(m.K). In order to investigate the influence of the heat conductivity coefficients of different soil frameworks on the overall equivalent heat conductivity coefficient, the heat conductivity coefficients of all phases are respectively set as: the thermal conductivity of the soil skeleton is 1, 2, 4, 8W/(m.K), the thermal conductivity of ice is 2.25W/(m.K), the thermal conductivity of the water phase is 0.5W/(m.K), and the thermal conductivity of air is 0.02W/(m.K).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (inclusion phase) is circular 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、YminMaximum and minimum values of the upper and lower horizontal coordinates of the boundary of the dispersion phase throwing area, where Xmax-Xmin＝Ymax-Ymin＝100。
Considering that the inclusion phase of the simulated composite material 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 "take and put" algorithm. Because the dispersed phases are not mutually contacted in the simulation process, an influence area can be set around each dispersed phase particle, other inclusion phases cannot enter the influence area within the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of adjacent inclusion 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、YOReference point for dispersed particles that have been generated and dosedCoordinates are numbered, i belongs to R; r is1、r2The radius of the dispersed phase generated this time and the radius of the inclusion phase already put in are respectively.
(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. A certain temperature difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are heat insulation boundaries.
(5) Finite element calculation and post-processing. And performing steady-state thermal analysis, obtaining the distribution conditions such as the temperature field, the heat flow density and the like of the final model through a finite element post-processing module, and extracting the heat flow density value of each node at the top of the model.
(6) And (4) calculating the equivalent thermal conductivity, and substituting the heat flow density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent thermal conductivity. The specific expression is as follows:
where Δ Q/Δ T is the heat flux passing per unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient.
Wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffIs the equivalent thermal conductivity of the final heterogeneous material.
(6) The above steps are repeated to change the thermal conductivity of the soil framework, and 600 Monte Carlo simulations are respectively performed to obtain statistical distribution results, as shown in FIG. 7. The result shows that the heat conductivity of the soil framework has obvious influence on the equivalent heat conductivity. Along with the increase of the porosity, the volume fraction of the soil framework is reduced, the contribution of the heat conductivity coefficient of the soil framework to the whole heat conductivity coefficient is reduced, and the equivalent heat conductivity coefficient is gradually reduced. Meanwhile, the higher the heat conductivity coefficient of the soil framework is, the more sensitive the equivalent heat conductivity coefficient is to the porosity.
Example 3
In the present example, according to the research method for performing mesoscale on the equivalent thermal conductivity of the multiphase composite material based on the finite element method, the influence of the porosity and the saturation on the thermal conductivity of the multiphase composite material is researched. The method comprises the following specific steps:
(1) the study object attributes are determined.
① determining input parameters (porosity and saturation)
The influence of porosity and saturation on equivalent thermal conductivity is mainly researched, the porosity is not specifically limited in simulation, and a multi-phase soil body structure with a certain porosity is randomly generated. The saturation levels were set to 0%, 20%, 40%, 60%, 80%, and 100%, respectively. The volume fraction of each phase is determined according to the porosity (n) and the saturation (Sr), wherein the porosity is the percentage of the dispersed phase in the total volume, the saturation represents the percentage of the water phase in the pore volume, and the other phases can be obtained by conversion according to the two parameters: the volume content of the soil skeleton is 1-n, the volume content of the pore phase is n, the volume content of the water phase is n.Sr, and the volume content of the air phase is n (1-Sr).
② determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The individual dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 1-5mm and do not touch each other.
③ determining the material parameters of each phase
The thermal conductivity of each phase was set as: the thermal conductivity of the soil skeleton is 2W/(m.K), the thermal conductivity of ice is 2.25W/(m.K), the thermal conductivity of the water phase is 0.5W/(m.K), and the thermal conductivity of air is 0.02W/(m.K).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (inclusion phase) is circular 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、YminMaximum and minimum values of the upper and lower horizontal coordinates of the boundary of the dispersion phase throwing area, where Xmax-Xmin＝Ymax-Ymin＝100。
Considering that the inclusion phase of the simulated composite material 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 "take and put" algorithm. Because the dispersed phases are not mutually contacted in the simulation process, an influence area can be set around each dispersed phase particle, other inclusion phases cannot enter the influence area within the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of adjacent inclusion 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 inclusion phase already put in are respectively.
(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. A certain temperature difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are heat insulation boundaries.
(5) Finite element calculation and post-processing. And performing steady-state thermal analysis, obtaining the distribution conditions such as the temperature field, the heat flow density and the like of the final model through a finite element post-processing module, and extracting the heat flow density value of each node at the top of the model.
(6) And (4) calculating the equivalent thermal conductivity, and substituting the heat flow density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent thermal conductivity. The specific expression is as follows:
where Δ Q/Δ T is the heat flux passing per unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient.
Wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffIs the equivalent thermal conductivity of the final heterogeneous material.
(6) Repeating the steps, changing different soil states, and performing Monte Carlo simulation for 600 times respectively. Fig. 9(a), (b) and (c) are the results of 600 monte carlo simulations of unfrozen soil, partially frozen soil and fully frozen soil, respectively. In general, as the porosity increases, the thermal conductivity shows a decreasing trend except for completely saturated frozen soil; the thermal conductivity coefficient of different saturation degrees is different under the same porosity. Under the condition of low porosity, the equivalent thermal conductivity value is not sensitive to saturation, the thermal conductivity is continuously reduced along with the increase of the porosity, and the difference value of the two adjacent thermal conductivity values is increased. The results show that the thermal conductivity is different for the three soil conditions. As a three-phase material, the unfrozen soil has a simpler linear relationship between porosity and saturation. The equivalent thermal conductivity of the soil body is linearly increased along with the gradual filling of the soil pores by the water. For the frozen soil body in different saturation states, the equivalent thermal conductivity coefficient difference is large. The change of the saturation can cause the change of the equivalent thermal conductivity of the frozen soil, and the influence is more obvious when the porosity is larger. The difference between different saturation degrees of the soil body in the completely frozen state is the largest, and the equivalent heat conductivity coefficient change of partial frozen soil is between the completely frozen soil state and the natural soil body state.
Example 4
In the embodiment, according to the research method for carrying out the mesoscale on the equivalent thermal conductivity of the multiphase composite material based on the finite element method, the influence of the soil body state on the thermal conductivity of the multiphase composite material is researched.
The method comprises the following specific steps:
(1) the study object attributes are determined.
④ determining input parameters (porosity and saturation)
The example mainly studies the influence of the soil state on the equivalent thermal conductivity coefficient, mainly considers three soil states, which are respectively: the natural soil body state, the partial freezing state and the complete freezing state, wherein the volume ratio of the water phase to the ice phase in the partial freezing state is 1: 1. The porosity is not particularly limited, and a multi-phase soil body structure with a certain porosity is randomly generated. The saturation levels are set to 0%, 20%, 40%, 60%, 80%, and 100%. The volume fraction of each phase is determined according to the porosity (n) and the saturation (Sr), wherein the porosity is the percentage of the dispersed phase in the total volume, the saturation represents the percentage of the water phase in the pore volume, and the other phases can be obtained by conversion according to the two parameters: the volume content of the soil skeleton is 1-n, the volume content of the pore phase is n, the volume content of the water phase is n.Sr, and the volume content of the air phase is n (1-Sr).
⑤ determining the geometric dimensions
The simulated sample size was 100mm by 100 mm. The individual dispersed phases are regarded as circular and randomly distributed in the matrix with a radius of 1-5mm and do not touch each other.
⑥ determining the material parameters of each phase
The thermal conductivity of each phase was set as: the thermal conductivity of the soil skeleton is 2W/(m.K), the thermal conductivity of ice is 2.25W/(m.K), the thermal conductivity of the water phase is 0.5W/(m.K), and the thermal conductivity of air is 0.02W/(m.K).
(2) And constructing a numerical simulation model for the pre-simulated multiphase composite material. Wherein the dispersed phase (inclusion phase) is circular 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、YminMaximum and minimum values of the upper and lower horizontal coordinates of the boundary of the dispersion phase throwing area, where Xmax-Xmin＝Ymax-Ymin＝100。
Considering that the inclusion phase of the simulated composite material 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 "take and put" algorithm. Because the dispersed phases are not mutually contacted in the simulation process, an influence area can be set around each dispersed phase particle, other inclusion phases cannot enter the influence area within the influence area, namely, the input condition is met, and the influence area can be judged by the center distance of adjacent inclusion 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;r1、r2the radius of the dispersed phase generated this time and the radius of the inclusion phase already put in are respectively.
(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. A certain temperature difference is applied to the upper surface and the lower surface of the model, and the left side and the right side are heat insulation boundaries.
(5) Finite element calculation and post-processing. And performing steady-state thermal analysis, obtaining the distribution conditions such as the temperature field, the heat flow density and the like of the final model through a finite element post-processing module, and extracting the heat flow density value of each node at the top of the model.
(6) And (4) calculating the equivalent thermal conductivity, and substituting the heat flow density of each node at the top of the simulated sample obtained in the fifth step into a Fourier formula to obtain the equivalent thermal conductivity. The specific expression is as follows:
where Δ Q/Δ T is the heat flux passing per unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient.
Wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffIs the equivalent thermal conductivity of the final heterogeneous material.
(6) Repeating the steps, changing different soil states, and performing Monte Carlo simulation for 600 times respectively. Fig. 8 is a partial diagram of a finite element mesh in three different states, and fig. 10 is a result of numerical simulation calculation, which shows that the thermal conductivity of the fully frozen earth is significantly higher than that of the other two cases at a certain saturation, and the thermal conductivity in the natural state is the lowest. As can be seen from fig. 10(a), the thermal conductivity of the soil in the natural state decreases almost linearly with the increase of the porosity. At 20% saturation, the equivalent thermal conductivity of ice-containing phase (partially or fully frozen earth) soils has a similar tendency. With the increase of the saturation degree, particularly when the saturation degree reaches more than 60%, the thermal conductivity coefficient in the ice-containing state shows a nonlinear descending trend. In particular, at 80% saturation, the thermal conductivity of the whole frozen earth decreases by only 0.2W/(mK). The thermal conductivity of ice is close to that of a soil framework and is one order of magnitude larger than that of water, so that when the water phase in the frozen soil is completely changed into ice, the thermal conductivity is linearly increased along with the increase of the porosity, and the saturated frozen soil can be regarded as a composite material consisting of a gas phase with low thermal conductivity and a solid phase with higher thermal conductivity.
Claims (1)
1. A microscopic scale research method for equivalent thermal conductivity of a multiphase composite material is characterized by comprising the following steps: comprises 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:
firstly, determining the size of a simulation sample, and regarding a soil body as a multi-phase composite material consisting of air, water, a soil framework and ice, wherein the soil framework is used as a matrix phase, and a pore phase is randomly distributed in the matrix as a dispersion phase; the volume fraction of each phase is expressed according to the porosity n and the saturation Sr, wherein the porosity is the percentage of the dispersed phase in the total volume, the saturation represents the percentage of the water phase in the pore volume, and other phases can be obtained by converting the following two parameters: the volume content of a soil framework is 1-n, the volume content of a pore phase is n, the volume content of a water phase is n.Sr, and the volume content of an air phase is n (1-Sr);
the simulated sample size and the specific size of each dispersed phase are as follows: the simulated sample is a square sample of 100mm multiplied by 100mm, each dispersed phase is regarded as a circle, the radius is 1-5mm, the dispersed phases are randomly distributed in the simulated sample and are not contacted with each other, and meanwhile, the size of the ice phase and the size of the water phase are kept consistent without considering the volume change when water is changed into ice;
the thermal conductivity of each phase is respectively as follows: the thermal conductivity of the soil skeleton is 1.2-7.5W/(m.K), the thermal conductivity of ice is 2.25W/(m.K), the thermal conductivity of the water phase is 0.5W/(m.K), and the thermal conductivity of air is 0.02W/(m.K);
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) based on a steady state analysis method, applying boundary conditions to the simulated sample:
when the heat flux passing through the sample reaches a certain condition and the temperature of the model at any moment is consistent with the time, the heat conductivity coefficient can be measured; in the numerical simulation process, the temperature difference of 10 ℃ is applied to the upper surface and the lower surface of the sample, and the left surface and the right surface are completely heat-insulating boundaries;
4) and (3) carrying out finite element solving calculation under a given boundary condition, substituting the heat flow density at the top of the sample obtained by the finite element calculation into a Fourier formula to obtain an equivalent heat conductivity coefficient:
after steady-state analysis and calculation are carried out by finite element software, the heat flux density of a top node of the simulation sample can be obtained and is substituted into a Fourier formula, and the equivalent heat conductivity coefficient can be obtained; the specific expression is as follows:
where Δ Q/Δ T is the heat flux passing in a unit time, k represents the thermal conductivity, A is the material area orthogonal to the heat transfer direction, ▽ T represents the temperature gradient, and considering the applied boundary conditions and model dimensions, the above equation can be expressed as:
wherein q isiFor the heat flux density of each top node, n is the total number of top nodes, TtopAnd TbottomThe temperature values of the upper and lower surfaces, respectively, L is the length of the sample in the heat flow transfer direction, keffThe equivalent thermal conductivity of the final heterogeneous material;
5) based on the steps, the influence of the spatial arrangement of the disperse phase, the soil types with different soil framework heat conductivity coefficients, the saturation, the porosity and three different soil states on the heat conductivity coefficient is considered;
considering the influence of soil body types on the thermal conductivity, the concrete results are that the soil framework is analyzed by adopting different thermal conductivity coefficients, namely 1W/(m.K), 2W/(m.K), 4W/(m.K) and 8W/(m.K);
the saturation and porosity ranges from 0 to 100% and from 0 to 65%, respectively;
considering the influence of three different soil body states on the equivalent heat conductivity coefficient, the three states are respectively as follows: the natural soil body state, the partial freezing state and the complete freezing state, wherein the volume ratio of the water phase to the ice phase in the partial freezing state is 1: 1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911043580.1A CN111027236B (en) | 2019-10-30 | 2019-10-30 | Microscopic scale numerical value research method for equivalent thermal conductivity of rock-soil body |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911043580.1A CN111027236B (en) | 2019-10-30 | 2019-10-30 | Microscopic scale numerical value research method for equivalent thermal conductivity of rock-soil body |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111027236A true CN111027236A (en) | 2020-04-17 |
| CN111027236B CN111027236B (en) | 2021-09-14 |
Family
ID=70204711
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911043580.1A Active CN111027236B (en) | 2019-10-30 | 2019-10-30 | Microscopic scale numerical value research method for equivalent thermal conductivity of rock-soil body |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111027236B (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111678945A (en) * | 2020-06-24 | 2020-09-18 | 河海大学 | Calculation method of concrete heat conductivity coefficient considering aggregate shape |
| CN112632746A (en) * | 2020-11-23 | 2021-04-09 | 浙江大学 | Optimized soil statistics physical thermal conductivity coefficient model construction method |
| CN114441590A (en) * | 2021-12-22 | 2022-05-06 | 中国航天空气动力技术研究院 | Method and system for determining heat transfer and mechanical properties of gradient heat-proof material |
| CN114858849A (en) * | 2022-07-11 | 2022-08-05 | 中国空气动力研究与发展中心低速空气动力研究所 | Method for obtaining thermal conductivity coefficient of dynamic ice |
| CN115659598A (en) * | 2022-09-27 | 2023-01-31 | 哈尔滨工业大学 | Soil body thermal conductivity prediction method based on Sigmoid function |
Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102262102A (en) * | 2011-04-27 | 2011-11-30 | 东南大学 | Method for determining thermal diffusivity of rock and earth mass for earth source heat pump |
| CN102879425A (en) * | 2012-10-25 | 2013-01-16 | 东南大学 | System and method for testing comprehensive heat conductivity coefficient and specific heat capacity of rock-soil body |
| CN103308550A (en) * | 2013-05-31 | 2013-09-18 | 中国建筑材料科学研究总院 | Method for testing relative heat-conductivity coefficients of phase-change energy storage composite materials |
| CN104111270A (en) * | 2014-07-04 | 2014-10-22 | 南京航空航天大学 | Calculation method of rapid heat conduction coefficient of period-like distribution unidirectional fiber toughening composite material |
| CN104330412A (en) * | 2014-11-12 | 2015-02-04 | 上海师范大学 | Non-contact nondestructive testing method for heat conductivity coefficient of rock and earth mass |
| US20150274092A1 (en) * | 2014-03-26 | 2015-10-01 | Ford Global Technologies, Llc | Method and device for forming a composite material |
| CN105044146A (en) * | 2015-07-02 | 2015-11-11 | 西安电子科技大学 | Random thermal homogenizing analysis method of two-phase composite material |
| CN105069203A (en) * | 2015-07-23 | 2015-11-18 | 西安电子科技大学 | Thermoelasticity homogenizing method for three-dimensional random heterogeneous material under finite deformation |
| CN106093108A (en) * | 2016-05-19 | 2016-11-09 | 南京航空航天大学 | Unidirectional fibre toughening composition Equivalent Thermal Conductivities predictor method based on interstitial defect identification |
| CN107451308A (en) * | 2016-05-31 | 2017-12-08 | 西北工业大学 | A kind of complex composite material structure effective thermal expansion coefficient multiscale simulation method |
| CN109271738A (en) * | 2018-10-16 | 2019-01-25 | 山东科技大学 | It is a kind of for obtaining the Method for Numerical Inversion of roadway surrounding rock Weibull distribution parameter |
| CN110261427A (en) * | 2019-07-04 | 2019-09-20 | 西安交通大学 | Multilayer materials thermal conductivity measurement method based on conjugate gradient method |
| CN110261432A (en) * | 2019-07-04 | 2019-09-20 | 西安交通大学 | Non-embedded multilayer materials thermal coefficient steady state measurement method |
-
2019
- 2019-10-30 CN CN201911043580.1A patent/CN111027236B/en active Active
Patent Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102262102A (en) * | 2011-04-27 | 2011-11-30 | 东南大学 | Method for determining thermal diffusivity of rock and earth mass for earth source heat pump |
| CN102879425A (en) * | 2012-10-25 | 2013-01-16 | 东南大学 | System and method for testing comprehensive heat conductivity coefficient and specific heat capacity of rock-soil body |
| CN103308550A (en) * | 2013-05-31 | 2013-09-18 | 中国建筑材料科学研究总院 | Method for testing relative heat-conductivity coefficients of phase-change energy storage composite materials |
| US20150274092A1 (en) * | 2014-03-26 | 2015-10-01 | Ford Global Technologies, Llc | Method and device for forming a composite material |
| CN104111270A (en) * | 2014-07-04 | 2014-10-22 | 南京航空航天大学 | Calculation method of rapid heat conduction coefficient of period-like distribution unidirectional fiber toughening composite material |
| CN104330412A (en) * | 2014-11-12 | 2015-02-04 | 上海师范大学 | Non-contact nondestructive testing method for heat conductivity coefficient of rock and earth mass |
| CN105044146A (en) * | 2015-07-02 | 2015-11-11 | 西安电子科技大学 | Random thermal homogenizing analysis method of two-phase composite material |
| CN105069203A (en) * | 2015-07-23 | 2015-11-18 | 西安电子科技大学 | Thermoelasticity homogenizing method for three-dimensional random heterogeneous material under finite deformation |
| CN106093108A (en) * | 2016-05-19 | 2016-11-09 | 南京航空航天大学 | Unidirectional fibre toughening composition Equivalent Thermal Conductivities predictor method based on interstitial defect identification |
| CN107451308A (en) * | 2016-05-31 | 2017-12-08 | 西北工业大学 | A kind of complex composite material structure effective thermal expansion coefficient multiscale simulation method |
| CN109271738A (en) * | 2018-10-16 | 2019-01-25 | 山东科技大学 | It is a kind of for obtaining the Method for Numerical Inversion of roadway surrounding rock Weibull distribution parameter |
| CN110261427A (en) * | 2019-07-04 | 2019-09-20 | 西安交通大学 | Multilayer materials thermal conductivity measurement method based on conjugate gradient method |
| CN110261432A (en) * | 2019-07-04 | 2019-09-20 | 西安交通大学 | Non-embedded multilayer materials thermal coefficient steady state measurement method |
Non-Patent Citations (3)
| Title |
|---|
| 张勤等: "基于细观均匀化的膨润土有效热传导特性研究", 《岩土力学》 * |
| 李典庆等: "基于蒙特卡洛模拟的岩质边坡可靠度设计方法", 《岩石力学与工程学报》 * |
| 许模等: "岩土体导热系数研究进展", 《地球科学与环境学报》 * |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111678945A (en) * | 2020-06-24 | 2020-09-18 | 河海大学 | Calculation method of concrete heat conductivity coefficient considering aggregate shape |
| CN112632746A (en) * | 2020-11-23 | 2021-04-09 | 浙江大学 | Optimized soil statistics physical thermal conductivity coefficient model construction method |
| CN112632746B (en) * | 2020-11-23 | 2022-04-26 | 浙江大学 | Optimized soil statistics physical thermal conductivity coefficient model construction method |
| CN114441590A (en) * | 2021-12-22 | 2022-05-06 | 中国航天空气动力技术研究院 | Method and system for determining heat transfer and mechanical properties of gradient heat-proof material |
| CN114441590B (en) * | 2021-12-22 | 2024-05-14 | 中国航天空气动力技术研究院 | Method and system for determining heat transfer and mechanical properties of gradient heat-resistant material |
| CN114858849A (en) * | 2022-07-11 | 2022-08-05 | 中国空气动力研究与发展中心低速空气动力研究所 | Method for obtaining thermal conductivity coefficient of dynamic ice |
| CN114858849B (en) * | 2022-07-11 | 2022-10-04 | 中国空气动力研究与发展中心低速空气动力研究所 | Method for obtaining thermal conductivity coefficient of dynamic ice |
| CN115659598A (en) * | 2022-09-27 | 2023-01-31 | 哈尔滨工业大学 | Soil body thermal conductivity prediction method based on Sigmoid function |
| CN115659598B (en) * | 2022-09-27 | 2023-06-02 | 哈尔滨工业大学 | Soil thermal conductivity prediction method based on Sigmoid function |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111027236B (en) | 2021-09-14 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111027236B (en) | Microscopic scale numerical value research method for equivalent thermal conductivity of rock-soil body | |
| Zhao et al. | Effects of architectural shapes on surface wind pressure distribution: case studies of oval-shaped tall buildings | |
| Millward-Hopkins et al. | Estimating aerodynamic parameters of urban-like surfaces with heterogeneous building heights | |
| Yang et al. | Model test and numerical simulation on the development of artificially freezing wall in sandy layers considering water seepage | |
| CN105160162B (en) | Lake based on splitting algorithm three-dimensional hydrodynamic force water temperature and quality simulating and predicting method | |
| Stylianou et al. | Modeling of vertical ground heat exchangers in the presence of groundwater flow and underground temperature gradient | |
| CN104899351A (en) | Temperature field analysis method of bituminous mixture test piece on the basis of discrete element simulation | |
| CN109992846B (en) | Simulation method for solar cross-season buried pipe heat storage | |
| Varol et al. | CFD modeling of heat transfer and fluid flow inside a pent-roof type combustion chamber using dynamic model | |
| Taylor et al. | A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid | |
| CN108536912A (en) | A kind of method that Transmission Tower mechanical analysis and its App make | |
| CN108661089B (en) | Numerical analysis method for ultimate expansion shear force of pile foundation in expansive land area | |
| Abbas et al. | Performance analysis of seasonal soil heat storage system based on numerical simulation and experimental investigation | |
| Wang et al. | The effect of heat and moisture coupling migration of ground structure without damp-proof course on the indoor floor surface temperature and humidity: Experimental study | |
| Chen et al. | Toward improved forecasts of sea-breeze horizontal convective rolls at super high resolutions. Part II: The impacts of land use and buildings | |
| CN111159794A (en) | Geometric damage rheological analysis method for mechanical properties of multi-fracture rock sample | |
| CN110987749B (en) | Method for researching equivalent permeability coefficient microscopic scale of multiphase composite material | |
| Gao et al. | Correlation study of shallow layer rock and soil thermal physical tests in laboratory and field | |
| Shymanskyi et al. | Simulation of the heat conduction process in the claydite-block construction with taking into account the fractal structure of the material | |
| Ma et al. | Numerical study of natural convection heat transfer in porous media square cavity with multiple cold walls based on LBM | |
| Chollet et al. | Direct and Large-Eddy Simulation II: Proceedings of the ERCOFTAC Workshop Held in Grenoble, France, 16–19 September 1996 | |
| CN111852461B (en) | Method for simulating unsteady state crossflow between tight reservoir bedrock and fracture | |
| Zhang et al. | Research Status on Inflow turbulence generation method with Large Eddy Simulation of CFD numerical wind tunnel | |
| Si et al. | Development of simulation program for temperature field of mass concrete structures | |
| CN111581858A (en) | Design method of heat preservation and insulation system for power transmission and transformation foundation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |