A method for predicting thermal conductivity of a foamed paste thermal insulation material

Abstract

The application provides a foam slurry thermal insulation material thermal conductivity prediction method, a series-parallel connection fractal model corrected by a fractal dimension is established, comparative analysis is conducted on the series-parallel connection model, a series-parallel connection fractal thermal conduction prediction model containing water is established, the thermal conductivity of the foam slurry thermal insulation material can be accurately calculated, and the thermal conductivities of the materials with different moisture contents and water contents are calculated, so as to guide the test by using the above model.

Description

TECHNICAL FIELD

[0001] The application relates to the field of thermal conductivity of thermal insulation materials, and particularly provides a method for predicting the thermal conductivity of a foamed slurry thermal insulation material. BACKGROUND

[0002] The thermal insulation ring is a kind of active deep high-temperature roadway meteorological environment maintenance concept mainly for prevention, which not only ensures the stability of the roadway surrounding rock, but also realizes the heat insulation and cooling of the roadway. The basic principle of the roadway heat insulation technology is to cover the composite thermal insulation material on the surface of the roadway surrounding rock or inject it into the surrounding rock in the form of guniting or grouting to form a composite heat-blocking structure to block the heat transfer of the surrounding rock to the working face through the air flow. Due to the complex shaft and roadway environment, the basic properties of the thermal insulation material have special requirements, that is, the mine thermal insulation material should have low thermal conductivity, high compressive strength, non-toxic and harmless, anti-static, non-flammable and the like.

[0003] As shown in Figure 1 The heat insulation effect of the foamed slurry porous material is mainly due to its microstructure and heat transfer mechanism. The foamed slurry contains a large amount of pores in addition to solid aggregates, and the pores are usually filled with air or other low thermal conductivity gases, which have a thermal conductivity much lower than that of solid materials, thereby reducing the effective thermal conductivity of the foamed slurry and significantly reducing the heat conduction. At the same time, the structure of the foamed slurry makes it necessary to bypass a large number of pores during heat transfer, and the heat is conducted in the solid aggregates, thereby increasing the heat transfer path and effectively reducing the heat transfer rate.

[0004] The thermal conductivity is an important parameter of the thermal properties of a material. Domestic and foreign scholars have carried out researches on the effective thermal conductivity of composite materials through experiments, mathematical modeling and the like. The effective thermal conductivity of multiphase composite materials is calculated by using the series and parallel thinking, which is simple and convenient, but only the upper and lower limits of the thermal conductivity of the composite material can be obtained, and a correction coefficient needs to be added to the model for accurate solution. The fractal geometry theory can describe the microstructure of the composite material and is more close to the description of the true properties and state of the complex structure, but the existing researches mainly focus on the processes such as penetration and gas diffusion in the porous medium under multiple scales, and the theory and model related to the thermal conductivity need to be researched. SUMMARY

[0005] The application aims to provide a method for predicting the thermal conductivity of a foamed slurry thermal insulation material, which can accurately calculate the thermal conductivity of the foamed slurry thermal insulation material and the thermal conductivity of the material with different moisture contents and water contents.

[0006] A method for predicting the thermal conductivity of a foamed slurry thermal insulation material, which comprises the following steps:

[0007] S1, obtaining an equivalent thermal conductivity of a series model of a solid-gas two-phase composite material of a foamed slurry thermal insulation material and an equivalent thermal conductivity of a parallel model of the solid-gas two-phase composite material of the foamed slurry thermal insulation material;

[0008] S2, obtaining an equivalent thermal conductivity corresponding to a series-parallel model by using the equivalent thermal conductivities of the series model and the parallel model;

[0009] S3, substituting a fractal dimension into the series-parallel model to obtain a series-parallel fractal model;

[0010] S4, substituting a gas part thermal conductivity of the foamed slurry thermal insulation material into the series-parallel fractal model to obtain an effective thermal conductivity of the material containing water vapor and liquid water.

[0011] Further, in step S1, the equivalent thermal conductivity of the series model of the solid-gas two-phase composite material of the foamed slurry thermal insulation material is formula (1) below, and the equivalent thermal conductivity of the parallel model of the solid-gas two-phase composite material of the foamed slurry thermal insulation material is formula (2) below:

[0012] (1)

[0013] (2)

[0014] In the formula, λ c is an effective thermal conductivity calculated by the series model of the foamed slurry material, W / m·K; λ p is an effective thermal conductivity calculated by the parallel model of the foamed slurry material, W / m·K; λ s is a thermal conductivity of a solid in the foamed slurry material, W / m·K; λ g is a thermal conductivity of a gas in the foamed slurry material, W / m·K; and α is a porosity of the foamed slurry material, %.

[0015] Further, in step S2, the equivalent thermal conductivity corresponding to the series-parallel model formula can be obtained by using the series model formula (1) and the parallel model formula (2) as formula (4) below:

[0016] (4)

[0017] λ cp is an effective thermal conductivity calculated by the series-parallel model of the foamed slurry material, W / m·K.

[0018] Further, in step S3, the fractal dimension is formula (6) and formula (7) below:

[0019] (6)

[0020] In formula (6), D f is a fractal dimension, d E is a topological dimension, l max is a maximum diameter of the particle, m; l min is a minimum diameter of the particle, m;

[0021] The foam slurry thermal insulation material of the present application is a cubic test block, and d E = 3, let ξ = l max / l min , substitute into formula (6), to obtain:

[0022] (7).

[0023] Further, in step S3, formula (7) is substituted into formula (4) to obtain a series-parallel fractal model as follows (11):

[0024] (11);

[0025] λ ′ cp is an effective thermal conductivity of the series-parallel fractal model of the foam slurry material, W / m·K.

[0026] Further, in step S4, the thermal conductivity of the gas part of the foam slurry thermal insulation material is as follows (14):

[0027] (12)

[0028] (13)

[0029] (14)

[0030] In the formula, is a moisture content, i.e., a volume proportion of the wet component in the pore channel; ω is a water content, i.e., a volume proportion of the liquid water in the wet component; Vg is a dry air volume, m 3 ; V wg is a water vapor volume, m 3 ; V w is a liquid water volume, m 3 ; λwg is a thermal conductivity of water vapor, W / m·K; λ w is a thermal conductivity of liquid water, W / m·K.

[0031] Further, in step S4, formula (14) is substituted into formula (11) to obtain an effective thermal conductivity of the material containing water vapor and liquid water as follows (15):

[0032] (15);

[0033] λ cp is the effective thermal conductivity of water vapor, liquid water.

[0034] Compared with the prior art, the application has the following beneficial effects:

[0035] The application provides a foam slurry thermal insulation material thermal conductivity prediction method, a fractal dimension corrected series-parallel fractal model is established, comparison and analysis are conducted on the series-parallel model, a water-containing series-parallel fractal thermal conductivity prediction model is established, the thermal conductivity of the foam slurry thermal insulation material can be accurately calculated, and the thermal conductivities of materials with different moisture contents and water contents can be accurately calculated, so as to guide the test by using the above model. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed to be used in the embodiment description will be briefly introduced as follows.

[0037] Figure 1 is a schematic diagram of a foam slurry material thermal insulation mechanism;

[0038] Figure 2 is an equivalent thermal resistance network diagram of a series model and a parallel model;

[0039] Figure 3 is a series-parallel model calculation result;

[0040] Figure 4 is a fractal thermal conductivity model calculation result;

[0041] Figure 5 is a comparison diagram of a thermal conductivity model calculation result and a test result;

[0042] Figure 6 is a characteristic diagram of a thermal conductivity of a thermal insulation material changing with water content. DETAILED DESCRIPTION

[0043] In order to solve the problem that the existing model cannot accurately calculate the thermal conductivity of the foam slurry thermal insulation material, the application provides a foam slurry thermal insulation material thermal conductivity prediction method, a fractal dimension corrected series-parallel fractal model is established, comparison and analysis are conducted on the series-parallel model, and a water-containing series-parallel fractal thermal conductivity prediction model is established; the mixing ratio of cement, fly ash and mineral powder is taken as the thermal conductivity of the solid part in the foam slurry thermal insulation material, the thermal conductivity of air at different temperatures is taken as the thermal conductivity of the gas, and the model is compared and verified, and the value of the fractal dimension is determined, so that the thermal conductivity of the foam slurry thermal insulation material can be accurately calculated, and the thermal conductivities of materials with different moisture contents and water contents can be accurately calculated; the above model is used to guide the test, and a basis is provided for calculating the thermal conductivity of the composite material, as shown in the following formula: Figure 1 The method comprises the following steps:

[0044] Step S1: series-parallel heat conduction calculation model

[0045] According to the structure of the foam slurry thermal insulation material, the series model and the parallel model of the solid-gas two-phase composite material system and the corresponding equivalent thermal resistance network diagram Figure 2 The equivalent thermal conductivity coefficients of the series model and the parallel model of the two-phase composite material are formula (1) and formula (2) respectively

[0046] (1)

[0047] (2)

[0048] λ c The effective thermal conductivity coefficient of the foam slurry material calculated by the series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the parallel model is W / m·K; the thermal conductivity coefficient of the solid in the foam slurry material is W / m·K; the thermal conductivity coefficient of the gas in the foam slurry material is W / m·K; and the porosity of the foam slurry material is %. p The effective thermal conductivity coefficient of the foam slurry material calculated by the series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the parallel model is W / m·K; the thermal conductivity coefficient of the solid in the foam slurry material is W / m·K; the thermal conductivity coefficient of the gas in the foam slurry material is W / m·K; and the porosity of the foam slurry material is %. s The effective thermal conductivity coefficient of the foam slurry material calculated by the series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the parallel model is W / m·K; the thermal conductivity coefficient of the solid in the foam slurry material is W / m·K; the thermal conductivity coefficient of the gas in the foam slurry material is W / m·K; and the porosity of the foam slurry material is %. g The effective thermal conductivity coefficient of the foam slurry material calculated by the series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the parallel model is W / m·K; the thermal conductivity coefficient of the solid in the foam slurry material is W / m·K; the thermal conductivity coefficient of the gas in the foam slurry material is W / m·K; and the porosity of the foam slurry material is %.

[0049] Step S2: parallel-series and series-parallel heat conduction calculation model

[0050] Assuming that the dispersed phase particles are of the same size and are uniformly and regularly distributed in the continuous phase matrix, taking a unit length particle as an equivalent representative unit, the dispersed phase is located in the middle; at this time, according to the interface between the two phases, the layer perpendicular to the heat flow direction is divided, then the dispersed phase first parallel and then series model (referred to as parallel-series) is formed, according to the interface between the two phases, the channel parallel to the heat flow direction is divided, then the dispersed phase first series and then parallel model (referred to as series-parallel) is formed; the equivalent thermal conductivity coefficients corresponding to formula (3) of the parallel-series model and formula (4) of the series-parallel model can be obtained by using formula (1) and formula (2):

[0051] (3)

[0052] (4)

[0053] λ pc The effective thermal conductivity coefficient of the foam slurry material calculated by the parallel-series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the series-parallel model is W / m·K. cp The effective thermal conductivity coefficient of the foam slurry material calculated by the parallel-series model is W / m·K; the effective thermal conductivity coefficient of the foam slurry material calculated by the series-parallel model is W / m·K.

[0054] Step S3: fractal heat conduction calculation model

[0055] The above series-parallel heat conduction model is given according to the regular and ordered structure. In fact, the internal structure of porous media is mostly irregular and disordered, so the above model needs to be modified. In recent years, fractal theory provides a new way to study and solve complex scientific and practical problems. Based on the fractal description and analysis method, the transport characteristic analysis model is established according to the microstructure characteristics of porous media, which can reveal the relationship between nonlinear quantity change and quality change, local and global, finite and infinite in the complex phenomena of porous media. In order to accurately analyze and reveal the micro heat conduction process and transfer mechanism of porous media, the fractal method can be used to modify the above model;

[0056] The basic relationship of the analytic geometry theory is that the measure M(x) of a fractal object and the measuring scale x obey the following scaling relationship:

[0057] (5)

[0058] M(x) can be the mass, volume, area or length of a curve of an object. Yumengming et al. proved the following relationship:

[0059] (6)

[0060] In formula (6), D f is the fractal dimension, d E is the topological dimension, l max is the maximum diameter of the particle, m; l min is the minimum diameter of the particle, m; in two-dimensional space: d E =2, 1<D f <2; in three-dimensional space: d E =3, 2<D f <3;

[0061] In this paper, the foam slurry thermal insulation material is made into a cubic test block, d E =3, let ξ=l max / l min , substitute into formula (6), we get:

[0062] (7)

[0063] On the basis of series, parallel, parallel-serial, serial-parallel models, the fractal dimension is introduced, and formula (7) is substituted into formula (1), (2), (3), (4) respectively, to get series-fractal, parallel-fractal, parallel-serial-fractal, serial-parallel-fractal models, as formula (8), (9), (10), (11):

[0064] (8)

[0065] (9)

[0066] (10)

[0067] (11)

[0068] λ ′ c is the effective thermal conductivity of the foam slurry material calculated by the series fractal model, W / m K; λ ′ p is the effective thermal conductivity of the foam slurry material calculated by the parallel fractal model, W / m K; λ ′ pc is the effective thermal conductivity of the foam slurry material calculated by the parallel-serial fractal model, W / m K; λ ′ cp is the effective thermal conductivity of the foam slurry material calculated by the serial-parallel fractal model, W / m K;

[0069] Step S4: Water-containing fractal heat conduction calculation model:

[0070] Due to the high temperature and high humidity environment in the mine, after spraying the thermal insulation material, water vapor and liquid water gradually penetrate into the material, causing the thermal conductivity of the material to change. The foam slurry thermal insulation material prepared in this paper has a large number of pores inside, which is easy to store water vapor and liquid water. Therefore, this paper considers the influence of the moisture content formula (12) and the water content formula (13) of the foam slurry thermal insulation material on the thermal conductivity of the material, and obtains the gas part thermal conductivity of the foam slurry thermal insulation material as formula (14):

[0071] (12)

[0072] (13)

[0073] (14)

[0074] In the formula, is the moisture content, that is, the volume proportion of moisture in the pore channel; ω is the water content, that is, the volume proportion of liquid water in the moisture; V g is the dry air volume, m 3 ; Vwg is the water vapor volume, m 3 ; V w is the liquid water volume, m 3 ; λ wg is the thermal conductivity of water vapor, W / m K; λ w is the thermal conductivity of liquid water, W / m K;

[0075] Substituting formula (14) into formula (11), the effective thermal conductivity of the material containing water vapor and liquid water λcp The rest of the calculation formula is not described again, as formula (15):

[0076] (15).

[0077] Selection and proportion of foam slurry thermal insulation material:

[0078] In this paper, animal protein foaming agent is selected to generate foam by foaming machine, P.O 42.5 ordinary portland cement, fly ash, S95 slag powder and deionized water are used as cementitious materials, and a certain amount of redispersible latex powder, polycarboxylate superplasticizer and liquid alkali-free accelerating admixture are added. In this paper, the proportioning design is carried out by changing the dosage of fly ash and slag powder. The specific dosage is as follows:

[0079] (1) The sum of cement, fly ash and slag powder is 4000g, the water-cement ratio is 0.45, the dosage of fly ash in each group is 0%, 10%, 15%, 20%, 25% and 30%, and the dosage of each material is as follows: the dosage of foam is fixed at 8.0%, the dosage of polycarboxylate superplasticizer is 0.2%, the dosage of accelerating agent is 1.0%, the dosage of redispersible latex powder is 0.5%, and the dosage of slag powder is 30%.

[0080] (2) The sum of cement, fly ash and slag powder is 4000g, the water-cement ratio is 0.45, the dosage of slag powder in each group is 0%, 10%, 20%, 30%, 40% and 50%, and the dosage of each material is as follows: the dosage of foam is fixed at 8.0%, the dosage of polycarboxylate superplasticizer is 0.2%, the dosage of accelerating agent is 1.0%, the dosage of redispersible latex powder is 0.5%, and the dosage of fly ash is 20%.

[0081] Preparation of foam slurry thermal insulation material:

[0082] The preparation of foam slurry thermal insulation material adopts the method of pre-prepared foam mixing, the room temperature is controlled at (25±2)℃, the corresponding raw materials are weighed, and the preparation process is as follows:

[0083] (1) According to the calculation method of foam content of foam concrete in "Technical Specification for Application of Foam Concrete" JGJ / T 341-2014, the dosage of foam is determined. The foaming agent and water are stirred in the proportion of 1:25ml for 2-5min to obtain foaming liquid, the foaming liquid is injected into the cavity of foaming machine, then air is continuously pressed into the foaming machine through air pump, finally the air valve and liquid valve are adjusted, the foaming liquid is quickly pressed into the bubble mixing pipe in the foaming machine to finally produce foam.

[0084] (2) The amount of fly ash, cement, and fly ash and water is calculated according to the foam concrete mix design method in the "Regulations". The cementing material is fly ash, cement, and mineral powder, and the basic dosage range of the additive is determined. The weighed cementing material and additive are pre-mixed by dry method at a stirring speed of 100 r / min for 2 min, and then the amount of liquid accelerator and water is weighed. After that, the dry material after stirring is mixed with water and accelerator for 5 min.

[0085] (3) The prepared foam is poured into the slurry at a stirring speed of 200 r / min for 1-2 min until there is no white foam on the surface of the mixture. The water-cement ratio of the slurry material and the stirring time are the key factors to determine the stability of the overall material performance.

[0086] (4) The uniformly stirred foam slurry insulation material is poured into a 100x100x100mm, 300x300x30mm plastic mold, and the excess foam slurry on the surface is scraped off. After curing at room temperature (25±2) °C for 48 h, the mold is removed. The prepared test sample is placed in a standard curing box with a relative humidity of more than 95% and a temperature of (20±2) °C for testing and analysis.

[0087] Thermal conductivity test:

[0088] The test of the thermal conductivity of the foam slurry insulation material can be carried out according to the "Transient Plane Source Method for Testing Thermal Conductivity and Thermal Diffusivity of Building Materials" GB / T32064-2015. In this test, a DHR thermal conductivity tester produced by Xiangke Instrument is used. A plate-shaped sample with a size of 300mmx300mmx30mm is prepared and dried after standard curing for 28 days. The dried sample is placed in the thermal conductivity tester for testing, and the average value of three samples is the test result.

[0089] Mathematical calculation and experimental verification:

[0090] At standard atmospheric pressure, the thermal conductivity of air is about 0.026 W / (m·K) at 20°C, and about 0.023 W / m·K at 25°C. To explore the effect of air thermal conductivity on the total thermal conductivity of the material, the air thermal conductivity is selected as 0.023, 0.026, 0.029, and 0.032 W / m·K. The thermal conductivity of cement λ s1 is 0.5~0.65 W / m·K, and the value is 0.6 W / m·K; the thermal conductivity of mineral powder λ s2 is 0.27 W / m·K; the thermal conductivity of fly ash λ s3is 0.23 W / m·K. Assuming that each component is uniformly distributed in the mixture, the volume average method is used for calculation, and the volume fraction of cement is 60%, the volume fractions of fly ash and slag are 20% respectively, so the calculation formula and results of the thermal conductivity of the solid part of the thermal insulation material are as formula (16)

[0091] (16)

[0092] wherein λse is the effective thermal conductivity of the solid composite material, W / (m·K). Vi is the volume fraction of the i-th material, %.

[0093] Series-parallel model calculation results:

[0094] To analyze the calculation results of the series model, the parallel model, the series-parallel model, and the parallel-series model, and compare the influence of different air thermal conductivities on the thermal conductivity of the foam slurry material, the above numerical values are substituted into formula (1), (2), (3), and (4) to obtain the calculation results as shown in Figure 3 .

[0095] From the calculation results in the figure, it can be seen that the thermal conductivities calculated by the series formula, the series-parallel model, and the parallel-series model are smaller, mainly in the range of 0.03~0.07 W / (m·K), which is the numerical lower limit of the thermal conductivity of the thermal insulation material. When the thermal conductivity of the gas is fixed, the thermal conductivities calculated by different porosities are also smaller, which shows that the porosity has a smaller influence on the calculation results. In the calculation of the effective thermal conductivity of the foam slurry thermal insulation material, the thermal conductivity of the gas and the porosity need to be more accurate to make the thermal conductivity calculated by the model more accurate. The thermal conductivity calculated by the parallel formula has a larger value and a larger range, which is the numerical upper limit of the thermal conductivity of the thermal insulation material. The change of the thermal conductivity of the gas has a smaller influence on the calculation results, and the porosity has a significant influence on the calculation results, which shows that the numerical value of the porosity needs to be more accurate in the calculation of the effective thermal conductivity by the parallel model.

[0096] Fractal thermal conductivity model calculation results:

[0097] To analyze the calculation results of the series-fractal model, the parallel-fractal model, the series-parallel-fractal model, and the parallel-series-fractal model, and compare the influence of different air thermal conductivities on the thermal conductivity of the foam slurry material, the above numerical values are substituted into formula (8), (9), (10), and (11) to obtain the calculation results as shown in Figure 4 ;

[0098] After introducing the fractal dimension into the series-parallel model, it can be seen from the figure that the series-fractal model, the parallel-fractal model, and the series-parallel-fractal model are more accurate in calculating the thermal conductivity of the foam slurry material, but the result calculated by the series-parallel-fractal formula is too large, which is not suitable for the calculation of the thermal conductivity of the foam slurry thermal insulation material.

[0099] The effective thermal conductivities of the thermal insulation materials with different gas thermal conductivities in the series fractal model calculation results are similar, and the calculation range is about 0~0.2 W / (m·K), wherein the fractal dimension is in the range of 2.5~2.8, which can be used to approximate the thermal insulation material of the foam slurry; the thermal conductivities calculated by the parallel fractal model and the series-parallel fractal model are in the range of 0~0.45 W / (m·K), and the fractal dimension is in the range of [2.85, 3], which is more reasonable compared with the series fractal model value, and the parallel fractal model and the series-parallel fractal model have higher accuracy requirements for the fractal dimension.

[0100] Comparison and verification of the thermal conduction model and the test results:

[0101] λg=0.026 is the thermal conductivity of dry air in the pores; ξ=100; the thermal conductivity of the solid material λs is calculated according to the volume fraction; from Figure 5 the value range of the fractal dimension can be determined, and the test results are compared with the series fractal, parallel fractal and series-parallel fractal models as Figure 5 .

[0102] Table 1 Calculation result deviation value

[0103]

[0104] As can be seen from the chart, when the fractal dimension of the series fractal model is 2.6 and 2.7, the calculation results are the upper and lower limits of the test results, and the calculation deviation is still large when the fractal dimension difference is 0.1, which requires a more accurate fractal dimension; when the fractal dimension is 2.66 and 2.67, the calculation deviation is smaller when the fractal dimension difference is 0.01; when the fractal dimension is 2.67, the relative deviation between the calculation model and the test value reaches the lowest point, and the series fractal model can effectively predict the thermal conductivity of the foam slurry thermal insulation material.

[0105] When the relative deviation between the parallel fractal and series-parallel fractal calculation models and the test value reaches the lowest point, the fractal dimension is 2.96, and compared with the parallel fractal and series-parallel fractal calculation values, the series-parallel fractal calculation value is about 0.55% different from the test value, indicating that the series-parallel fractal calculation value is more accurate.

[0106] During the test, a small amount of other additives were added, water vapor and liquid water penetrated into the test block on the heating surface of the test instrument, resulting in a certain error in the test, which can be ignored.

[0107] Comparison and verification of the thermal conduction model and the test results:

[0108] The above content has been obtained that the series-parallel fractal model can accurately predict the thermal conductivity of foam slurry insulation material. In this paper, the series-parallel fractal model is used for calculation, and the influence of the content of water vapor and liquid water in the foam slurry insulation material on the thermal conductivity is further explored. It is known that λg=0.026 is the thermal conductivity of dry air in the pore; λwg=0.02 is the thermal conductivity of water vapor in the pore; λw=0.598 is the thermal conductivity of water in the pore; λs=0.46 is the thermal conductivity of solid material; ξ=100; Df=2.96; is the volume fraction of water vapor in the pore, which takes the value of 10, 20, 30, 40, 50; ω is the volume fraction of water in the pore, which takes the value of 0, 5, 10, 15, 20. The data is substituted into the series-parallel fractal model, and the comparison with the measured thermal conductivity of foam slurry insulation material is as follows Figure 6 .

[0109] From the figure, when dry air and water vapor coexist in the foam concrete, the thermal conductivity of the material decreases due to the smaller thermal conductivity of water vapor. When the moisture content increases, the thermal conductivity of the material changes little. When the pore contains liquid water, the thermal conductivity of water is much larger than that of dry air and water vapor, and the thermal conductivity of the material increases with the increase of water content. When liquid water, dry air and water vapor coexist, the combined increase of moisture content and water content significantly increases the thermal conductivity of the material. From the calculation results of the series-parallel fractal model in the figure, when only dry air and water vapor coexist, the thermal conductivity of the material is similar, and then increases with the increase of water content and moisture content, and the maximum increase is about 0.15 W / (m·K).

[0110] From the experimental data, the regression line in the figure shows a positive slope, indicating that there is a positive correlation between water content and thermal conductivity, and the fitting degree of the model is high. When the water content is less than 15%, the thermal conductivity increases slightly with the change of water content, because the proportion of dry air or water vapor is large, and the pore structure formed by this proportioning parameter is relatively uniform, which can limit the heat transfer to a certain extent. By comparing the calculation results of the series-parallel fractal model and the experimental results, it can be seen that the values are similar, which proves that the series-parallel fractal model is accurate and can further determine the content of gas and liquid in the foam slurry insulation material, and effectively predict the change of the thermal conductivity of the material.

[0111] In this paper, ordinary Portland cement, fly ash, S95 slag powder and deionized water are selected as cementitious materials to prepare foam slurry insulation materials with different proportions. The series-parallel thermal conductivity calculation model and the fractal thermal conductivity model are compared and coupled to obtain the modified thermal conductivity prediction model and the water-containing thermal conductivity prediction model. The test results are compared with the model calculation to obtain the following conclusions.

[0112] (1) The thermal conductivity calculated by parallel model, series formula, series-parallel and series-parallel model is the upper and lower limit of the thermal conductivity of the thermal insulation material. After introducing the fractal dimension in series-parallel model, the thermal conductivity of the foam slurry material calculated by series fractal model, parallel fractal model and series-parallel fractal model is more accurate.

[0113] (2) When the fractal dimension is taken to two decimal places, the calculation deviation is small. When the fractal dimension is taken to 2.67, the relative deviation between the calculation model and the test value reaches the lowest point, and the series fractal model can effectively predict the thermal conductivity of the foam slurry thermal insulation material. When the fractal dimension of parallel fractal and series-parallel fractal model is taken to 2.96, the relative deviation between the calculation value and the test value is small, and the calculation value of series-parallel fractal model is more accurate.

[0114] (3) When only the moisture content increases, the thermal conductivity of the thermal insulation material changes little, and the increase of water content has a significant effect on the thermal conductivity. When liquid water, dry air and water vapor coexist, the increase of moisture content and water content makes the thermal conductivity of the material increase significantly. The calculation results and the test results are similar, which further proves the accuracy of the calculation of series fractal model and series-parallel fractal model.

[0115] As described above, one or more embodiments are provided in combination with specific content, and it is not intended that the specific implementation of the present application is limited to these descriptions. Any approximation, similarity or replacement of the method and structure of the present application, or any technical deduction or replacement under the concept of the present application, should be considered as the protection scope of the present application.

Claims

1. A method of predicting the thermal conductivity of a foamed slurry insulation material, characterized by: The method comprises the following steps: S1, obtaining the equivalent thermal conductivity of the series model of the solid-gas two-phase composite material of the foam slurry thermal insulation material, and obtaining the equivalent thermal conductivity of the parallel model of the solid-gas two-phase composite material of the foam slurry thermal insulation material; S2, obtaining the equivalent thermal conductivity corresponding to the series-parallel model by using the equivalent thermal conductivities of the series model and the parallel model; S3, substituting the fractal dimension into the series-parallel model to obtain a series-parallel fractal model; S4, substituting the gas part thermal conductivity of the foam slurry thermal insulation material into the series-parallel fractal model to obtain the effective thermal conductivity of the material containing water vapor and liquid water; In step S4, the gas part thermal conductivity of the foam slurry thermal insulation material is as follows formula (14), and the formula (14) is substituted into the series-parallel fractal model to obtain the effective thermal conductivity of the material containing water vapor and liquid water as follows formula (15): （12）； （13）； （14）； (15)； wherein is the moisture content, i.e. the volume proportion of the moisture occupying the pore channel; ω is the water content, i.e. the volume proportion of the liquid water occupying the moisture; V g is the dry air volume, m 3 ; V wg is the water vapor volume, m 3 ; V w is the liquid water volume, m 3 ; λ wg is the thermal conductivity of water vapor, W / m K; λ w is the thermal conductivity of liquid water, W / m K; λ g is the thermal conductivity of the gas within the foamed paste material; λ cp is the effective thermal conductivity of the water vapor, liquid water; λ s is the thermal conductivity of the solid within the foamed paste material, D f is the fractal dimension, l max is the maximum diameter of the particles, m; l min is the minimum diameter of the particles, m; ξ = l max / l min .

2. The method of claim 1, wherein: In step S1, the equivalent thermal conductivity of the series model of the solid-gas two-phase composite material of the foam slurry thermal insulation material is as follows formula (1), and the equivalent thermal conductivity of the parallel model of the solid-gas two-phase composite material of the foam slurry thermal insulation material is as follows formula (2): (1)； (2)； wherein λ c is the effective thermal conductivity of the foamed paste material calculated by the series model, W / m-K; λ p is the effective thermal conductivity of the foamed paste material calculated by the parallel model, W / m-K; λ s is the thermal conductivity of the solid within the foamed paste material, W / m-K; λ g is the thermal conductivity of the gas within the foamed paste material, W / m-K; and α is the porosity of the foamed paste material, %.

3. The method of claim 2, wherein: In step S2, the equivalent thermal conductivity corresponding to the series-parallel model formula is as follows formula (4) by using the series model formula (1) and the parallel model formula (2): （4）； λ cp is the effective thermal conductivity of the foam slurry material calculated with the series-parallel model, W / m·K.

4. The method of claim 3, wherein: In step S3, the fractal dimension is as follows formula (6) and formula (7): （6）； In formula (6), D f is the fractal dimension, d E is the topological dimension, l max is the maximum diameter of the particle, m; l min is the minimum diameter of the particle, m; The foam slurry thermal insulation material is a cubic test block, and d E = 3, let ξ = l max / l min , and substituting equation (6) gives: （7）。 5. The method of claim 4, wherein: In step S3, the formula (7) is substituted into the formula (4) to obtain the series-parallel fractal model as follows formula (11): （11）； λ ′ cp is the effective thermal conductivity of the foam slurry material calculated by the series-parallel fractal model, W / m·K.

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