Honeycomb sandwich structure heat conductivity coefficient analysis method based on thermal finite element method

Abstract

The invention relates to a honeycomb sandwich structure heat conductivity coefficient analysis method based on a thermal finite element method, and the method comprises the steps: building a honeycomb sandwich structure thermal finite element unit cell model, applying and setting periodic temperature boundary conditions to the unit cell model, setting radiation coefficients on honeycomb core layer cell walls and honeycomb upper and lower skins, and carrying out the steady-state temperature field calculation. And obtaining the unit cell temperature field distribution of the honeycomb sandwich structure, and obtaining the heat conductivity coefficient of the honeycomb sandwich structure based on the obtained temperature field. The influence of structural parameters such as the heat conductivity coefficient of the honeycomb material, the honeycomb height, the honeycomb cell wall thickness and the skin thickness on the heat conductivity coefficient of the honeycomb sandwich structure is considered in detail, and the method has the advantages of being high in calculation precision and wide in application range.

Description

Technical Field

[0001] The invention belongs to the field of structural heat protection analysis, and in particular relates to a method for analyzing thermal conductivity of a honeycomb sandwich structure based on a thermal finite element method. Background Art

[0002] Structural heat protection is one of the bottleneck technologies that restricts the improvement of aircraft performance. When an aircraft flies for a long time, its heat protection structure is subjected to long-term severe aerodynamic heat loads. The material may undergo obvious physical and chemical changes when working in a high-temperature environment for a long time. Its material pyrolysis, oxidation, ablation, etc. will cause a significant decrease in the aircraft's carrying capacity. Under the effect of long-term high-temperature cumulative damage, the aircraft's heat protection bearing performance may fail, seriously threatening flight safety.

[0003] Honeycomb sandwich structure is a commonly used thermal protection material. With its own low thermal conductivity, it can effectively isolate heat flow. Accurately obtaining the thermal conductivity of the honeycomb sandwich structure is of great significance for estimating the heat insulation capacity of the honeycomb sandwich structure and evaluating its use effect. At present, the prediction methods for the thermal conductivity of the honeycomb sandwich structure include theoretical analysis method, experimental method and finite element method. Among them, the applicability of the theoretical analysis method is limited, the calculation error is large under some structures, the experimental method has requirements for the test conditions, and the process is more complicated. The finite element method can achieve more accurate predictions, and does not require complex test equipment, and has a broad application prospect. Summary of the invention

[0004] The purpose of the present invention is to provide a method for analyzing the thermal conductivity of a honeycomb sandwich structure based on the thermal finite element method. Aiming at the composite heat transfer process inside the honeycomb sandwich structure, a thermal finite element unit cell model of the honeycomb sandwich structure is established, temperature boundary conditions are imposed on the unit cell model, radiation coefficients are set on the honeycomb core layer cell walls and the upper and lower skins of the honeycomb, and a steady-state temperature field calculation is performed to obtain the temperature field distribution of the unit cell of the honeycomb sandwich structure. Based on the obtained temperature field, the thermal conductivity of the honeycomb sandwich structure is obtained.

[0005] The above-mentioned purpose of the present invention is mainly achieved through the following technical solutions:

[0006] A method for analyzing thermal conductivity of a honeycomb sandwich structure based on a thermal finite element method comprises the following steps:

[0007] (1) Establish a finite element unit cell model of the honeycomb sandwich structure. The finite element unit cell is a hexagonal prism with a bottom side length of L, skins at both ends, and a skin thickness of h1; the middle is a core layer structure, which is a hollow structure with a wall thickness of t and a height of h2. Divide the finite element unit cell model into grids;

[0008] (2) setting the thermal conductivity, specific heat capacity and density of the skin and core layer in the finite element unit cell model of the honeycomb sandwich structure obtained in step (1), setting the hollow part inside the core layer to air, and setting the thermal conductivity, specific heat capacity and density of the air;

[0009] (3) setting the radiation heat transfer parameter α between the inner surfaces of the upper and lower skins and the inner wall surface of the core layer in the finite element unit cell model of the honeycomb sandwich structure obtained in step (2) to 1;

[0010] (4) applying periodic boundary conditions to the side of the finite element unit cell model of the honeycomb sandwich structure obtained in step (3);

[0011] (5) Apply incident heat flux density q to all unit nodes on the outer surface of the upper skin, and apply a fixed temperature T0 to the outer surface of the lower skin. After the application is completed, the surface temperature distribution T of the honeycomb unit cell is calculated. ij ;

[0012] (6) According to the temperature distribution T obtained in step (5) ij , calculate the thermal conductivity k in the honeycomb thickness direction z , the method is as follows: According to Fourier's law get:

[0013]

[0014] where q z is the heat flux component perpendicular to the bottom surface of the hexagonal prism, k z is the thermal conductivity perpendicular to the bottom surface of the hexagonal prism, d is the total thickness of the honeycomb sandwich structure unit cell, h1 and h2 are the skin thickness and core layer height respectively.

[0015] The skin material is set to carbon fiber and the core layer structure is aluminum alloy.

[0016] The method for applying the periodic boundary conditions in step (4) is as follows: applying the coupling equation T(x,y)-T(x+h0,y)=0 on two opposite side surfaces, where T(x,z) and T(x+h0,z) are the temperatures of two opposite points on the opposite side surfaces, and h0 is the distance between the two opposite surfaces. By applying the coupling equation, the temperatures of corresponding points on the opposite surfaces are made the same, maintaining the balance between heat input and output, and simulating the periodic structure of the unit cell.

[0017] Step (5) The honeycomb cell surface temperature distribution T ij The calculation method is as follows:

[0018] (1) The Oxyz coordinate system is established with the center of the unit cell bottom surface as the origin O, the direction perpendicular to the bottom surface as the z-axis, and the line connecting the two opposite vertices of the bottom hexagonal prism as the y-axis. The material density ρ, the material specific heat capacity c, and the thermal conductivity Kxx, Kyy, and Kzz of the material in the x, y, and z directions are defined, and the following is obtained:

[0019] in

[0020]

[0021] t is time; {v} is the velocity vector of heat mass transfer; {q} is the heat flux vector, is the unit heat generation rate;

[0022] (2) From {q}=-[D]{L}T ij and

[0023]

[0024] Combined with step (1), we get:

[0025]

[0026] (3) When the heat flux q is loaded onto the surface of the honeycomb unit cell, we get:

[0027] {q} T {n}=-q*, where {n} represents the outward normal vector of the unit and q* represents the loading heat flux;

[0028] Substituting into step (2) we get:

[0029]

[0030] (4) Integrate the time t to obtain the temperature T ij .

[0031] A thermal conductivity analysis system for a honeycomb sandwich structure based on a thermal finite element method comprises a finite element model building module, a meshing module, a parameter setting module and a calculation module, wherein the finite element model building module is used to build a finite element unit cell model of a honeycomb sandwich structure, the meshing module is used to mesh the finite element unit cell model of the honeycomb sandwich structure, the parameter setting module is used to set the material type and parameters in the finite element unit cell model of the honeycomb sandwich structure, and to apply periodic boundary conditions and incident heat flux density, and the calculation module is used to calculate the surface temperature distribution T of the honeycomb unit cell according to the parameters of the finite element unit cell model of the honeycomb sandwich structure. ij and the thermal conductivity k in the honeycomb thickness direction z， And output the calculation results.

[0032] Compared with the prior art, the present invention has at least the following beneficial effects:

[0033] (1) The present invention comprehensively considers the material parameters of different materials constituting the honeycomb sandwich structure, and can set the material parameters of different parts of the honeycomb sandwich structure according to actual conditions, so that the calculation results are more in line with the actual conditions;

[0034] (2) The present invention is based on the difference in heat transfer performance of different parts of the honeycomb sandwich structure, that is, different parts have different temperature fields, so the thermal conductivity of different parts of the honeycomb sandwich structure can be calculated, which is more precise for temperature control;

[0035] (3) The present invention comprehensively considers the heat conduction of the honeycomb wall in the honeycomb sandwich structure, the radiation heat exchange between the inner surface of the upper and lower skins and the inner wall of the honeycomb core, and the calculation results are more precise and accurate;

[0036] (4) The present invention takes into account the periodicity of the honeycomb sandwich structure and sets periodic boundary conditions, so that the calculation results are more consistent with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of the method for analyzing the thermal conductivity of the honeycomb sandwich structure of the present invention;

[0038] Figure 2 The unit cell model of the honeycomb sandwich structure and the schematic diagram of the internal structure of the honeycomb of the present invention;

[0039] Figure 3 It is a schematic diagram of the mesh of a unit cell model of a honeycomb sandwich structure of the present invention;

[0040] Figure 4 It is a schematic diagram of boundary conditions of a unit cell model of a honeycomb sandwich structure of the present invention;

[0041] Figure 5 It is a schematic diagram of the temperature field of the unit cell model of the honeycomb sandwich structure of the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0043] like Figure 1 The basic flow chart of the method of the present invention is shown in FIG. 1 , and the specific implementation process of the present invention is as follows:

[0044] (1) Establish a single-cell finite element model of the honeycomb sandwich structure. The finite element unit cell is a hexagonal prism with a bottom side length of L, skins at both ends, and a skin thickness of h1; the middle is a core layer structure, which is a hollow structure with a wall thickness of t and a height of h2. Divide the single-cell finite element model into grids, such as Figure 2 and Figure 3 As shown;

[0045] (2) setting the thermal conductivity, specific heat capacity and density of the skin and core layer in the honeycomb sandwich structure unit cell finite element model obtained in step (1), wherein the thermal conductivity and specific heat capacity are functions related to temperature, and the hollow part inside the core layer is set to air, and the thermal conductivity, specific heat capacity and density of the air are set;

[0046] (3) setting the radiation heat transfer parameter α between the inner surfaces of the upper and lower skins and the inner wall surface of the core layer in the honeycomb sandwich structure unit cell finite element model obtained in step (2) to 1;

[0047] (4) applying periodic boundary conditions to the side surfaces of the honeycomb sandwich structure unit cell finite element model obtained in step (3);

[0048] (5) Apply incident heat flux density q to all unit nodes on the outer surface of the upper skin, and apply a fixed temperature T0 to the outer surface of the lower skin. After loading, calculate the surface temperature distribution T of the honeycomb unit cell. ij ,like Figure 5 shown.

[0049] (6) According to the temperature distribution T obtained in step (5) ij , calculate the thermal conductivity k in the honeycomb thickness direction z , the method is as follows: According to Fourier's law Get the thermal conductivity of the honeycomb thickness direction where q z is the heat flux component perpendicular to the bottom surface of the hexagonal prism, k z is the thermal conductivity perpendicular to the bottom surface of the hexagonal prism, d is the total thickness of the honeycomb sandwich structure unit cell, h1 and h2 are the skin thickness and core layer height respectively.

[0050] In the calculation results, the highest temperature T1 and the lowest temperature T2 of the upper skin outer surface are calculated according to Fourier's law. The maximum value of the thermal conductivity in the honeycomb thickness direction is derived Minimum thermal conductivity It can be seen from the temperature cloud map and calculation results that since the thermal conductivity of the honeycomb wall is better than that of the honeycomb core, the thermal conductivity of the honeycomb structure gradually increases from the center of the honeycomb to the outside, and the thermal conductivity at the center of the honeycomb is the lowest.

[0051] The skin material is set to carbon fiber and the core layer structure is aluminum alloy.

[0052] like Figure 4As shown, the method for applying the periodic boundary conditions in step (4) is as follows: applying the coupling equation T(x,y)-T(x+h0,y)=0 on two opposite side surfaces, T(x,z) and T(x+h0,z) are the temperatures of two opposite points on the opposite side surfaces, and h0 is the distance between the two opposite surfaces. By applying the coupling equation, the temperatures of corresponding points on the opposite surfaces are made the same, maintaining the balance between heat input and output, and simulating the periodic structure of the unit cell.

[0053] Step (5) The honeycomb cell surface temperature distribution T ij The calculation method is as follows:

[0054] (1) With the center of the unit cell bottom surface as the origin and the Z axis perpendicular to the bottom surface as the coordinate system, define the material density ρ, material specific heat capacity c, and the thermal conductivity Kxx, Kyy, and Kzz of the material in the x, y, and z directions, and obtain:

[0055]

[0056] Where, t is time; {v} represents the velocity vector of heat and mass transfer, {q} represents the heat flux vector, represents the unit heat generation rate;

[0057] (2) From {q}=-[D]{L}T ij ,

[0058] get:

[0059]

[0060] (3) When the heat flux q is loaded onto the surface of the honeycomb unit cell, we have:

[0061] {q} T {n}=-q*, where {n} represents the outward normal vector of the unit and q* represents the loading heat flux;

[0062] (4) Get:

[0063] Integrate the time t to get the temperature T ij .

[0064] A thermal conductivity analysis system for a honeycomb sandwich structure based on a thermal finite element method comprises a finite element model building module, a meshing module, a parameter setting module and a calculation module, wherein the finite element model building module is used to build a finite element unit cell model of a honeycomb sandwich structure, the meshing module is used to mesh the finite element unit cell model of the honeycomb sandwich structure, the parameter setting module is used to set the material type and parameters in the finite element unit cell model of the honeycomb sandwich structure, and to apply periodic boundary conditions and incident heat flux density, and the calculation module is used to calculate the surface temperature distribution T of the honeycomb unit cell according to the parameters of the finite element unit cell model of the honeycomb sandwich structure. ij and the thermal conductivity k in the honeycomb thickness direction z， And output the calculation results.

[0065] The above description is only the best specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0066] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for analyzing thermal conductivity of a honeycomb sandwich structure based on a thermal finite element method, characterized in that: The following steps are involved: (1) Establish a finite element unit cell model of the honeycomb sandwich structure. The finite element unit cell is a hexagonal prism with a bottom side length of L, skins at both ends, and a skin thickness of h1; the middle is a core layer structure, which is a hollow structure with a wall thickness of t and a height of h2. Divide the finite element unit cell model into grids; (2) setting the thermal conductivity, specific heat capacity and density of the skin and core layer in the finite element unit cell model of the honeycomb sandwich structure obtained in step (1), setting the hollow part inside the core layer to air, and setting the thermal conductivity, specific heat capacity and density of the air; (3) setting the radiation heat transfer parameter α between the inner surfaces of the upper and lower skins and the inner wall surface of the core layer in the finite element unit cell model of the honeycomb sandwich structure obtained in step (2) to 1; (4) applying periodic boundary conditions to the side of the finite element unit cell model of the honeycomb sandwich structure obtained in step (3); (5) Apply incident heat flux density q to all unit nodes on the outer surface of the upper skin, and apply a fixed temperature T0 to the outer surface of the lower skin. After the application is completed, the surface temperature distribution T of the honeycomb unit cell is calculated. ij ; (6) According to the temperature distribution T obtained in step (5) ij , calculate the thermal conductivity k in the honeycomb thickness direction z , the method is as follows: According to Fourier's law get: where q z is the heat flux component perpendicular to the bottom surface of the hexagonal prism, k z is the thermal conductivity perpendicular to the bottom surface of the hexagonal prism, d is the total thickness of the honeycomb sandwich structure unit cell, h1 and h2 are the skin thickness and core layer height respectively.

2. The method for analyzing thermal conductivity of a honeycomb sandwich structure based on thermal finite element method according to claim 1, characterized in that: The skin material is set to carbon fiber and the core layer structure is aluminum alloy.

3. The method for analyzing thermal conductivity of a honeycomb sandwich structure based on thermal finite element method according to claim 1, characterized in that: The method for applying the periodic boundary conditions in step (4) is as follows: applying the coupling equation T(x,y)-T(x+h0,y)=0 on two opposite side surfaces, where T(x,z) and T(x+h0,z) are the temperatures of two opposite points on the opposite side surfaces, and h0 is the distance between the two opposite surfaces. By applying the coupling equation, the temperatures of corresponding points on the opposite surfaces are made the same, maintaining the balance between heat input and output, and simulating the periodic structure of the unit cell.

4. The method for analyzing thermal conductivity of a honeycomb sandwich structure based on thermal finite element method according to claim 1, characterized in that: Step (5) The surface temperature distribution T of the honeycomb unit cell ij The calculation method is as follows: (1) The Oxyz coordinate system is established with the center of the unit cell bottom surface as the origin O, the direction perpendicular to the bottom surface as the z-axis, and the line connecting the two opposite vertices of the bottom hexagonal prism as the y-axis. The material density ρ, the material specific heat capacity c, and the thermal conductivity Kxx, Kyy, and Kzz of the material in the x, y, and z directions are defined, and the following is obtained: in t is time; {v} is the velocity vector of heat and mass transfer; {q} is the heat flux vector, is the unit heat generation rate; (2) From {q}=-[D]{L}T ij and Combined with step (1), we get: (3) When the heat flux q is loaded onto the surface of the honeycomb unit cell, we get: {q} T {n}=-q*, where {n} represents the outward normal vector of the unit and q* represents the loading heat flux; Substituting into step (2) we get: (4) Integrate the time t to obtain the temperature T ij .

5. A thermal conductivity analysis system for honeycomb sandwich structures based on thermal finite element method, characterized in that: The method comprises a finite element model building module, a meshing module, a parameter setting module and a calculation module, wherein the finite element model building module is used to build a finite element unit cell model of a honeycomb sandwich structure, the meshing module is used to mesh the finite element unit cell model of the honeycomb sandwich structure, the parameter setting module is used to set the material type and parameters in the finite element unit cell model of the honeycomb sandwich structure, and to apply periodic boundary conditions and incident heat flux density, and the calculation module is used to calculate the surface temperature distribution T of the honeycomb unit cell according to the parameters of the finite element unit cell model of the honeycomb sandwich structure. ij and the thermal conductivity k in the honeycomb thickness direction z， And output the calculation results.

Images