Electromagnetic-thermal performance analysis method of honeycomb wave-absorbing material
By using the electromagnetic-thermal equivalent analysis method of honeycomb absorbing materials, the porous multi-scale honeycomb structure is equivalent to a uniform block, which solves the problem of low simulation calculation efficiency, realizes high-precision and rapid evaluation and design optimization, and is suitable for high-power application scenarios.
Patent Information
- Application Number
- CN202511916718.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-02-13
AI Technical Summary
Existing technologies have low electromagnetic-thermal simulation efficiency for cellular absorbing materials in high-power electromagnetic environments. In particular, the porous and multi-scale characteristics result in a large number of meshes, long calculation time, and even make it impossible to perform simulation calculations and parameter optimization.
An electromagnetic-thermal equivalent analysis method for honeycomb absorbing materials is adopted. The equivalent electromagnetic parameters and thermal properties are calculated through effective medium theory. The complex porous multi-scale honeycomb structure is equivalent to a uniform block, and an electromagnetic-thermal analysis model is established to simplify mesh generation and improve simulation calculation efficiency.
It enables rapid prediction and evaluation of the electromagnetic and thermal properties of cellular absorbing materials, with high simulation accuracy and significantly shortened simulation time. It is applicable to single-layer and multi-layer gradient cellular absorbing materials and supports integrated electromagnetic and thermal co-design in high-power application scenarios.
Smart Images
Figure CN121525409A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power-resistant microwave absorbing materials, specifically a method for analyzing the electromagnetic and thermal properties of honeycomb microwave absorbing materials. Background Technology
[0002] Stealth materials are key to improving the battlefield survivability and strategic penetration capabilities of equipment. With the continuous escalation of modern military confrontation, the demand for high-power radar antennas has increased significantly, primarily due to their significant advantages in extending detection range and improving detection accuracy. This trend places higher demands on the power tolerance of the accompanying absorbing materials and presents interdisciplinary challenges in the design and analysis of their thermal, structural, and electromagnetic properties. To ensure the safety and stability of absorbing materials in high-power electromagnetic environments, it is urgent to conduct comprehensive multiphysics simulation research integrating electromagnetics, thermodynamics, and materials science to achieve rapid prediction and optimized design of absorbing material performance under high-power scenarios.
[0003] Currently, high-power antenna absorbing materials are mainly honeycomb absorbing materials, prepared by impregnating a honeycomb substrate with absorbing slurry. Electromagnetic-thermal research primarily employs both experimental and simulation methods; however, experimental methods are costly, thus simulation research is dominant. Existing simulation studies typically construct actual geometric models and use coupled electromagnetic and thermal conduction modules in simulation software to predict temperature field distribution. However, for honeycomb absorbing materials with high porosity and multi-scale characteristics, the internal dimensional differences can reach two orders of magnitude or more, resulting in massive mesh counts, extremely high computational loads, long calculation times, and even computation failures during full-scale honeycomb model simulations. For large-size absorbing honeycomb structures, simulation calculations and parameter optimization are even more impossible, representing a bottleneck problem that urgently needs to be solved for engineering applications. Summary of the Invention
[0004] To address the challenge of evaluating the electromagnetic and thermal performance of cellular absorbing materials, this invention provides a method for analyzing the electromagnetic and thermal performance of cellular absorbing materials. It constructs an equivalent electromagnetic and thermal analysis model for cellular absorbing materials, significantly improving simulation efficiency while ensuring accuracy. This enables rapid prediction and evaluation of the electromagnetic and thermal performance of cellular absorbing materials, providing a new approach for the integrated electromagnetic and thermal design of cellular absorbing materials.
[0005] A method for analyzing the electromagnetic and thermal properties of a honeycomb absorbing material, comprising the following steps:
[0006] Step 1: Define the honeycomb absorbing material and structural parameters, including air domain A, absorbing paste B, aramid paper C, and the number of honeycomb gradient layers N. Take one honeycomb cycle as the research object, and each layer is a unit honeycomb structure.
[0007] Step 2: Calculate the equivalent electromagnetic parameters and equivalent thermal properties of the cellular network.
[0008] a. Based on the effective medium theory, calculate the equivalent electromagnetic parameter ε2 of the cellular structure.
[0009] For a cellular gradient structure with N layers, the equivalent electromagnetic parameters of each cellular structure are calculated layer by layer and independently.
[0010] Furthermore, the calculation of the equivalent electromagnetic parameter ε2 of the honeycomb structure is divided into two steps:
[0011] 1) Calculate the equivalent electromagnetic parameters of air domain A and absorbing slurry B:
[0012]
[0013] in, The relative permittivity of air domain A and absorbing paste B after equivalent conversion; Let be the relative permittivity of the microwave absorbing paste B; It is the vacuum permittivity; This represents the proportion of the area of absorbing paste B in the honeycomb unit relative to the total area of absorbing paste B and air domain A.
[0014] 2) Perform a second equivalent transformation on the region obtained in step 1) and aramid paper C to obtain the equivalent dielectric of the entire honeycomb structure. :
[0015]
[0016] in, Let C be the relative permittivity of the aramid paper. This represents the proportion of air region A to the total area of the cell cross-section.
[0017] b. Calculate the equivalent thermal properties of the honeycomb, including the equivalent density. Equivalent specific heat capacity Equivalent thermal conductivity .
[0018] Furthermore, the calculation of the equivalent thermal properties of the honeycomb structure is specifically as follows:
[0019] 1) Calculate the equivalent density and equivalent specific heat capacity of the honeycomb. For a honeycomb structure with N layers, calculate the equivalent density and equivalent specific heat capacity of each layer independently.
[0020]
[0021] in, This is the equivalent density of the honeycomb. Let the density of air in region A be denoted as . The density of microwave absorbing slurry B, The density of aramid paper C; Let A be the volume of the air domain A within the cellular structure. Let B be the volume of the microwave absorbing slurry within the unit honeycomb structure. The volume of aramid paper C within the unit honeycomb structure; This refers to the total volume of the cell unit; This refers to the equivalent specific heat capacity of the honeycomb structure. Let A be the specific heat capacity of air domain A. The specific heat capacity of microwave absorbing slurry B is... The specific heat capacity of aramid paper C is given.
[0022] 2) Based on the principle of gradient honeycomb thermal resistance series, solve for the equivalent thermal conductivity of the honeycomb, which includes two parts: equivalent conductive thermal conductivity and equivalent radiative thermal conductivity.
[0023] 2-1) The heat conduction process includes two parts: heat conduction along the solid walls of the honeycomb (absorbing paste B and aramid paper C) and heat conduction through the air domain A. For a honeycomb structure with N layers, the equivalent thermal conductivity of each layer is calculated independently. Equivalent thermal conductivity The specific expression is:
[0024]
[0025] in, The equivalent thermal conductivity of the honeycomb structure for heat transfer via thermal conduction; , , The intrinsic thermal conductivity of air domain A, microwave absorbing paste B, and aramid paper C are respectively: , , These represent the areas corresponding to air domain A, microwave absorbing paste B, and aramid paper C within the honeycomb periodic unit, respectively. This represents the total area of the cellular cycle.
[0026] 2-2) Calculate the equivalent radiative thermal conductivity of the honeycomb.
[0027] To reduce computational load, the cellular unit is equivalent to a cylindrical unit of the same volume and height, and the surfaces are divided in a gradient layering manner. Each surface is numbered as follows: upper cylindrical side surface 4, lower cylindrical side surface 5, top surface 6, and bottom surface 7.
[0028] When the number of cell gradient layers N=1, the equivalent radiative thermal conductivity of the cell is... Calculations can be performed using the SP empirical formula:
[0029]
[0030] in, This refers to the height of the honeycomb. The side length of the honeycomb; Material emissivity; is the Stefan-Boltzmann constant.
[0031] When the number of gradient layers N > 1, the entire gradient cell is treated as an N-layer thermal resistance series model for solution. For an absorbing cell with N = 2, the ratio of the equivalent radiative thermal conductivity of the upper and lower cells can be expressed as:
[0032]
[0033] in, and The equivalent radiative thermal conductivity of the upper and lower layers of the honeycomb, respectively; , The thicknesses of the upper and lower layers of the honeycomb are respectively, in order. , The temperature differences are, in order, between the upper and lower layers of the honeycomb.
[0034] According to the formula for radiative heat transfer between two surfaces, the ratio of the equivalent radiative thermal conductivity of the upper and lower honeycomb layers can be expressed as:
[0035]
[0036] in, and These represent the radiative heat transfer between the corresponding numbered surfaces of the honeycomb; This represents the total height of the cell; Indicates the height of the upper absorbing cell. With total height The ratio of .
[0037] Equivalent radiative thermal conductivity of upper and lower absorbing honeycomb layers , They can be represented as:
[0038]
[0039] because Very small, its higher-order terms are ignored:
[0040]
[0041] in, B 64 and B 75 These are the Gebhart (radiative heat transfer) factors between the corresponding numbered surfaces.
[0042] For absorbing cells with N > 2, they are considered as a combination of multiple absorbing cells with N = 2. The calculation process for the equivalent radiative thermal conductivity of the top and bottom absorbing cells is the same as that for the N = 2 absorbing cells described above. The equivalent radiative thermal conductivity of any intermediate layer is calculated as follows. It can be represented as:
[0043] .
[0044] in, Let be the equivalent radiative thermal conductivity of the i-th layer of the gradient absorbing cell; The equivalent radiative thermal conductivity corresponding to the total height of the first i-th layer of absorbing cell; The equivalent radiative thermal conductivity corresponding to the total height of the first i-1 layer of absorbing cell;
[0045] Therefore, the total equivalent thermal conductivity of each honeycomb layer is... This can be expressed as the equivalent thermal conductivity per layer. Equivalent radiative thermal conductivity per layer sum:
[0046]
[0047] Equivalent thermal conductivity is temperature-dependent and can be characterized as equivalent thermal conductivity. , where T is the temperature, and its value ranges from greater than or equal to room temperature.
[0048] Step 3: Establish a homogeneous equivalent model for the absorbing honeycomb structure. For a honeycomb structure with N layers, establish an equivalent model with N layers. Apply the honeycomb equivalent thermal properties calculated in Step 2. , , With equivalent electromagnetic parameters The electromagnetic and thermal properties were analyzed by substituting each layer into the equivalent honeycomb model.
[0049] Furthermore, the electromagnetic-thermal performance analysis method of the above-mentioned cellular absorbing materials is applied to the rapid evaluation of the electromagnetic-thermal performance of cellular absorbing materials and their integrated collaborative design.
[0050] In summary, the core idea of this invention is to evaluate the electromagnetic-thermal multiphysics performance of absorbing honeycomb materials. It equates the complex porous, multi-scale absorbing honeycomb material to a uniform bulk absorbing material, deriving equivalent electromagnetic and thermal properties, and then establishing an equivalent electromagnetic-thermal analysis model. The electromagnetic-thermal performance analysis method for honeycomb absorbing materials provided by this invention balances computational accuracy and efficiency, eliminates the need for detailed modeling of the honeycomb structure, and features simple mesh generation and a small number of meshes for the equivalent bulk material. This enables efficient and rapid evaluation of the electromagnetic-thermal performance of the honeycomb, providing support for the integrated electromagnetic-thermal co-design of honeycomb absorbing materials in high-power applications. Attached Figure Description
[0051] Figure 1 Flowchart of the electromagnetic-thermal performance analysis method for honeycomb absorbing materials;
[0052] Figure 2 A schematic diagram of a honeycomb absorbing material and its equivalent model;
[0053] Figure 3 A comparison of electromagnetic and thermal simulation results between the actual model and the equivalent model of a single-layer uniform honeycomb absorbing material in the example;
[0054] Figure 4 An equivalent thermal conductivity analysis model for heat transfer via radiation of two layers of honeycomb absorbing material is provided as an example.
[0055] Figure 5 This example compares the electromagnetic and thermal simulation results of the actual model and the equivalent model of the two-layer honeycomb absorbing material.
[0056] Figure 6 An equivalent thermal conductivity analysis model for radiative heat transfer in multilayer honeycomb absorbing materials, as an example;
[0057] Figure 7 This example compares the electromagnetic and thermal simulation results of the actual model and the equivalent model of the multilayer honeycomb absorbing material.
[0058] Figure labels: 1-actual cell model, 2-equivalent model, 3-skin. Detailed Implementation
[0059] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.
[0060] An electromagnetic-thermal performance analysis method for honeycomb absorbing materials, such as Figure 1 As shown, it includes the following steps:
[0061] Step 1: Define the honeycomb absorbing material and structural parameters, including air domain A, absorbing paste B, aramid paper C, and the number of honeycomb gradient layers N. Take one honeycomb cycle as the research object, and each layer is a unit honeycomb structure.
[0062] Step 2: Calculate the equivalent electromagnetic parameters of the cellular network. and equivalent thermophysical parameters , , .
[0063] a. Based on the effective medium theory, calculate the equivalent electromagnetic parameter ε2 of the cellular structure; for a cellular gradient structure with N layers, calculate the equivalent electromagnetic parameter of each layer of the cellular structure independently.
[0064] b. Calculate the equivalent thermal properties of the honeycomb, including the equivalent density. Equivalent specific heat capacity Equivalent thermal conductivity .
[0065] Step 3: Establish a homogeneous equivalent model for the absorbing honeycomb structure. For a honeycomb structure with N layers, establish an equivalent model with N layers. Calculate the equivalent thermal properties of the honeycomb structure in Step 2. , , With equivalent electromagnetic parameters The electromagnetic and thermal properties were analyzed by substituting each layer into the equivalent honeycomb model.
[0066] Example 1
[0067] like Figure 2 The diagram shows the actual model 1 and equivalent model 2 of the single-layer uniform honeycomb absorbing material in this embodiment 1. The actual honeycomb absorbing material is prepared by impregnating a honeycomb substrate (made by drawing aramid paper) with an absorbing slurry.
[0068] In this embodiment, the total thickness of the honeycomb absorbing material is 25 mm, the thickness of a single aramid paper sheet is 50 μm, the side length of the hexagonal honeycomb cell is 1 mm, and the thickness of the absorbing paste coated on the honeycomb wall is 15 μm. Natural convection and thermal radiation heat dissipation boundaries are set on both the upper and lower surfaces of the absorbing honeycomb. Electromagnetic-thermal coupling simulation was performed at a frequency of 10 GHz, and the electromagnetic-thermal results of the actual model and the equivalent model were compared.
[0069] Figure 3 This figure compares the transient temperature rise results of the actual model (solid line) and the equivalent model (dashed line) in the embodiment. As shown in the figure, with an incident electromagnetic wave power density of 2kW / m², the temperature rise is... 2 3kW / m 2 5kW / m 2 The actual model steady-state temperatures were 156.81℃, 204.67℃, and 278.53℃, respectively, while the corresponding equivalent model steady-state temperatures were 150.93℃, 196.12℃, and 266.74℃. The errors of the two models were 3.74%, 4.18%, and 4.23%, respectively, all within 5%. The transient temperature rise results and trends of the two models showed high agreement, verifying the accuracy of the equivalent model. However, there was a significant difference in simulation time between the two models. The actual model took 7 hours, 44 minutes, and 48 seconds to simulate under three different incident power densities, while the equivalent model only required 48 seconds, which is 1 / 580th the time of the actual model, achieving efficient calculation of the electromagnetic-thermal performance of the cellular absorbing material.
[0070] Example 2
[0071] Figure 4 This is an analysis model for the equivalent thermal conductivity of two-layer honeycomb absorbing materials through radiative heat transfer. To simplify the calculation, the hexagonal honeycomb lattice is approximated as a cylinder of equal volume and height, and each radiating surface is numbered. The equivalent radiative thermal conductivity of the upper radiating surface 4 and the lower radiating surface 5 of the honeycomb needs to be calculated separately.
[0072] In this embodiment 2, the thickness of the upper honeycomb absorbing material is 18mm, and the thickness of the lower honeycomb absorbing material is 7mm.
[0073] Figure 5 This section compares the electromagnetic and thermal simulation results of the actual model and the equivalent model of the two-layer honeycomb absorbing material in Example 2. The electromagnetic wave incident power density is 2kW / m². 2 3kW / m 2 5kW / m 2 The steady-state temperatures of the actual model were 137.47℃, 181.41℃, and 248.52℃, respectively, while those of the equivalent model were 133.47℃, 173.96℃, and 238.60℃, respectively. The errors of the two models were 2.91%, 4.11%, and 3.99%, respectively, all within 5%. Comparing the simulation times, the actual model took 40 hours, 9 minutes, and 49 seconds to complete the simulation, while the equivalent model only required 68 seconds, which is 1 / 2126th the time of the actual model.
[0074] Example 3
[0075] Figure 6 This paper presents an analytical model for the equivalent thermal conductivity of multilayer honeycomb absorbing materials through radiative heat transfer. Taking a three-layer honeycomb as an example, the three-layer honeycomb is first considered as a double-layer gradient combination of the upper material 1 and the two lower materials (material 2 and material 3), and the equivalent radiative thermal conductivity of the top layer material 1 is solved. Equivalent radiative thermal conductivity of the total height of the two lower layers (material 2 and material 3) Then, considering the three-layer honeycomb as a double-layer gradient combination of the top two materials (material 1 and material 2) and the bottom material 3, the equivalent radiative thermal conductivity of the bottom material 3 can be solved. Finally, the equivalent radiative thermal conductivity of the intermediate layer material 2 was calculated. , can be represented as and The difference.
[0076] In this embodiment 3, the thickness of the upper honeycomb absorbing material is 3mm, the thickness of the middle honeycomb absorbing material is 7mm, and the thickness of the lower honeycomb absorbing material is 15mm.
[0077] Figure 7 This section compares the electromagnetic and thermal simulation results of the actual model and the equivalent model of the multilayer honeycomb absorbing material in Example 3. The incident electromagnetic wave power density is 2kW / m². 2 3kW / m 2 5kW / m 2The steady-state temperatures of the actual model were 156.81℃, 204.67℃, and 278.53℃, respectively, while those of the equivalent model were 158.8℃, 206.97℃, and 283.75℃, respectively. The errors of the two models were 1.26%, 1.12%, and 1.87%, respectively. A comparison of simulation times revealed that the actual model took 7 hours, 44 minutes, and 48 seconds to simulate, while the equivalent model only required 62 seconds. This demonstrates that the multilayer equivalent model can achieve rapid evaluation of cellular electromagnetic-thermal processes while maintaining simulation accuracy.
[0078] As can be seen from the above embodiments, this invention addresses the problem of low efficiency in electromagnetic-thermal simulation of current honeycomb absorbing materials by proposing a novel electromagnetic-thermal equivalent model analysis method. This method not only ensures simulation accuracy but also offers significant advantages in simulation efficiency. Furthermore, this method is applicable not only to single-layer uniform honeycomb absorbing materials but also to multi-layer gradient honeycomb absorbing materials. This invention provides an efficient and reliable solution for evaluating and optimizing the electromagnetic and thermal performance of porous, multi-scale absorbing materials.
Claims
1. A method for analyzing the electromagnetic and thermal properties of a honeycomb absorbing material, characterized in that, Includes the following steps: Step 1: Define the honeycomb absorbing material and structural parameters, including air domain A, absorbing paste B, aramid paper C, and the number of honeycomb gradient layers N, with each layer being a unit honeycomb structure; Step 2: Calculate the equivalent electromagnetic parameters of the cellular network. and equivalent thermophysical parameters; a. Calculate the equivalent electromagnetic parameters of the cellular structure based on the effective medium theory. For a cellular gradient structure with N layers, the equivalent electromagnetic parameters of each cellular structure are calculated layer by layer and independently. b. Calculate the equivalent thermal properties of the honeycomb, including the equivalent density. Equivalent specific heat capacity Equivalent thermal conductivity ; Step 3: Establish a homogeneous equivalent model for the absorbing honeycomb structure. For a honeycomb structure with N layers, establish an equivalent model with N layers. Calculate the equivalent thermal properties of the honeycomb structure in Step 2. , , With equivalent electromagnetic parameters The electromagnetic and thermal properties were analyzed by substituting each layer into the equivalent honeycomb model.
2. The method for analyzing the electromagnetic and thermal properties of the honeycomb absorbing material as described in claim 1, characterized in that, The equivalent electromagnetic parameters of the cellular The calculation consists of two steps: 1) Calculate the equivalent electromagnetic parameters of air domain A and absorbing slurry B: ； in, The relative permittivity of air domain A and absorbing paste B after equivalent conversion; Let be the relative permittivity of the microwave absorbing paste B; It is the vacuum permittivity; This represents the proportion of the area of absorbing paste B in the honeycomb unit relative to the total area of absorbing paste B and air domain A. 2) Perform a second equivalent transformation between the region obtained in step 1) and the aramid paper C to obtain the equivalent dielectric ε2 of the entire honeycomb structure: ； in, Let C be the relative permittivity of the aramid paper. This represents the proportion of air region A to the total area of the cell cross-section.
3. The method for analyzing the electromagnetic and thermal properties of the honeycomb absorbing material as described in claim 1, characterized in that, The calculation of the equivalent thermal properties of the honeycomb is specifically as follows: 1) Calculate the equivalent density and equivalent specific heat capacity of the honeycomb; for a honeycomb structure with N layers, calculate the equivalent density and equivalent specific heat capacity of each layer of the honeycomb structure independently. ； in, This is the equivalent density of the honeycomb. Let the density of air in region A be denoted as . The density of microwave absorbing slurry B, The density of aramid paper C; Let A be the volume of the air domain A within the cellular structure. Let B be the volume of the microwave absorbing slurry within the unit honeycomb structure. The volume of aramid paper C within the unit honeycomb structure; This refers to the total volume of the cell unit; This refers to the equivalent specific heat capacity of the honeycomb structure. Let A be the specific heat capacity of air domain A. The specific heat capacity of microwave absorbing slurry B is... The specific heat capacity of aramid paper C; 2) Based on the principle of gradient honeycomb thermal resistance series connection, solve for the equivalent thermal conductivity of the honeycomb, including the equivalent conductive thermal conductivity and the equivalent radiative thermal conductivity. 2-1) The heat conduction process includes two parts: heat conduction along the solid wall of the honeycomb and heat conduction through air domain A. For a honeycomb structure with N layers, the equivalent thermal conductivity of each layer of the honeycomb structure is calculated independently. The specific expression is: ； in, The equivalent thermal conductivity of the honeycomb structure for heat transfer via thermal conduction; The intrinsic thermal conductivity of air domain A. The intrinsic thermal conductivity of microwave absorbing paste B is given. The intrinsic thermal conductivity of aramid paper C; This represents the area corresponding to air domain A within a cellular periodic cell. This represents the area corresponding to the microwave absorbing slurry B within the unit honeycomb structure. This represents the area corresponding to aramid paper C within the honeycomb periodic unit. This represents the total area of the unit cell honeycomb structure; 2-2) Calculate the equivalent radiative thermal conductivity of the honeycomb; The cellular unit is equivalent to a cylindrical unit of the same volume and height, and the surfaces are divided in a gradient layering manner. Each surface is numbered as follows: upper cylindrical side surface 4, lower cylindrical side surface 5, top surface 6, and bottom surface 7. When the number of cell gradient layers N=1, the equivalent radiative thermal conductivity of the cell is... Calculations can be performed using the SP empirical formula: ； in, This refers to the height of the honeycomb. The side length of the honeycomb; Material emissivity; It is the Stefan-Boltzmann constant; When the number of gradient layers N > 1, the entire gradient cell is treated as an N-layer thermal resistance series model for solution; for an absorbing cell with N = 2, the ratio of the equivalent radiative thermal conductivity of the upper and lower cell layers can be expressed as: ； in, and The equivalent radiative thermal conductivity of the upper and lower layers of the honeycomb, respectively; , The thicknesses of the upper and lower layers of the honeycomb are respectively, in order. , The temperature differences between the upper and lower layers of the honeycomb, respectively; According to the formula for radiative heat transfer between two surfaces, the ratio of the equivalent radiative thermal conductivity of the upper and lower honeycomb layers can be expressed as: ； in, and These represent the radiative heat transfer between the corresponding numbered surfaces of the honeycomb; This represents the total height of the cell; Indicates the height of the upper absorbing cell. With total height The ratio; Equivalent radiative thermal conductivity of upper and lower absorbing honeycomb layers , They can be represented as: ； because Very small, its higher-order terms are ignored: ； in, B 64 and B 75 These are the Gebhart radiative heat transfer factors between the corresponding numbered surfaces; For absorbing cells with N > 2, they are considered as a combination of multiple absorbing cells with N = 2. The calculation process for the equivalent radiative thermal conductivity of the top and bottom absorbing cells is the same as that for the N = 2 absorbing cells mentioned above. The equivalent radiative thermal conductivity of any intermediate layer is calculated as follows. It can be represented as: ； in, Let be the equivalent radiative thermal conductivity of the i-th layer of the gradient absorbing cell; The equivalent radiative thermal conductivity corresponding to the total height of the first i-th layer of absorbing cell; The equivalent radiative thermal conductivity corresponding to the total height of the first i-1 layer of absorbing cell; Therefore, the total equivalent thermal conductivity of each honeycomb layer is... This can be expressed as the equivalent thermal conductivity per layer. Equivalent radiative thermal conductivity per layer sum: ； Equivalent thermal conductivity is temperature-dependent and can be characterized as equivalent thermal conductivity. , where T is the temperature, and its value ranges from greater than or equal to room temperature.
4. The method for analyzing the electromagnetic and thermal properties of the honeycomb absorbing material as described in claim 1, characterized in that: Rapid evaluation of electromagnetic and thermal properties and integrated collaborative design for cellular absorbing materials.