Aerogel composite material thermal conductivity calculation method

Abstract

The application provides a kind of aerogel composite thermal conductivity calculation method, it is related to aerogel composite field, by circulation nesting and collaborative parallel to construct target function model, specifically: step A, obtain input parameter, step B, four-level model is established, step C, three-level model is established, step D, two-level model is established, step E, one-level model is established, step F, target function is constructed.The method can quickly and accurately determine the optimal volume ratio and the best diameter size of basalt fiber in the composite material, providing guidance for the research and design of fiber reinforced aerogel composite material, and balancing the mechanical properties of basalt fiber aerogel composite material, so that its thermal insulation performance is best.

Description

Technical Field

[0001] This invention relates to the field of aerogel composite materials technology, and more specifically to a method for calculating the thermal conductivity of aerogel composite materials. Background Technology

[0002] Silica-based aerogels are ideal thermal insulation materials formed by the spatial aggregation of amorphous silica-based nanoparticles, possessing high porosity, high specific surface area, extremely low density, and ultra-low thermal conductivity. However, the extremely high porosity also leads to low toughness and mechanical strength in aerogels, thus limiting their application and promotion in the field of thermal insulation. To improve the mechanical properties of aerogel materials, fiber skeletons are currently commonly used as their mechanical property reinforcement. On the other hand, silica-based aerogels have a low extinction coefficient at high temperatures, and correspondingly, their emissivity increases sharply with increasing temperature, resulting in a decrease in thermal insulation performance at high temperatures. To improve the high-temperature thermal insulation performance of aerogels, basalt fibers are typically used as a light-blocking agent to enhance the infrared radiation scattering and absorption of aerogels under high-temperature environments. Studies have shown that ultrafine basalt fibers, compared to other fiber bodies, have the following advantages when applied to aerogel materials: firstly, they have higher thermal stability, exceeding 650℃; secondly, they possess higher monofilament mechanical strength, exceeding that of glass fibers by 30%; thirdly, they have a higher creep rupture limit; and fourthly, they have higher corrosion resistance. Therefore, basalt fiber aerogel composites have great application prospects in the fields of thermal insulation and heat preservation.

[0003] In basalt fiber aerogel composites, a higher fiber reinforcement density results in better mechanical properties, but also increases the solid-phase thermal conductivity. Conversely, a lower density makes it difficult for the composite to meet application requirements. Furthermore, a larger fiber reinforcement diameter leads to stronger aerogel support skeletons and better mechanical properties, but also increases high-temperature thermal conductivity and causes aerogel shedding. While a smaller diameter can improve near-infrared light scattering and absorption at high temperatures, it also generates static electricity during preparation, causing short fibers to agglomerate and become poorly dispersed, ultimately reducing the composite's thermal insulation performance. Therefore, it is necessary to determine the optimal volume fraction and optimal diameter of basalt fiber in composite materials to balance the relationship between mechanical properties and thermal conductivity, and to avoid problems such as poor high-temperature thermal conductivity, "dust shedding," agglomeration, and poor dispersibility in basalt fiber reinforced aerogel composite materials. However, existing technologies mainly rely on a large amount of experimental data and practical experience to obtain the optimal volume fraction and optimal diameter. This method has problems such as long design cycle, high consumption of manpower and resources, high requirements for R&D personnel, numerous calculation errors, and large cumulative errors. It cannot obtain the optimal volume fraction and optimal diameter of basalt fiber in composite materials in real time, quickly, and accurately. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a method for calculating the thermal conductivity of aerogel composite materials. This method can quickly and accurately determine the optimal volume ratio and optimal diameter of basalt fiber in the composite material, thereby providing effective guidance for the design of basalt fiber-reinforced aerogel composite materials and achieving optimal thermal insulation performance while balancing the mechanical properties of basalt fiber aerogel composite materials.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for calculating the thermal conductivity of aerogel composite materials is proposed, which constructs an objective function model through a nested loop and a synergistic parallel approach, specifically as follows:

[0007] Step A: Obtain input parameters, including parameters of silicon-based aerogel, nanoporous structure, environmental parameters, and basalt fiber parameters;

[0008] Step B, Level 4 Model Establishment: Based on the input parameters, establish calculation models for the contact properties and size parameters of nanoparticles in the silicon-based framework, the calculation models for the surface area and volume boundary of freely moving gas molecules within the framework cavity, and the calculation model for the extinction coefficient of basalt fibers as a function of the incident angle.

[0009] Step C, Three-level model establishment: The four-level model is embedded as a subroutine to construct each three-level model with a single-level nesting.

[0010] Step D, Second-level model establishment: Embed each third-level model as a subroutine to construct each second-level model with double-layer nesting;

[0011] Step E, First-level model establishment: Each second-level model is treated as a subroutine and coupled separately to construct each first-level model with three levels of nesting;

[0012] Step F, Objective Function Construction: Couple all first-level models as subroutines to construct an objective function for the thermal insulation performance of composite materials with four nested layers.

[0013] Based on further optimization of the above scheme, the parameters of the silicon-based aerogel include porosity, specific surface area, density, and extinction coefficient distribution with wavelength, the parameters of the nanopore structure include the internal characteristics of normal or skewed distribution of pore size, the environmental parameters include temperature, pressure, and specific heat of air, and the parameters of the basalt fiber include the distribution of the complex refractive index of the basalt material with wavelength; the input parameters are obtained by consulting literature and experimental experience data.

[0014] Based on further optimization of the above scheme, the specific method for constructing the calculation model of the contact properties and size parameters of nanoparticles in the silicon-based framework is as follows:

[0015] First, a cubic array aerogel framework model formed by regular cubic nanospheres is constructed, where the diameter of the nanospheres, the contact length between two adjacent spheres, and the side length of the cubic array unit are parameters to be determined.

[0016] Then, based on the measured aerogel porosity, specific surface area, and target thermal conductivity, the contact state and size parameters of the particles in the cubic array aerogel framework are determined using the equal volume method and the equal area method.

[0017] Based on further optimization of the above scheme, the calculation model for the surface area and volume boundary of the gas molecule skeleton cavity is as follows: using the molecular collision theory in a closed space, the surface area boundary and volume boundary are analyzed when a single gas molecule moves freely in the cavity and when the aerogel cubic nanosphere particles collide with other gas molecules.

[0018] Based on further optimization of the above scheme, the calculation model for the extinction coefficient of basalt fiber with incident angle is as follows: by utilizing the relationship between the extinction coefficient, absorption coefficient, and scattering coefficient in photoelectric properties, the extinction coefficient with wavelength and incident angle distribution required for calculating the radiation coefficient of basalt fiber is determined.

[0019] Based on further optimization of the above scheme, the three-level model includes a contact thermal resistance calculation model between silicon-based nanoparticles, a gas molecule number distribution model and mean free path model within the framework cavity, and a basalt fiber mean extinction coefficient model and a silicon-based aerogel mean extinction coefficient model. The contact thermal resistance calculation model between silicon-based nanoparticles uses nested subroutines to calculate the contact properties and size parameters of nanoparticles within the silicon-based framework. Through thermal boundary layer theory, it determines the relationship between the contact thermal resistance of nanospheres within the silicon-based framework and the relationship between particle contact state, particle surface roughness, and lattice defects. The gas molecule number distribution model and mean free path model within the framework cavity use nested subroutines to calculate the surface area and volume boundary of freely moving gas molecules within the framework cavity. Based on gas molecule dynamics theory, it determines the number distribution and mean free path of freely moving gas molecules within the silicon-based framework cavity. The mean extinction coefficient models of basalt fibers and silicon-based aerogels both use nested subroutines to calculate the basalt fiber extinction coefficient distribution with incident angle. The mean extinction coefficients of basalt fibers and silicon-based aerogels are determined respectively through the radiative heat transfer equation.

[0020] Based on further optimization of the above scheme, the radiation heat transfer equation adopts the Rosseland approximation method:

[0021]

[0022] In the formula, This represents the Rosseland average extinction coefficient specific to the composite material; w f and w a These represent the mass fractions of basalt fiber and silicon-based aerogel in the composite material, respectively. , These represent the specific Rosseland average extinction coefficients of basalt fibers and silica-based aerogels, respectively.

[0023]

[0024] In the formula: , Let represent the average emissivity and spectral emissivity of the blackbody, respectively; The spectral extinction coefficient of a material can be obtained through experimental testing of the infrared transmittance of aerogels based on Beer's Law.

[0025]

[0026] In the formula: L and The values ​​represent the thickness of the silicon-based aerogel and the infrared spectral transmittance through the silicon-based aerogel, respectively. This indicates the density of the silicon-based aerogel.

[0027] Based on further optimization of the above scheme, the secondary model includes a silicon-based framework thermal conductivity prediction model, a framework cavity gas phase thermal conductivity model, a basalt fiber radiation coefficient model, and a silicon-based aerogel radiation coefficient model. The silicon-based framework thermal conductivity prediction model uses a model for calculating the contact thermal resistance between silicon nanoparticles as a nested subroutine. It utilizes classical heat conduction theory to determine the prediction of the thermal conductivity of the silicon-based framework with respect to the contact thermal resistance of silicon nanoparticles. The framework cavity gas phase thermal conductivity model uses a model for the number distribution of gas molecules within the framework cavity and a mean free path model as nested subroutines. Based on the theory of thermal motion of gas molecules, it determines the prediction of the thermal conductivity of the pores within the silicon-based framework cavity with respect to the mean free path of the gas, as described in the Kaganer model.

[0028] The basalt fiber radiation coefficient model and the silicon-based aerogel radiation coefficient model are nested as subroutines, respectively, using the average extinction coefficient model of basalt fiber and the average extinction coefficient model of silicon-based aerogel. Based on the Rosseland approximation method, the radiation coefficient prediction of basalt fiber and the radiation coefficient of silicon-based aerogel are determined respectively.

[0029] Based on further optimization of the above scheme, the Kaganer model is specifically as follows:

[0030]

[0031] In the formula: This represents the thermal conductivity of the cavities formed by the nano-void structure within the silicon-based aerogel. The viscosity of the gas within the nanopores is represented by the product of the gas density within the silicon-based aerogel and the mean free path of the gas within the silicon-based framework cavity. for:

[0032]

[0033] In the formula: k B This represents Boltzmann's constant; T Indicates temperature; d This represents the diameter of the nanosphere particles within the framework model; p This indicates environmental pressure.

[0034] Based on further optimization of the above scheme, the radiation coefficient of the basalt fiber is... for:

[0035]

[0036] In the formula: Indicates the synthetic extinction coefficient of columnar fibers.

[0037]

[0038] In the formula: f v Indicates the volume fraction of basalt fibers in the composite material; This indicates the angle of incidence between the incident light wave and the columnar basalt fibers; d f Indicates fiber diameter; Q ext The extinction efficiency is represented by the anomalous scattering estimation method (ADT) and Rayleigh-Debye light scattering theory, and is characterized as a function of the complex refractive index of basalt fibers.

[0039] Emissivity of silicon-based aerogels for:

[0040]

[0041] Based on the extinction coefficient distribution of the dried aerogel measured by Lawrence Berkeley, the extinction coefficient of the aerogel was calculated by intra-band integration. .

[0042] Based on further optimization of the above scheme, the primary model includes a comprehensive thermal conductivity prediction model and an emissivity prediction model for aerogel composite materials. The comprehensive thermal conductivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, and couples the thermal conductivity prediction model of silicon-based skeleton with the thermal conductivity model of gas phase in the skeleton cavity. The emissivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, and couples the emissivity model of basalt fiber with the emissivity model of silicon-based aerogel.

[0043] The following are the effects of the technical solution of the present invention:

[0044] This application constructs sub-function models of basalt fiber phase and silicon-based aerogel box, and utilizes a hierarchical stacking method of cyclic nesting and synergistic parallelism of these sub-function models to construct an objective function that couples the thermal insulation performance of the composite material and establishes a mapping relationship between material parameters and thermal insulation performance. This is used to predict the thermal insulation performance of basalt fiber aerogel composites, enabling timely, rapid, efficient, and accurate determination of the optimal volume ratio and optimal diameter of basalt fibers in the composite material. This provides guidance for the research of fiber-reinforced aerogels, effectively reducing the time and materials consumed in selection and matching tests in fiber-reinforced aerogels, thereby improving R&D efficiency and reducing R&D costs. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the cubic array model of the aerogel framework in Embodiment 1 of the present invention.

[0046] Figure 2 This is a schematic diagram of the fibrous phase in Embodiment 1 of the present invention.

[0047] Figure 3 This is a flowchart of constructing the objective function in Embodiment 1 of the present invention.

[0048] Figure 4 This is a schematic diagram of the operation in Embodiment 2 of the present invention.

[0049] Figure 5 This is a schematic diagram of the grid matrix in Embodiment 2 of the present invention.

[0050] Figure 6 This is a schematic diagram of the thermal insulation performance grid matrix in Embodiment 3 of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0052] Example 1:

[0053] A method for calculating the thermal conductivity of aerogel composite materials is proposed, which constructs an objective function model through a nested loop and a synergistic parallel approach, specifically as follows:

[0054] Step A: Obtain input parameters, including parameters for silicon-based aerogels such as porosity, specific surface area, density, and extinction coefficient distribution with wavelength; parameters for nanopore structure such as the internal characteristics of normal or skewed distribution of pore size; environmental parameters such as temperature, pressure, and specific heat of air; and parameters for basalt fibers such as the distribution of complex refractive index of basalt materials with wavelength. These input parameters are obtained by consulting literature and experimental data.

[0055] Step B, Level 4 Model Establishment: Based on the input parameters, establish calculation models for the contact properties and size parameters of nanoparticles in the silicon-based framework, the calculation models for the surface area and volume boundary of freely moving gas molecules within the framework cavity, and the calculation model for the extinction coefficient of basalt fibers as a function of the incident angle.

[0056] The calculation model for the contact properties and size parameters of nanoparticles in a silicon-based framework mainly uses silicon-based aerogel parameters and environmental parameters as inputs. The specific construction method is as follows:

[0057] First, a cubic array aerogel framework model formed by regular cubic nanospheres is constructed, where the diameter of the nanospheres, the contact length between two adjacent spheres, and the side length of the cubic array unit are parameters to be determined.

[0058] Then, based on the measured aerogel porosity, specific surface area, and target thermal conductivity, the contact state and size parameters of the particles in the cubic array aerogel framework are determined using the equal volume method and the equal area method.

[0059] The calculation model for the surface area and volume boundaries of freely moving gas molecules within the gas molecule framework cavity is based on environmental parameters and nanopore structure parameters. Specifically, it uses molecular collision theory in a closed space to analyze the surface area and volume boundaries of single gas molecules moving freely within the aerogel cavity and when aerogel cubic nanospheres collide with other gas molecules.

[0060] The calculation model for the extinction coefficient of basalt fiber with incident angle is based on the input of basalt fiber parameters. Specifically, it uses the relationship between the extinction coefficient, absorption coefficient, and scattering coefficient in photoelectric properties to determine the extinction coefficient with wavelength and incident angle required for calculating the radiation coefficient of basalt fiber.

[0061] Step C, Establishment of the three-level model: The four-level model is embedded as a subroutine to construct each three-level model with a single-layer nesting; the three-level model includes the contact thermal resistance calculation model between silicon-based nanoparticles, the gas molecule number distribution model and mean free path model in the framework cavity, the average extinction coefficient model of basalt fiber and the average extinction coefficient model of silicon-based aerogel.

[0062] Among them, the calculation model of contact thermal resistance between silicon-based nanoparticles uses the calculation model of contact properties and size parameters of nanoparticles in silicon-based framework as a nested subroutine. Through thermal boundary layer theory, the relationship between the contact thermal resistance of nanosphere particles in silicon-based framework and particle contact state, particle surface roughness and lattice defects is determined.

[0063] The model for the number distribution of gas molecules in the framework cavity and the model for the mean free path of gas molecules are nested as subroutines using the calculation model of the surface area and volume boundary of gas molecules that can move freely in the framework cavity. Based on the theory of gas molecule dynamics, the model for the number distribution and mean free path of gas molecules that can move freely in the silicon-based framework cavity are determined.

[0064] Both the average extinction coefficient model for basalt fiber and the average extinction coefficient model for silicon-based aerogel use a subroutine nested with the calculation model of the distribution of the extinction coefficient of basalt fiber with incident angle. The average extinction coefficients of basalt fiber and silicon-based aerogel are determined by the radiation heat transfer equation.

[0065] The radiation heat transfer equation uses the Rosseland approximation method:

[0066]

[0067] In the formula, This represents the Rosseland average extinction coefficient specific to the composite material; w f and w a These represent the mass fractions of basalt fiber and silicon-based aerogel in the composite material, respectively. , These represent the specific Rosseland average extinction coefficients of basalt fibers and silica-based aerogels, respectively.

[0068]

[0069] In the formula: , Let represent the average emissivity and spectral emissivity of the blackbody, respectively; The spectral extinction coefficient of a material can be obtained through experimental testing of the infrared transmittance of aerogels based on Beer's Law.

[0070]

[0071] In the formula: L and The values ​​represent the thickness of the silicon-based aerogel and the infrared spectral transmittance through the silicon-based aerogel, respectively. This indicates the density of the silicon-based aerogel.

[0072] Step D, Secondary Model Establishment: Embed each tertiary model as a subroutine to construct each secondary model with double-layer nesting; the secondary models include the silicon-based skeleton thermal conductivity prediction model, the skeleton cavity gas phase thermal conductivity model, the basalt fiber radiation coefficient model, and the silicon-based aerogel radiation coefficient model.

[0073] Among them, the silicon-based framework thermal conductivity prediction model uses the contact thermal resistance calculation model between silicon-based nanoparticles as a nested subroutine, and uses classical heat conduction theory (any heat conduction theory commonly used in this field can be used) to determine the prediction of the thermal conductivity of the silicon-based framework with respect to the contact thermal resistance of silicon-based nanoparticles.

[0074] The gas-phase thermal conductivity model within the framework cavity uses a nested subroutine model of gas molecule number distribution and a mean free path model within the framework cavity. Based on the theory of gas molecule thermal motion, it determines the prediction of the thermal conductivity of the pores within the silicon-based framework cavity with respect to the gas mean free path, see the Kaganer model:

[0075]

[0076] In the formula: This represents the thermal conductivity of the cavities formed by the nano-void structure within the silicon-based aerogel, i.e., the gas-phase thermal conductivity of the silicon-based aerogel. k s ; The viscosity of the gas within the nanopores is represented by the product of the gas density within the silicon-based aerogel and the mean free path of the gas within the silicon-based framework cavity. for:

[0077]

[0078] In the formula: k B This represents Boltzmann's constant; T Indicates temperature; d This represents the diameter of the nanosphere particles within the framework model; p Indicates environmental pressure;

[0079] in:

[0080]

[0081] In the formula, k s0This represents the thermal conductivity of a single silica nanosphere particle; R c This indicates the contact thermal resistance between two adjacent silica nanospheres; H This represents the center-to-center distance between two adjacent nanospheres.

[0082] The basalt fiber radiation coefficient model and the silicon-based aerogel radiation coefficient model are nested as subroutines, respectively, using the average extinction coefficient model of basalt fiber and the average extinction coefficient model of silicon-based aerogel. Based on the Rosseland approximation method, the radiation coefficient prediction of basalt fiber and the radiation coefficient of silicon-based aerogel are determined respectively.

[0083] Emissivity of basalt fiber for:

[0084]

[0085] In the formula: Indicates the synthetic extinction coefficient of columnar fibers.

[0086]

[0087] In the formula: f v Indicates the volume fraction of basalt fibers in the composite material; Indicates the angle of incidence between the incident light wave and the columnar basalt fibers (see...). Figure 2 (as shown) d f Indicates fiber diameter; Q ext The extinction efficiency is represented by the anomalous scattering estimation method (ADT) and Rayleigh-Debye light scattering theory, and is characterized as a function of the complex refractive index of basalt fibers.

[0088] Emissivity of silicon-based aerogels for:

[0089]

[0090] Based on the extinction coefficient distribution of the dried aerogel measured by Lawrence Berkeley, the extinction coefficient of the aerogel was calculated by intra-band integration. .

[0091] Step E, First-level model establishment: Each second-level model is treated as a subroutine and coupled to construct a first-level model with three nested layers. The first-level model includes a comprehensive thermal conductivity prediction model and an emissivity prediction model for aerogel composite materials. The comprehensive thermal conductivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, coupled with the thermal conductivity prediction model of silicon-based skeleton and the thermal conductivity model of gas phase in the skeleton cavity. The emissivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, coupled with the emissivity model of basalt fiber and the emissivity model of silicon-based aerogel.

[0092] The coupled silicon-based framework thermal conductivity prediction model and the gas phase thermal conductivity model within the framework cavity are shown below (the coupled basalt fiber radiation coefficient model and the silicon-based aerogel radiation coefficient model are similar). The thermal conductivity of this model... k a Including the thermal conductivity of the solid skeleton k g With gas phase thermal conductivity k s Specifically:

[0093]

[0094] In the formula: N This indicates the number of nanospheres on each edge of the skeletal model; d This represents the diameter of the nanosphere particles within the framework model; H This represents the center-to-center distance between two adjacent nanospheres;

[0095]

[0096] In the formula: a This indicates the contact length between two adjacent nanospheres;

[0097] in:

[0098]

[0099] In the formula: Indicates specific heat capacity at constant pressure c pg and specific heat capacity at constant volume c vg The ratio; p Indicates environmental pressure; k B This represents Boltzmann's constant; T Indicates temperature; m g Indicates the molecular mass of a gas; S This indicates the specific surface area of ​​the aerogel matrix; Indicates the density of the aerogel matrix; Indicates the porosity of the aerogel matrix; d g Indicates the diameter of gas molecules; N A denoted as Avogadro's constant.

[0100] Step F, Objective Function Construction: Couple all first-level models as subroutines (e.g., Figure 3 As shown in the figure, construct the objective function for the thermal insulation performance of the composite material with four nested layers.

[0101] Example 2:

[0102] As another preferred embodiment of this application, since the calculation of the comprehensive thermal conductivity and comprehensive emissivity of basalt fiber aerogel based on the theoretical model in Example 1, especially the calculation of the comprehensive emissivity, involves a large number of integral calculations, such as extinction efficiency. Q ext Extinction coefficient Numerical integration is required for expansion calculations, and to ensure the accuracy of the numerical results, a smaller discrete step size, such as the angle of incidence, is also needed. The discrete step size in the range of 0° to 90° can be set to 0.01° or even smaller than 0.005°, or the discrete value in the range of fiber diameter 2 to 12 μm can be set to 0.01 μm. If iteration is performed using this discrete step size, tens of thousands of iterations are required, and the parameter iterations after combining various discrete step sizes can even reach millions of iterations. Therefore, based on the scheme of Example 1, in order to improve the computational efficiency and reduce the computational power consumption when calculating the spectral extinction coefficient corresponding to each wavelength within a certain band range using numerical integration, this embodiment adopts the parallel pool method to divide the independent iteration tasks in the numerical integration calculation into multiple parallel processes in each parallel pool for independent calculation (e.g., Figure 4 (as shown in the figure), and then the calculation results are combined.

[0103] Specifically, in this embodiment, performing calculations sequentially for tens of thousands of basalt fiber diameter and volume ratio combinations would consume significant computational resources and time. Considering that the algorithm for calculating the corresponding thermal insulation performance objective function value is consistent for each fiber parameter combination, it was decided to generate a mesh matrix based on the fiber diameter sequence and fiber volume ratio sequence. This matrix represents all fiber variable combinations that need to be traversed during the thermal insulation performance calculation. (Refer to...) Figure 5 As shown: The basalt fiber parameter mesh matrix is ​​input as a parameter into the thermal insulation performance objective function model established in Example 1 for matrix calculation, where... d f Indicates the diameter of basalt fibers. υ This indicates the volume percentage of basalt fiber in the composite material. K This indicates the overall thermal insulation performance index of composite materials.

[0104] Example 3:

[0105] As another preferred embodiment of this application, in the above-mentioned process of meshing fiber diameter and fiber volume ratio based on parallel pool + matrix method, the calculation time is proportional to the product of the discrete resolution of fiber diameter and the discrete resolution of fiber volume ratio. In order to improve the resolution of the calculation result by one order of magnitude, the calculation time often increases by at least two orders of magnitude. Therefore, there is a contradictory relationship between the high resolution value of basalt fiber parameters and the reduction of computing resource occupation and calculation time.

[0106] To resolve the aforementioned contradictory relationship, based on the method in Example 2, a higher discrete resolution mesh matrix is ​​first applied to the larger range of basalt fiber diameters and the larger range of fiber volume proportions. Then, a parallel pooling + matrix method is employed, i.e., independent parallel computation of integral numerical operations and basalt fiber parameter matrix operations, to quickly determine the approximate distribution of the composite material's thermal insulation performance corresponding to the basalt fiber parameter variables over a large range. (See [link to relevant documentation]). Figure 6 As shown.

[0107] Then, based on the obtained coarse thermal insulation performance distribution grid matrix of basalt fiber aerogel composite material under a large range of fiber parameters (diameter, volume ratio), the fiber parameter boundary ranges where multiple local optimal solutions of the composite material's thermal insulation performance exist are determined, and these local boundary ranges of fiber parameters are extracted.

[0108] Finally, based on the local boundary ranges of the extracted basalt fiber parameters, the globally optimal high-resolution basalt fiber parameter values ​​are further explored. In this embodiment, the fmincon solver built into MATLAB is used to handle the optimization problem with nonlinear constraints. The high-resolution optimal fiber parameter solution is searched within the narrowed local boundary range, thereby solving the problem of constrained multivariate nonlinear optimization problems and the difficulty in directly solving for the optimal parameter values ​​(i.e., determining the optimal parameter values ​​by solving for the zero value of the first derivative of the objective function) due to the complexity of the function.

Claims

1. A method for calculating the thermal conductivity of aerogel composite materials, characterized in that: The objective function model is constructed using nested loops and a collaborative parallel approach, specifically as follows: Step A: Obtain input parameters, including parameters of silicon-based aerogel, nanoporous structure, environmental parameters, and basalt fiber parameters; Step B, Level 4 Model Establishment: Based on the input parameters, establish calculation models for the contact properties and size parameters of nanoparticles in the silicon-based framework, the calculation models for the surface area and volume boundary of freely moving gas molecules within the framework cavity, and the calculation model for the extinction coefficient of basalt fibers as a function of the incident angle. Step C, Establishing the Three-Level Model: The four-level model is embedded as a subroutine to construct various three-level models with single-layer nesting. The three-level models include a model for calculating the contact thermal resistance between silicon-based nanoparticles, a model for the number distribution of gas molecules within the framework cavity and a model for the mean free path, a model for the average extinction coefficient of basalt fibers, and a model for the average extinction coefficient of silicon-based aerogels. Among these, the model for calculating the contact thermal resistance between silicon-based nanoparticles uses a model for calculating the contact properties and size parameters of nanoparticles in the silicon-based framework as a nested subroutine. Through thermal boundary layer theory, the contact thermal resistance of nanospheres in the silicon-based framework is determined with respect to the particle contact state and particle surface... The relationship between surface roughness and lattice defects; the model of gas molecule number distribution and mean free path in the framework cavity is nested with the calculation model of the surface area and volume boundary of gas molecules that can move freely in the framework cavity as subroutines. Based on the theory of gas molecule dynamics, the distribution of gas molecules that can move freely in the silicon-based framework cavity and the mean free path are determined; the model of average extinction coefficient of basalt fiber and the model of average extinction coefficient of silicon-based aerogel are both nested with the calculation model of the extinction coefficient of basalt fiber with incident angle as subroutines. The average extinction coefficients of basalt fiber and silicon-based aerogel are determined by the radiation heat transfer equation, respectively. Step D, Secondary Model Establishment: Each tertiary model is embedded as a subroutine to construct a series of secondary models with double-layer nesting. The secondary models include a silicon-based framework thermal conductivity prediction model, a framework cavity gas phase thermal conductivity model, a basalt fiber radiation coefficient model, and a silicon-based aerogel radiation coefficient model. Specifically, the silicon-based framework thermal conductivity prediction model uses a silicon nanoparticle contact thermal resistance calculation model as a nested subroutine, utilizing classical heat conduction theory to determine the prediction of the silicon-based framework's thermal conductivity with respect to the silicon nanoparticle contact thermal resistance. The framework cavity gas phase thermal conductivity model uses a framework cavity gas molecule number distribution model and a mean free path model as nested subroutines, based on the thermal motion theory of gas molecules, to determine the prediction of the silicon-based framework cavity pore thermal conductivity with respect to the gas mean free path. The basalt fiber radiation coefficient model and the silicon-based aerogel radiation coefficient model are nested as subroutines, respectively, using the average extinction coefficient model of basalt fiber and the average extinction coefficient model of silicon-based aerogel. Based on the Rosseland approximation method, the radiation coefficient prediction of basalt fiber and the radiation coefficient of silicon-based aerogel are determined respectively. Step E, First-level model establishment: Each second-level model is treated as a subroutine and coupled to construct a first-level model with three nested layers. The first-level model includes a comprehensive thermal conductivity prediction model and an emissivity prediction model for aerogel composite materials. The comprehensive thermal conductivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, coupled with the thermal conductivity prediction model of silicon-based skeleton and the thermal conductivity model of the gas phase in the skeleton cavity. The emissivity prediction model for aerogel composite materials is based on the heat transfer coupling theory of different phases in a closed space, coupled with the emissivity model of basalt fiber and the emissivity model of silicon-based aerogel. Step F, Objective Function Construction: Couple all first-level models as subroutines to construct an objective function for the thermal insulation performance of composite materials with four nested layers.

2. The method for calculating the thermal conductivity of aerogel composite materials according to claim 1, characterized in that: The parameters of the silicon-based aerogel include the distribution of porosity, specific surface area, density, and extinction coefficient with wavelength; the parameters of the nanopore structure include the internal characteristics of the normal or skewed distribution of pore size; the environmental parameters include temperature, pressure, and specific heat of air; and the parameters of the basalt fiber include the distribution of the complex refractive index of the basalt material with wavelength. The input parameters were obtained by consulting literature and experimental experience data.

3. The method for calculating the thermal conductivity of an aerogel composite material according to claim 1 or 2, characterized in that: The specific method for constructing the calculation model for the contact properties and size parameters of nanoparticles in the silicon-based framework is as follows: First, a cubic array aerogel framework model formed by regular cubic nanospheres is constructed, where the diameter of the nanospheres, the contact length between two adjacent nanospheres, and the side length of the cubic array unit are parameters to be determined. Then, based on the measured aerogel porosity, specific surface area, and target thermal conductivity, the contact state and size parameters of the particles in the cubic array aerogel framework are determined using the equal volume method and the equal area method.

4. The method for calculating the thermal conductivity of aerogel composite materials according to claim 3, characterized in that: The calculation model for the surface area and volume boundary of the freely moving gas molecule framework cavity is as follows: using the molecular collision theory in a closed space, the surface area boundary and volume boundary are analyzed when a single gas molecule moves freely in the cavity and when the aerogel cubic nanosphere particles collide with other gas molecules.

5. The method for calculating the thermal conductivity of an aerogel composite material according to claim 3, characterized in that: The calculation model for the extinction coefficient of basalt fiber with the distribution of incident angle is as follows: by utilizing the relationship between the extinction coefficient, absorption coefficient, and scattering coefficient in photoelectric properties, the extinction coefficient with wavelength and incident angle distribution required for calculating the radiation coefficient of basalt fiber is determined.

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