Method for calculating thermal conductivity of gases in porous structures

Abstract

The application discloses a kind of calculation methods of gas thermal conductivity in porous structure, to any shape of porous structure and the gas structure contained in porous structure is discretized, i.e. grid, it is divided into grid porous structure unit and gas unit with node coordinate determination;All gas units are traversed, the space where gas unit is located is evenly divided into several small regions, the equivalent diameter of each small region compared with adjacent gas unit surface solid unit is calculated, and the equivalent thermal conductivity corresponding to the diameter is calculated using the effect of krusen, finally, the equivalent thermal conductivity of the gas unit is obtained by weighted average of all regions.This application solves the problem that porous material cannot directly use the relationship between thermal conductivity, pore diameter and gas pressure under the effect of krusen to calculate the gas thermal conductivity in the pore.

Description

Technical Field

[0001] This invention relates to the field of gas-bonded geometric structure calculation technology, specifically, a method for calculating the thermal conductivity of gas in porous structures. Background Technology

[0002] Porous materials exhibit low thermal conductivity due to their low density and high porosity. Furthermore, at small pore sizes, the thermal conductivity of gases is significantly reduced because the mean free path of molecules is confined by the pores; this is known as the Krusen effect, which causes the thermal conductivity of porous materials to become extremely low. The Krusen effect has extremely wide applications in porous structures. For regularly shaped spherical pores, the relationship between thermal conductivity and pore diameter and gas pressure under the Krusen effect can be calculated using classical molecular dynamics:

[0003]

[0004] In this formula, λg is the static gas thermal conductivity in an open environment, β is a constant coefficient, and D is the pore diameter. However, porous materials have random and complex structures, and their shapes are far from spherical. Furthermore, at high porosity, the pores often exhibit an open-pore shape, making it impossible to use this formula to calculate the gas thermal conductivity in complex pores. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the thermal conductivity of gas in porous structures, which solves the problem in the prior art that the relationship between thermal conductivity under the Krusen effect and pore diameter and gas pressure cannot be used to calculate the thermal conductivity of gas in the pores of porous materials.

[0006] The present invention solves the above problems through the following technical solution:

[0007] A method for calculating the thermal conductivity of gas in a porous structure, comprising:

[0008] Step S1: Discretize the porous structure of arbitrary shape and the gas structure contained in the porous structure, and divide it into meshed porous structure units and gas units with node coordinates determined.

[0009] Step S2: Traverse all gas units to determine their porous environment and calculate their equivalent thermal conductivity.

[0010] Further, step S2 specifically includes:

[0011] Step S2-1: Using the gas cell being traversed as the origin of the coordinate system, and the XY, XZ and YZ planes as the dividing planes, the space is divided into 8 large regions. All solid cells within a set length range in each large region are traversed. Based on the angle between the solid cell and the YZ plane, the solid cells in the large region are divided into several smaller regions of equal size, thus realizing the secondary division of the space of the traversed gas cell.

[0012] Step S2-2: Traverse all small regions and determine whether the neighboring unit of the solid unit pointing in the gas direction is a gas unit. If it is a gas unit, determine whether there are other solid units on the line connecting the solid unit and the gas unit. If not, put it into container 1.

[0013] Step S2-3: Calculate the equivalent diameter of the small region using the average distance or weighted average distance method, and put the diameter values ​​of all small regions into container 2;

[0014] Step S2-4: Based on the diameter value in container 2, according to the formula... Calculate the thermal conductivity of each small region, and then take a weighted average of all thermal conductivity values ​​to obtain the equivalent thermal conductivity of the gas unit.

[0015] Step S2-5: Repeat steps S2-1 to S2-4 above to continue traversing the remaining gas units until all gases have been traversed. The definition of the thermal conductivity properties of the entire porous gas is then completed.

[0016] Furthermore, the average distance method is as follows: the equivalent diameter is obtained by averaging the distances between all solid units and gas units in container 1; the weighted average distance method is as follows: the equivalent average diameter of the region is calculated based on the central angle occupied by the solids in container 1 and their distances from the gas units.

[0017] Furthermore, if the size of the porous model exceeds a set threshold, step S2-4 is replaced by: taking a set number of integer diameters D, such as calculating a list 1 of equivalent thermal conductivity under different diameters D, traversing the diameter values ​​in container 2, selecting the D value in list 1 that is closest to the traversed diameter value as the equivalent diameter to calculate the equivalent thermal conductivity of the small region, and calculating the weighted average of the equivalent thermal conductivity of all small regions to obtain the equivalent thermal conductivity of the gas unit.

[0018] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0019] This invention first divides the solid and gas structures into grid cells, then divides the space containing the gas cells into several small regions. The equivalent diameter of each small region is calculated, and its equivalent thermal conductivity is obtained using a formula. Finally, the equivalent thermal conductivity of the gas cell is obtained by weighted averaging the thermal conductivity of all small regions. This solves the problem that the thermal conductivity of gas within pores cannot be directly calculated using the relationship between thermal conductivity under the Krusen effect and pore diameter and gas pressure in porous materials. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention;

[0021] Figure 2 This is a schematic diagram of a solid structure model consisting of hexahedral elements.

[0022] Figure 3 This is a schematic diagram of the spatial division of a gas cell.

[0023] Figure 4 A schematic diagram of solid units surrounding a gas unit;

[0024] Figure 5 This is a thermal conductivity distribution diagram for a hexahedral porous structure model. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to embodiments, but the implementation of the present invention is not limited thereto.

[0026] Example 1:

[0027] Combined with appendix Figure 1 As shown, a method for calculating the thermal conductivity of gas in a porous structure includes:

[0028] Step S1: Discretize the porous structure of arbitrary shape and the gas structure contained within it, dividing it into meshed porous structure elements and gas elements with defined node coordinates. A hexahedral element porous model is shown below. Figure 2 As shown;

[0029] Step S2: Traverse all gas units to determine their porous environment and calculate their equivalent thermal conductivity, specifically including:

[0030] Step S2-1: Using the gas cell being traversed as the origin of the coordinate system, and the XY, XZ, and YZ planes as dividing planes, divide the space containing the gas cell into 8 large regions. Traverse all solid cells within a certain length of space in each large region. Based on the angle between the solid cells and the YZ plane, divide the solid cells in the large region into several smaller regions of equal size, thus achieving a secondary division of the space of the traversed gas cell. The division of the gas cell is as follows: Figure 3 As shown;

[0031] Step S2-2: Traverse all small regions and determine whether the neighboring unit of a solid unit pointing in the gas direction is a gas unit. If it is a gas unit, then determine whether there are other solid units on the line connecting the solid unit and the gas unit. If not, put it into container 1. The two types of surface solid units and internal solid units are shown in the figure. Figure 4 As shown, the region composed of solid unit-1 will be loaded into container 1.

[0032] Step S2-3: Calculate the equivalent diameter of the small region using the average distance or weighted average distance method, and put the diameter values ​​of all small regions into container 2;

[0033] The average distance method is as follows: the equivalent diameter is obtained by averaging the distances between all solid units and gas units in container 1; specifically, the solid units in container 1 are traversed, the distance between the unit and the gas unit is calculated, and the average of all distance values ​​is taken as the equivalent average radius of the small region, and the average diameter of all small regions is put into container 2.

[0034] The weighted average distance method is as follows: Based on the central angle occupied by the solid element in container 1 and its distance from the gas element, the equivalent average radius of the region is calculated, and the distance values ​​of all regions are stored in the container. Specifically, the solid elements in container 1 are traversed, and the distance L between the solid element and the gas element and the proportion w of the solid element's central angle are calculated. The value calculated using the formula ΣLw is used as the equivalent average radius of the small region, and the average diameter value of all small regions is stored in container 2.

[0035] Step S2-4: Based on the diameter value in container 2, according to the formula... Calculate the thermal conductivity of each small region, and then take a weighted average of all thermal conductivity values ​​to obtain the equivalent thermal conductivity of the gas unit.

[0036] Step S2-5: Repeat steps S2-1 to S2-4 to continue traversing the remaining gas units until all gases have been traversed. The definition of the thermal conductivity properties of the entire porous gas is then complete. The thermal conductivity distribution diagram of the hexahedral porous structure model is shown below. Figure 5 As shown.

[0037] Furthermore, if the size of the porous model exceeds a set threshold, step S2-5 is replaced by: taking multiple set integer diameters D, such as calculating the equivalent thermal conductivity under different diameters D, as shown in Table 1 below:

[0038] Table 1. Equivalent thermal conductivity for different diameters D

[0039]

[0040] The diameter values ​​in container 2 are iterated through, and the D value closest to the iterated diameter value in list 1 is selected as the equivalent diameter to calculate the equivalent thermal conductivity of the small region. A weighted average of the equivalent thermal conductivity of all small regions is then calculated to obtain the equivalent thermal conductivity of the gas unit. This invention is based on the continuity of the open-pore porous structure, the small fluctuations between adjacent structures, and the close distance between the porous structure and the gas at a relatively distant location. Several adjacent solid structures are approximated as a sector structure. Furthermore, the entire porous structure can be considered as a series of sectors with different radii. Since a sector is part of a sphere, its thermal conductivity is consistent with that of the sphere. Therefore, the porous structure can be divided into regions, equivalent to several sectors with different radii. The equivalent thermal conductivity is obtained based on the sector's radius, and its contribution to the thermal conductivity is obtained based on the central angle it occupies. Thus, the equivalent thermal conductivity of the porous structure is calculated.

[0041] The present invention has been described herein with reference to illustrative embodiments. The above embodiments are merely preferred embodiments of the present invention, and the implementation of the present invention is not limited to the above embodiments. It should be understood that those skilled in the art can design many other modifications and implementations, which will fall within the scope and spirit of the principles disclosed in this application.

Claims

1. A method for calculating the thermal conductivity of gas in a porous structure, characterized in that, include: Step S1: Discretize the porous structure of arbitrary shape and the gas structure contained in the porous structure, and divide it into meshed porous structure units and gas units with node coordinates determined. Step S2: Traverse all gas units to determine their porous environment and calculate their equivalent thermal conductivity. Step S2 specifically includes: Step S2-1: Using the gas cell being traversed as the origin of the coordinate system, and the XY, XZ and YZ planes as the dividing planes, the space is divided into 8 large regions. All solid cells within a set length range in each large region are traversed. Based on the angle between the solid cell and the YZ plane, the solid cells in the large region are divided into several smaller regions of equal size, thus realizing the secondary division of the space of the traversed gas cell. Step S2-2: Traverse all small regions and determine whether the neighboring unit of the solid unit pointing in the gas direction is a gas unit. If it is a gas unit, determine whether there are other solid units on the line connecting the solid unit and the gas unit. If not, put it into container 1. Step S2-3: Calculate the equivalent diameter of the small region using the average distance or weighted average distance method, and put the diameter values ​​of all small regions into container 2; Step S2-4: Based on the diameter value in container 2, according to the formula... Calculate the thermal conductivity of each small region, and then take a weighted average of all thermal conductivity values ​​to obtain the equivalent thermal conductivity of the gas unit. Step S2-5: Repeat steps S2-1 to S2-4 above to continue traversing the remaining gas units until all gases have been traversed. The definition of the thermal conductivity properties of the entire porous gas is then completed.

2. The method for calculating the thermal conductivity of gas in a porous structure according to claim 1, characterized in that, The average distance method is as follows: the equivalent diameter is obtained by averaging the distances between all solid units and gas units in container 1; the weighted average distance method is as follows: the equivalent average diameter of the region is calculated based on the central angle occupied by the solids in container 1 and their distances from the gas units.

3. The method for calculating the thermal conductivity of gas in a porous structure according to claim 1, characterized in that, If the size of the porous model exceeds a set threshold, step S2-4 is replaced by: taking a set number of integer diameters D, calculating a list 1 of equivalent thermal conductivity under different diameters D, traversing the diameter values ​​in container 2, selecting the D value in list 1 that is closest to the traversed diameter value as the equivalent diameter to calculate the equivalent thermal conductivity of the small region, and calculating the weighted average of the equivalent thermal conductivity of all small regions to obtain the equivalent thermal conductivity of the gas unit.

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