Thermal conductivity analysis of fiber-reinforced resin-based honeycomb sandwich materials
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摘要: 玻璃纤维/环氧树脂蜂窝夹层复合材料由于重量轻、阻燃性能优异等优点，已成为民用飞机内饰壁板的主要材料。该类材料在高温下具有火灾危险性，因此研究其导热性对于飞机防火具有重要意义。以玻璃纤维/环氧树脂预浸料和芳纶纸蜂窝芯为原料制备九种不同厚度的蜂窝夹层材料开展导热性能研究，基于Fourier定律和Swan-Pittman半经验公式建立适用于树脂基复合材料蜂窝夹层结构板的传热理论模型，基于有限元软件模拟所得相关数据，计算蜂窝夹层材料导热系数的理论值。采用导热系数测试仪开展蜂窝夹层材料导热系数实验，并比较试验值和理论值。研究结果表明：室温情况下不同厚度蜂窝夹层材料导热系数的理论值与试验平均值吻合度较高，该理论模型适用于树脂基复合材料蜂窝夹层结构板；相比于面板厚度，蜂窝芯才是影响蜂窝夹层材料导热系数的主要因素。蜂窝夹层材料的孔隙率与导热系数成反比关系，比表面积与导热系数呈正比关系；随着蜂窝芯高度增加，热辐射取代热传导逐渐成为蜂窝芯内部热量传递的主要方式。Abstract: Fiberglass/epoxy honeycomb sandwich composites have become the main materials for interior wall panels of civil aircraft due to their light weight and excellent flame retardant properties. These materials are fire hazardous at high temperatures, so the study of their thermal conductivity is of great significance for aircraft fire protection. Nine kinds of honeycomb sandwich materials with different thicknesses were prepared from glass fiber/epoxy resin prepreg and aramid paper honeycomb core to carry out the thermal conductivity study. Based on Fourier's law and the semi-empirical formula of Swan-Pittman, a theoretical model of heat transfer of fiber-reinforced resin matrix composites was established, and the theoretical value of thermal conductivity of honeycomb sandwich materials was calculated based on the data obtained from the simulation of Finite Element Software. Based on the data obtained from the finite element software simulation, the theoretical value of thermal conductivity of the honeycomb sandwich is calculated. The thermal conductivity tester is used to carry out experiments on the thermal conductivity of honeycomb sandwich materials and compare the experimental and theoretical values. The results show that the theoretical values of the thermal conductivity of honeycomb sandwich materials with different thicknesses at room temperature are in good agreement with the average values of the experiments, and the theoretical model is applicable to the fiber-reinforced resin matrix composites with honeycomb sandwich structure; compared with the thickness of the panels, the honeycomb core is the main factor affecting the thermal conductivity of honeycomb sandwich materials. The porosity of the honeycomb sandwich material is inversely related to the thermal conductivity, and the specific surface area is positively related to the thermal conductivity; with the increase of the height of the honeycomb core, the thermal radiation replaces the thermal conduction to become the main way of heat transfer inside the honeycomb core gradually.
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图 1 蜂窝夹层材料传热原理示意图
Figure 1. Schematic diagram of heat transfer principle of honeycomb sandwich material
图 3 三层平壁稳态导热结构
Figure 3. Three layer flat wall steady-state thermal conductivity structure
图 5 各厚度面板导热系数误差范围
Figure 5. Error range of thermal conductivity of each thickness panel
图 8 蜂窝夹层材料表面温度的瞬时红外成像图
Figure 8. Transient infrared image of surface temperature of honeycomb sandwich materia
图 9 夹层结构导热系数与面板厚度的关系
Figure 9. Relationship between thermal conductivity of sandwich structure and panel thickness
图 11 夹层结构导热系数与孔隙率的关系
Figure 11. Relationship between thermal conductivity and porosity of sandwich structure
图 12 夹层结构导热系数与比表面积的关系
Figure 12. Relationship between thermal conductivity and specific surface area of sandwich structure
图 13 不同高度蜂窝芯对蜂窝夹层材料导热系数的贡献
Figure 13. Contribution of honeycomb cores of different heights to thermal conductivity of honeycomb sandwich materials
表 1 实验样品参数
Table 1. Experimental Sample Parameters
Samplenumber $ {h}_{1} /\mathrm{m}\mathrm{m} $ $ {h}_{c} /\mathrm{m}\mathrm{m} $ $ {h}_{3}/\mathrm{m}\mathrm{m} $ $ h/\mathrm{m}\mathrm{m} $ $ l /\mathrm{m}\mathrm{m} $ 1-1 0.70 3.00 0.30 4.00 2.29 1-2 0.90 3.00 0.30 4.20 2.29 1-3 1.10 3.00 0.30 4.40 2.29 2-1 0.70 5.00 0.30 6.00 2.75 2-2 0.90 5.00 0.30 6.20 2.75 2-3 1.10 5.00 0.30 6.40 2.75 3-1 0.70 10.00 0.30 11.00 4.50 3-2 0.90 10.00 0.30 11.20 4.50 3-3 1.10 10.00 0.30 11.40 4.50 Note:$ {h}_{1} $ is the thickness of the upper panel;$ {h}_{\mathrm{c}} $ is the height of the honeycomb core;$ {h}_{3} $ is the thickness of the lower panel;$ h $ is the thickness of the sandwich structure;$ l $ is the side length of the honeycomb. 
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表 2 不同面板导热系数测定值
Table 2. Measurement values of thermal conductivity of different panels
Panel thickness/mm 0.3 0.7 0.9 1.1 Thermal conductivity
$ \mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right) $0.589 0.46 0.364 0.338
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表 3 试样属性参数
Table 3. Sample attribute parameters
Name of material Density
kg/m3Thermal conductivity
$ \text{W/}\left(\mathrm{m}\cdot \mathrm{K}\right) $0.3 mm panel $ 2.58\times {10}^{3} $ 0.589 0.7 mm panel $ 2.4\times {10}^{3} $ 0.46 0.9 mm panel $ 2.04\times {10}^{3} $ 0.264 1.1 mm panel $ 1.87\times {10}^{3} $ 0.338 3 mm honeycomb core 40 0.993 5 mm honeycomb core 45 1.162 10 mm honeycomb core 80 1.289
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表 4 各厚度蜂窝芯体平均温度
Table 4. Average temperature of honeycomb cores with different thickness
Samplenumber $ {h}_{c}/\mathrm{m}\mathrm{m} $ $ h/\mathrm{m}\mathrm{m} $ Temperature/℃ 1-1 3.00 4.00 49.5 1-2 3.00 4.20 48.6 1-3 3.00 4.40 48.3 2-1 5.00 6.00 46.8 2-1 5.00 6.20 50.8 2-3 5.00 6.40 48.8 3-1 10.00 11.00 46.8 3-2 10.00 11.20 45.1 3-3 10.00 11.40 42.5 Note:$ {h}_{\mathrm{c}} $ is the height of the honeycomb core;$ h $ is the thickness of the sandwich structure;
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表 5 蜂窝夹层材料的导热系数
Table 5. Thermal conductivity of honeycomb sandwich materials
Sample number 1-1 1-2 1-3 2-1 2-2 2-3 3-1 3-2 3-3 Geometric dimensions/mm Bee grid edge length $ l/\mathrm{m}\mathrm{m} $ 2.290 2.290 2.290 2.750 2.750 2.750 4.500 4.500 4.500 Honeycomb core height $ {h}_{2}/\mathrm{m}\mathrm{m} $ 3.000 3.000 3.000 5.000 5.000 5.000 10.000 10.000 10.000 Panel thickness $ h/\mathrm{m}\mathrm{m} $ 1.000 1.200 1.400 1.000 1.200 1.400 1.000 1.200 1.400 Thermal conductivity of sandwich
structure $ k/(\mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right)) $Experimental average 0.218 0.222 0.219 0.214 0.213 0.212 0.204 0.199 0.202 Theoretical value 0.180 0.166 0.167 0.164 0.182 0.165 0.171 0.161 0.150 Error/% 17.4 25.2 23.8 23.3 14.6 22.1 16.1 19.0 25.7
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表 6 蜂窝夹层材料的隔热性能
Table 6. Thermal insulation properties of honeycomb sandwich materials
Height of
honeycomb
core/mmPorosity/
%specific surface
area/m2/m3Thermal
conductivity/
$ \mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right) $Flame
temperature/℃Burn time/s 60 120 180 Average
temperature/℃Average
temperature/℃Average
temperature/℃3 82 2259.035 0.222 950±20 150.79 214.47 250.62 5 85 1085.938 0.213 135.30 190.48 221.69 10 91 508.823 0.199 125.69 150.95 194.48
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表 7 不同高度蜂窝芯体孔隙率与比表面积
Table 7. Porosity and specific surface area of honeycomb cores with different heights
$ {h}_{c}/ $mm $ l/ $mm $ {l}_{m}/ $mm $ \Delta / $mm $ P/ $% $ {S}_{v}/ $m2/m3 3.000 2.290 2.078 0.183 82 2259.035 5.000 2.750 2.538 0.183 85 1085.938 10.000 4.500 4.288 0.183 91 508.823 Note: $ {h}_{\mathrm{c}} $ is the height of the honeycomb core;$ l $ is the side length of the honeycomb;$ {l}_{m} $ is the medial length of the edge of the honeycomb;$ \Delta $ is the thickness of the cell wall;$ P $ is the porosity of the honeycomb core; $ {S}_{v} $ is the specific surface area of the honeycomb core.
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