Method for determining heat conductivity coefficient of multi-scale three-dimensional structure of resin-based composite material

Abstract

The invention discloses a method for determining the heat conductivity coefficient of a multi-scale three-dimensional structure of a resin-based composite material. The method comprises the following steps: firstly, acquiring a three-dimensional nano-pore structure of a resin matrix of a composite material by adopting a high-resolution focused ion beam scanning electron microscope, and constructing a gas-phase heat conductivity coefficient and solid-phase heat conductivity coefficient model considering a confinement effect of gas nanoscale pores and nanoscale particles; calculating the effective heat conductivity coefficient of the resin matrix by utilizing a lattice Boltzmann method; then acquiring a three-dimensional structure of the resin-based composite material by adopting microscopic CT (Computed Tomography), constructing a gas-phase heat conductivity coefficient model, and calculating the effective heat conductivity coefficient of the resin-based composite material by taking the effective heat conductivity coefficient of the resin matrix as a solid-phase heat conductivity coefficient and utilizing a lattice Boltzmann method. According to the invention, micron-scale pore morphology and nano-scale pore morphology can be obtained, and multi-scale pore structure characterization is realized; the calculated effective heat conductivity coefficient of the resin-based composite material is closer to the actual heat conductivity coefficient, and the accuracy is higher.

Description

Technical Field

[0001] The present invention relates to the technical field of thermal protection materials, and particularly relates to a method for determining the thermal conductivity of a multi-scale three-dimensional structure of a resin matrix composite material. Background Art

[0002] Resin matrix composites have important application values as ablation materials in the aerospace field due to their excellent high-temperature oxidation resistance, ablation resistance and other characteristics. With the development of aerospace technology, the flight speed of aircraft is getting higher and higher, the air flow density is getting larger and larger, resulting in a more complex aerodynamic heating environment. The performance design of resin matrix composites faces higher challenges. Therefore, obtaining an accurate thermal conductivity is the key to ensuring the reliable heat insulation performance of resin matrix composites, thereby ensuring the stability of the thermal protection system.

[0003] The determination of the thermal conductivity of resin matrix composites generally includes experimental methods and numerical calculation methods.

[0004] There are problems such as long experimental periods, large sample sizes required for testing, and high requirements for sample preparation when using traditional experimental methods to test thermal conductivity. The commonly used methods for testing the thermal conductivity of thermal protection materials are the plane heat source method and the guarded hot plate method. Among them, the sample preparation size of the plane heat source method is 30×30×3 mm or even larger, and two identical samples with a flat and smooth surface are required. The sample preparation size of the guarded hot plate method is φ50.8×2 mm or even larger, and two identical samples with a flat and smooth surface are also required. In addition, it is difficult to process thin samples of this size for brittle resin matrix composites, and more materials will be wasted during processing. In reality, due to limitations in material preparation or acquisition methods, the sample size cannot meet the test requirements, and thus the thermal conductivity cannot be determined, which has become a bottleneck problem in the design of thermal protection materials.

[0005] The two key steps for calculating the thermal conductivity by numerical methods are microstructure characterization and modeling, and selecting a reliable model for calculation. Among them, the pore and particle structures of resin-based composites are considered to be the direct factors affecting the thermal conductivity. Therefore, how to accurately characterize and model the composites is the key to affecting the accuracy of calculating the thermal conductivity by numerical methods. At present, the methods for constructing the microstructure of resin-based composites that are more commonly used are the artificial construction method and the micro-CT scanning imaging method. However, the artificial construction method cannot reflect the true situation of the pores and particles inside the material, and the resolution of the micro-CT scanning imaging method is relatively low, and the morphology of nano-scale pores and particles cannot be obtained, resulting in an incomplete understanding of the internal structure information of the material and an inaccurate model constructed. In fact, the pore diameter distribution range of resin-based composites is very wide, and the pore diameter distribution ranges from more than a dozen nanometers to several micrometers, and the pore structure is complex, including non-connected pores, semi-connected pores and connected pores. Therefore, it is difficult to characterize the microstructure of resin-based composites, and the internal pore structure information obtained is inaccurate, which leads to a large error in the calculated thermal conductivity of the material. Summary of the Invention

[0006] In view of this, the present invention provides a method for determining the thermal conductivity of the multi-scale three-dimensional structure of resin-based composites, which can meet the needs of determining the thermal conductivity of small-size samples, and can multi-scale characterize the internal pore and particle structure information of resin-based composites, and can multi-scale model and calculate the overall effective thermal conductivity of the material on the premise of considering the nano-scale effect, with high accuracy.

[0007] The method for determining the thermal conductivity of the multi-scale three-dimensional structure of resin-based composites of the present invention includes:

[0008] S1. Perform focused ion beam scanning electron microscopy scanning on the resin matrix of the composite material. The spatial resolution of the focused ion beam scanning electron microscopy is better than 15 nm, obtain the three-dimensional nano-pore structure of the resin matrix, and calculate the average particle diameter and the average pore diameter;

[0009] S2. Based on the three-dimensional nano-pore structure parameters of the resin matrix obtained in S1, construct a gas-phase thermal conductivity model and a solid-phase thermal conductivity model considering the confinement effects of gas nano-scale pores and nano-scale particles;

[0010] S3. Based on the gas-phase thermal conductivity model and the solid-phase thermal conductivity model constructed in S2, use the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional nano-pore structure of the resin matrix obtained in S1, and calculate the effective thermal conductivity of the resin matrix;

[0011] S4. Perform micro-CT scanning on the resin-based composite material, obtain the three-dimensional pore structure of the resin-based composite material, and calculate the average particle diameter, the average pore diameter and the spatial angles of each fiber;

[0012] S5. Based on the three-dimensional pore structure parameters of the resin matrix composite obtained in S4, construct a gas-phase thermal conductivity model; the solid-phase thermal conductivity is the effective thermal conductivity of the resin matrix obtained in S3, and based on the fiber spatial angle, through coordinate transformation, calculate the anisotropic thermal conductivity tensor of the fiber.

[0013] S6. Based on the gas-phase thermal conductivity model and solid-phase thermal conductivity constructed in S5, use the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional structure of the composite material obtained in S4, and calculate the effective thermal conductivity of the resin matrix composite.

[0014] Preferably, in S1 and S4, perform image processing and three-dimensional reconstruction on the scanned two-dimensional slice grayscale image to obtain a three-dimensional pore structure; the image processing includes: adjusting brightness-contrast, median filtering, threshold segmentation, removing noise, and filling holes.

[0015] Preferably, use Avizo software for image processing; use Image J for pore analysis to calculate the particle diameter and pore diameter.

[0016] Preferably, the gas-phase thermal conductivity model in S2 and S5 uses the ZENG gas-phase thermal conductivity model or the gas-phase thermal conductivity model based on the Gauss pore size distribution;

[0017] The solid-phase thermal conductivity model in S2 uses the Bi&Tang solid-phase thermal conductivity model.

[0018] Preferably, the ZENG gas-phase thermal conductivity model is:

[0019]

[0020] η = 0.461N g0 m g (8k B T / πm g ) 1 / 2 l m

[0021]

[0022] N g0 = n g / V∏ = p / k B T

[0023] where k n,g is the gas-phase thermal conductivity, T is the temperature, is the gas thermal conductivity in free space, γ = 1.4 is the adiabatic coefficient of diatomic gas molecules, Pr is the Prandtl constant, α is the energy adjustment coefficient in air, l ch is the distance between heat transfer surfaces, l mis the mean free path of randomly colliding gas molecules; η is the viscosity, c v is the volumetric specific heat capacity, N g0 is the gas molecular number density, m g is the gas mass, k B is the Boltzmann constant; S s is the specific surface area, ρ por is the density, ∏ is the porosity, d g is the gas molecular diameter; n g is the number of gas molecules, V is the volume, p is the pressure.

[0024] Preferably, the gas-phase thermal conductivity model based on the Gauss pore size distribution is:

[0025]

[0026] where k(D,σ) is the gas thermal conductivity, N is the normalization constant, D` is the pore diameter, D is the average pore diameter, σ is the standard deviation, is the thermal conductivity of the free gas, is the assumed parameter value, C 3 is the assumed material property constant, C 3 = 1.55, l g is the mean free path.

[0027] Preferably, the Bi&Tang solid-phase thermal conductivity model is:

[0028]

[0029] where λ 0 is the solid-phase thermal conductivity, c v is the volumetric specific heat capacity, v 0 is the average sound velocity of phonons, Λ 0 is the average phonon free path,

[0030] Λ V is the average phonon free path caused by scattering due to phonon volume thermal resistance, λ bulk is the bulk thermal conductivity; v bulk is the solid sound velocity of the material;

[0031] Λ S is the average phonon free path of boundary contact scattering, a is the contact diameter of interconnected particles, d p is the particle diameter, A inter and A sphere are the interface area and the spherical particle coverage area respectively, A eff = A sphere + 2A inter;

[0032] Λ T is the mean free path of the interface contact scattering phonons, Λ T = 3t AB L / 2; t AB is the A - B energy transfer rate. Under the assumption of a rough interface, L is the distance between the centers of the two spherical particles.

[0033] Preferably, it further includes:

[0034] S0. Perform a two - dimensional scanning electron microscope (SEM) scan on the resin - based composite material to obtain the pore and particle size ranges. If the pore diameters are all greater than 1μm, then use the traditional micro - CT scanning imaging method to obtain the morphology of the internal voids and particles of the material, and then model and calculate the thermal conductivity of the material; otherwise, execute S1.

[0035] Preferably, in the S0, the two - dimensional scanning electron microscope is S - 4800, JSM - 7500F or Sirion 200.

[0036] Preferably, in the S0, use the built - in program of the scanning electron microscope to measure the pore and particle diameters, or use Image J software to measure the pore and particle diameters of the scanning electron microscope images to obtain the pore and particle size ranges.

[0037] Beneficial effects:

[0038] (1) The present invention first uses a high - resolution focused ion beam scanning electron microscope to obtain the three - dimensional nano - pore structure of the resin matrix of the composite material, and constructs gas - phase and solid - phase thermal conductivity models considering the confinement effects of gas nano - pores and nano - particles. The lattice Boltzmann method is used to calculate the effective thermal conductivity of the resin matrix; then, micro - CT is used to obtain the three - dimensional structure of the resin - based composite material, construct a gas - phase thermal conductivity model, and use the effective thermal conductivity of the resin matrix as the solid - phase thermal conductivity, and the effective thermal conductivity of the resin - based composite material is calculated by the lattice Boltzmann method. The present invention can obtain both micron - scale pore morphology and nano - scale pore morphology, realizing multi - scale pore structure characterization; the calculated effective thermal conductivity of the resin - based composite material is closer to the actual thermal conductivity, with higher accuracy.

[0039] (2) The focused ion beam scanning electron microscope and micro - CT characterization methods used in the present invention require very small sample sizes. Among them, the sample preparation size of the focused ion beam scanning electron microscope can reach 3×3×2 mm, or even smaller, only 1 / 150 of the sample size tested by the plane heat source method. The scanning area size of the focused ion beam scanning electron microscope is about 10×10×10 μm, and the sample preparation size of micro - CT can reach φ1×10 mm. Therefore, the structure characterization and effective thermal conductivity calculation of small - size samples can be realized. Description of the Drawings

[0040] Figure 1 It is a flowchart of the calculation method.

[0041] Figure 2 It is a schematic diagram of multi-scale structure characterization.

[0042] Figure 3 It is a schematic diagram of the sample size.

[0043] Figure 4 It is a SEM image of the sample.

[0044] Figure 5 It is the particle diameter distribution calculated by Image J based on the SEM image.

[0045] Figure 6 It is a gray-scale image of a two-dimensional slice of a focused ion beam scanning electron microscope.

[0046] Figure 7 It is a gray-scale image of a two-dimensional slice of micro-CT.

[0047] Figure 8 It is a three-dimensional image reconstructed from the gray-scale images of two-dimensional slices scanned by a focused ion beam scanning electron microscope (a) and micro-CT (b).

[0048] Figure 9 It is the boundary condition for calculating the effective thermal conductivity by the lattice Boltzmann method. Detailed Embodiments

[0049] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.

[0050] The present invention provides a method for determining the thermal conductivity of a multi-scale three-dimensional structure of a resin-based composite material, as Figure 1 shown, which includes the following steps:

[0051] S1, perform a focused ion beam scanning electron microscope scan on the resin matrix of the resin-based composite material.

[0052] The resolution of the focused ion beam scanning electron microscope can reach up to several nanometers at most, and it can effectively resolve the morphology of nano-scale pores and particles. In the present invention, the resolution of the focused ion beam scanning electron microscope needs to be better than 15 nm.

[0053] Perform image processing and three-dimensional reconstruction on the gray-scale image of the two-dimensional slice obtained by the focused ion beam scanning electron microscope, specifically including: steps such as adjusting brightness-contrast, median filtering, threshold segmentation, removing noise, filling holes, and reconstructing the two-dimensional image into a three-dimensional image, to obtain the three-dimensional nano-porous structure of the matrix.

[0054] Perform pore structure analysis on the processed focused ion beam scanning electron microscope images, and calculate the average particle diameter, average pore diameter, pore diameter distribution, and porosity.

[0055] S2. Based on the three-dimensional nano-pore structure parameters of the resin matrix obtained in S1, construct a gas-phase thermal conductivity model and a solid-phase thermal conductivity model considering the confinement effects of gas nano-pores and nano-particles.

[0056] Among them, the gas-phase thermal conductivity model can adopt the ZENG gas-phase thermal conductivity model or the gas-phase thermal conductivity model based on the Gauss pore size distribution. The ZENG gas-phase thermal conductivity model considers the confinement effects of gas nano-pores and nano-particles during the modeling process; the gas-phase thermal conductivity model based on the Gauss pore size distribution can reflect the influence of the randomness and inhomogeneity of the pore distribution on gas heat transfer, and can also embody the confinement effects of gas nano-pores and nano-particles. The solid-phase thermal conductivity model can adopt the Bi&Tang solid-phase thermal conductivity model.

[0057] Among them, the ZENG gas-phase thermal conductivity model is:

[0058]

[0059] N g0 =n g / V∏=p / k B T

[0060] η=0.461N g0 m g (8k B T / πm g ) 1 / 2 l m

[0061]

[0062] Among them, k n,g is the gas-phase thermal conductivity, is the gas thermal conductivity in free space, γ = 1.4 is the adiabatic coefficient of diatomic gas molecules, Pr is the Prandtl constant, α is the energy adjustment coefficient in air, l ch is the distance between heat transfer surfaces, l m is the mean free path of randomly colliding gas molecules; S s is the specific surface area, ρ por is the density, ∏ is the porosity; N g0 is the gas molecule number density, n g is the number of gas molecules, V is the volume, m g is the gas mass, c v is the volume specific heat capacity, k Bk is the Boltzmann constant, T is the temperature, and d g is the diameter of the gas molecule; p is the pressure, and η is the viscosity. g0 k is the gas thermal conductivity in free space.

[0063] If the pore size distribution in the resin matrix satisfies the Gauss distribution, the gas thermal conductivity can be calculated using the gas thermal conductivity model based on the Gauss pore size distribution:

[0064]

[0065] where k(D,σ) is the gas thermal conductivity, N is the normalization constant, D` is the pore size, D is the average pore size, and σ is the standard deviation. k∞ is the thermal conductivity of the free gas. C is the assumed parameter value. 3 C is the assumed material property constant. 3 C = 1.55, and l g is the mean free path.

[0066] The Bi&Tang solid-phase thermal conductivity model is:

[0067]

[0068] where λ 0 is the solid-phase thermal conductivity, c v is the volume specific heat capacity, and v 0 is the average sound velocity of phonons; Λ 0 is the average phonon mean free path.

[0069] The average phonon mean free path Λ of the scattering caused by the phonon volume thermal resistance is V given by

[0070] The average phonon mean free path Λ of the boundary contact scattering is S given by A eff A = A sphere + 2A inter ;

[0071] The average phonon mean free path Λ of the interface contact scattering is T given by Λ T = 3t AB L / 2;

[0072] Under the assumption of a rough interface, t AB (the A-B energy transfer rate) can be expressed as

[0073] where λ bulk is the bulk thermal conductivity; v bulkis the solid sound velocity of the material (taking 4000 m / s); and A sphere are the interface area and the spherical particle coverage area respectively; a is the contact diameter of the interconnected particles, d p is the particle diameter, and L is the distance between the centers of the two spherical particles.

[0074] For S3, the lattice Boltzmann method is used to numerically simulate the heat transfer process of the three-dimensional nano-porous structure of the resin matrix obtained in S1, and the effective thermal conductivity of the resin matrix is calculated.

[0075] For the three-dimensional nano-porous structure of the resin matrix obtained in S1, and the gas-phase thermal conductivity model and solid-phase thermal conductivity model constructed in S2, according to the three-dimensional steady-state energy conservation equation calculate the effective thermal conductivity, where k c is the thermal conductivity of the cubic element, is the three-dimensional gradient operator, and T is the temperature. Through the multi-space discrete direction multi-relaxation lattice Boltzmann thermal conductivity model, MPI parallel programming is carried out, and the multi-relaxation time D3Q7 model is used to simulate the heat transfer process of the resin matrix, and the effective thermal conductivity k of the resin matrix is obtained eff，1 .

[0076] For S4, micro-CT scanning is performed on the resin matrix composite material.

[0077] The highest resolution of micro-CT scanning is 600 nm, and the pore morphology larger than 1 um can be distinguished.

[0078] Image processing and three-dimensional reconstruction are performed on the two-dimensional slice grayscale image obtained by micro-CT scanning, including steps such as adjusting brightness-contrast, median filtering, threshold segmentation, removing noise, filling holes, and reconstructing the two-dimensional image into a three-dimensional image, to obtain the three-dimensional pore structure of the resin matrix composite material.

[0079] Pore structure analysis is performed on the processed micro-CT image, and the average particle diameter, average pore diameter, pore diameter distribution, porosity, and various fiber spatial angles are calculated.

[0080] For S5, based on the three-dimensional pore structure of the resin matrix composite material obtained in S4, a gas-phase thermal conductivity model is constructed, where the gas-phase thermal conductivity model can be constructed in the same way as in S2;

[0081]

[0082] N g0 = n g / VΠ = p / k B T

[0083] η = 0.461N g0 mg (8k B T / πm g ) 1 / 2 l m

[0084]

[0085] Among them, k n,g is the gas thermal conductivity, is the gas thermal conductivity of free space, γ = 1.4 is the adiabatic coefficient of diatomic gas molecules, Pr is the Prandtl constant, α is the energy regulation coefficient in air, l ch is the distance between heat transfer surfaces, l m is the mean free path of randomly colliding gas molecules; S s is the specific surface area, ρ por is the density, Π is the porosity; N g0 is the gas molecular number density, n g is the number of gas molecules, V is the volume, m g is the gas mass, c v is the volume specific heat capacity, k B is the Boltzmann constant, T is the temperature, d g is the gas molecular diameter; p is the pressure, η is the viscosity. k g0 is the gas thermal conductivity of free space;

[0086] If the pore size distribution in the composite material is a Gauss distribution, then the gas thermal conductivity is

[0087]

[0088] Among them, N is the normalization constant, D` is the pore size, D is the average pore size, σ is the standard deviation, is the thermal conductivity of free gas, is the assumed parameter value, C 3 is the assumed material property constant, C 3 = 1.55, l g is the mean free path.

[0089] The solid thermal conductivity of the composite material is the effective thermal conductivity k obtained by modeling and calculating based on the three-dimensional image of the focused ion beam scanning electron microscope eff，1 , and based on the fiber space angle, through coordinate transformation, the anisotropic thermal conductivity tensor of the fiber is calculated.

[0090] S6, using the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional structure of the composite material obtained by S4, and calculate the effective thermal conductivity of the resin-based composite material.

[0091] For the three-dimensional structure of the composite material obtained in S4, first divide the model into grids with a size of 10×10×10 μm, and then based on the gas-phase thermal conductivity model and solid-phase thermal conductivity constructed in S5, also use the three-dimensional steady-state energy conservation equation to calculate the effective thermal conductivity. Through the multi-space discrete direction multi-relaxation lattice Boltzmann thermal conductivity model, carry out MPI parallel programming, and use the multi-relaxation time D3Q7 model to simulate the heat transfer process of the composite material to obtain the effective thermal conductivity k eff 。

[0092] k eff That is the effective thermal conductivity of the final output resin matrix composite material.

[0093] In order to improve the experimental efficiency and simplify the experimental process, before executing S1, the present invention can first use a two-dimensional scanning electron microscope to preliminarily scan the resin matrix composite material to determine the approximate range of the pore diameter. If the pore diameters are all greater than 1 μm, the traditional micro-CT scanning imaging method can be used to obtain the morphology of the internal voids and particles of the material, and then model and calculate the effective thermal conductivity of the material; if there are many pores with diameters less than 1 μm, even less than 50 nm, then execute S1 and use a high-resolution focused ion beam scanning electron microscope to obtain the nano-scale pore morphology.

[0094] Here, the resolution requirement for the two-dimensional scanning electron microscope is not high, and general scanning electron microscopes such as S-4800, JSM-7500F, and Sirion200 can be used to obtain a preliminary pore and particle size range. The built-in program of the two-dimensional scanning electron microscope can be used to measure the pore and particle diameters (more than 20 groups) to roughly determine the pore diameter range and statistically calculate the average particle diameter; or the Image J software can be used to measure the pore and particle diameters (more than 20 groups) of the scanning electron microscope image and statistically calculate the average particle diameter.

[0095] Example 1

[0096] (1) Observe the resin matrix composite material with a scanning electron microscope (S-4800) to roughly determine the pore and particle size range. If the pore diameters are all greater than 1 μm, the traditional micro-CT scanning imaging method can be used to obtain the pore structure and model and calculate the thermal conductivity; if there are many pores with diameters less than 1 μm, even less than 50 nm, then execute step (2).

[0097] (2) Use Image J to calculate the particle diameter of the scanning electron microscope image in step (1). The calculated average particle diameter d n is 112 nm.

[0098] (3) Perform a focused ion beam scanning electron microscope scan (Crossbeam550) on the resin matrix of the resin matrix composite material.

[0099] Among them, the sample preparation size of the resin matrix of the resin-based composite material is 3×3×2 mm (including but not limited to this size), the scanning size is about 10×10×10 μm (including but not limited to this size), and the resolution can reach up to several nanometers to resolve the nano-scale pore morphology and obtain a two-dimensional slice gray-scale image.

[0100] (4) Use Avizo software to perform image processing and three-dimensional reconstruction on the two-dimensional slice gray-scale image of the resin matrix, including: adjusting brightness-contrast, median filtering, threshold segmentation, removing noise, filling holes, and reconstructing the two-dimensional image into a three-dimensional image.

[0101] (5) Use Image J to perform pore analysis on the focused ion beam scanning electron microscope image processed in step (4), and calculate the pore diameter distribution and porosity. The calculated porosity is 50.62%, and the average pore diameter d n,p is 90.86 nm.

[0102] (6) Construct the ZENG gas-phase thermal conductivity model and the Bi&Tang solid-phase thermal conductivity model of the resin matrix; use the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional nano-pore structure of the resin matrix reconstructed in (4), and calculate the effective thermal conductivity of the resin matrix.

[0103] Among them, the boundary conditions are

[0104] T(x,y,0) = T h

[0105] T(x,y,L) = T c

[0106]

[0107] where T h is the high-temperature side temperature, and T c is the low-temperature side temperature.

[0108] According to the three-dimensional steady-state energy conservation equation calculate the effective thermal conductivity, where k c is the cubic element thermal conductivity, is the three-dimensional gradient operator, and T is the temperature.

[0109] Through the multi-space discrete direction multi-relaxation lattice Boltzmann thermal conductivity model, carry out MPI parallel programming, and use the multi-relaxation time D3Q7 model to simulate the heat transfer process of the resin matrix to obtain the effective thermal conductivity k eff，1 .

[0110] (7) Perform micro-CT scanning on the resin-based composite material.

[0111] The sample preparation size of the resin matrix composite is (including but not limited to this size). The highest resolution of micro-CT scanning is 600 nm to resolve the pore morphology larger than 1 μm, and two-dimensional slice grayscale images are obtained.

[0112] (8) Use Avizo software to perform image processing and three-dimensional reconstruction on the two-dimensional slice grayscale images of the resin matrix composite, including: adjusting brightness-contrast, median filtering, threshold segmentation, removing noise, filling holes, and reconstructing the two-dimensional image into a three-dimensional image.

[0113] (9) Use Image J to analyze the pore structure of the processed micro-CT images, and calculate the average pore diameter, pore diameter distribution, and porosity. The calculated porosity is 22.52%, and the average pore diameter is 2.68 μm.

[0114] (10) Construct the ZENG gas-phase thermal conductivity model of the resin matrix composite; the solid-phase thermal conductivity takes the effective thermal conductivity k eff，1 calculated in (6), and based on the fiber spatial angle, through coordinate transformation, calculate the anisotropic thermal conductivity tensor of the fiber.

[0115] Divide the model into grids with a size of 10×10×10 μm, and also use the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional structure of the resin matrix composite reconstructed in (8), and calculate the overall effective thermal conductivity of the resin matrix composite.

[0116] Among them, the boundary conditions are

[0117] T(x,y,0) = T h

[0118] T(x,y,L) = T c

[0119]

[0120] Among them, T h is the high-temperature side temperature, and T c is the low-temperature side temperature.

[0121] Similarly, use the three-dimensional steady-state energy conservation equation to calculate the effective thermal conductivity.

[0122] Through the multi-space discrete direction multi-relaxation lattice Boltzmann thermal conductivity model, carry out MPI parallel programming. Use the multi-relaxation time D3Q7 model to simulate the heat transfer process of the composite material, and obtain the final effective thermal conductivity k eff .

[0123] The effective thermal conductivity k of the resin matrix composite calculated in step (10) effIt is 0.612 W / m·k, with a difference of only 5.9% from the thermal conductivity (0.578 W / m·k) measured by the plane heat source method through experiments.

[0124] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for determining the thermal conductivity of a multi-scale three-dimensional structure of a resin-based composite material, characterized in that: include: S1, scanning the resin matrix of the composite material by a focused ion beam scanning electron microscope, wherein the spatial resolution of the focused ion beam scanning electron microscope is better than 15 nm, obtaining the three-dimensional nanoporous structure of the resin matrix, and calculating the average particle diameter and the average pore diameter; S2, based on the three-dimensional nanopore structure parameters of the resin matrix obtained in S1, a gas phase thermal conductivity model and a solid phase thermal conductivity model are constructed that take into account the confinement effect of gas nanopores and nanoparticles; S3, based on the gas phase thermal conductivity model and solid phase thermal conductivity model constructed in S2, uses the lattice Boltzmann method to numerically simulate the heat transfer process of the three-dimensional nanoporous structure of the resin matrix obtained in S1, and calculates the effective thermal conductivity of the resin matrix; S4, performing micro-CT scanning on the resin-based composite material to obtain the three-dimensional pore structure of the resin-based composite material, and calculating the average particle diameter, the average pore diameter, and the spatial angle of each fiber; S5, based on the three-dimensional pore structure parameters of the resin-based composite material obtained in S4, a gas phase thermal conductivity model is constructed; the solid phase thermal conductivity is the effective thermal conductivity of the resin matrix obtained in S3, and based on the fiber space angle, the anisotropic thermal conductivity tensor of the fiber is calculated through coordinate transformation; S6, based on the gas phase thermal conductivity model and solid phase thermal conductivity constructed in S5, the lattice Boltzmann method is used to numerically simulate the heat transfer process of the composite material three-dimensional structure obtained in S4, and the effective thermal conductivity of the resin-based composite material is calculated.

2. The method according to claim 1, characterized in that In S1 and S4, the two-dimensional slice grayscale image obtained by scanning is subjected to image processing and three-dimensional reconstruction to obtain a three-dimensional pore structure; the image processing includes: adjusting brightness-contrast, median filtering, threshold segmentation, removing noise and filling holes.

3. The method according to claim 2, characterized in that Avizo software was used for image processing, and image J was used for pore analysis to calculate particle diameter and pore diameter.

4. The method according to claim 1, characterized in that The gas phase thermal conductivity model in S2 and S5 adopts the ZENG gas phase thermal conductivity model or the gas phase thermal conductivity model based on Gauss pore size distribution; The solid phase thermal conductivity model in S2 adopts the Bi&Tang solid phase thermal conductivity model.

5. The method according to claim 4, characterized in that The ZENG gas phase thermal conductivity model is: η=0.461N g0 m g (8k B T / m g ) 1 / 2 l m N g0 =n g / VΠ=p / k B T Among them, k n,g is the gas phase thermal conductivity, T is the temperature, is the gas thermal conductivity of free space, γ = 1.4 is the thermal insulation coefficient of diatomic gas molecules, Pr is the Prandtl constant, α is the energy regulation coefficient in air, l ch is the distance between the heat exchange surfaces, l m is the mean free path of the random collision gas molecules; η is the viscosity, c v is the volume specific heat capacity, N g0 is the gas molecule number density, m g is the gas mass, k B is the Boltzmann constant; S s is the specific surface area, ρ por is the density, Π is the porosity, d g is the diameter of gas molecules; n g is the number of gas molecules, V is the volume, and p is the pressure.

6. The method according to claim 4, characterized in that The gas phase thermal conductivity model based on Gauss pore size distribution is: Where k(D,σ) is the thermal conductivity of the gas, N is the normalization constant, D' is the pore size, D is the average pore size, and σ is the standard deviation. is the thermal conductivity of free gas, is the assumed parameter value, C3 is the assumed material characteristic constant, C3=1.55, l g is the mean free path.

7. The method according to claim 4, characterized in that Bi&Tang solid phase thermal conductivity model is: Where λ0 is the solid phase thermal conductivity, c v is the volume specific heat capacity, v0 is the average sound velocity of phonons, Λ0 is the average phonon free path, Λ V is the phonon mean free path of scattering caused by phonon volume thermal resistance, λ bulk is the thermal conductivity of bulk material; v bulk is the solid sound velocity of the material; Λ S is the mean free path of phonon scattered by boundary contact, a is the contact diameter of interconnected particles, d p is the particle diameter, A inter and A sphere are the interface area and the spherical particle coverage area, A eff =A sphere +2A inter ; Λ T is the mean free path of phonon scattered by interface contact, Λ T =3t AB L / 2;t AB is the AB energy transfer rate, under the assumption of a rough interface, L is the distance between the centers of the two spherical particles.

8. The method according to any one of claims 1 to 7, characterized in that: Also includes: S0, perform a two-dimensional scanning electron microscope scan on the resin-based composite material to obtain the pore and particle size range. If the pore diameters are all greater than 1 μm, use the traditional micro-CT scanning imaging method to obtain the morphology of the internal voids and particles of the material, and then model and calculate the thermal conductivity of the material; otherwise, execute S1.

9. The method according to claim 8, characterized in that In the S0, the two-dimensional scanning electron microscope adopts S-4800, JSM-7500F or Sirion 200.

10. The method according to claim 8, characterized in that In the S0, the pore and particle diameters are measured using a built-in program of a scanning electron microscope, or the pore and particle diameters are measured using Image J software on a scanning electron microscope image to obtain the pore and particle size ranges.

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