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对多孔材料辐射-传热耦合计算的数学模型,即Rosseland方程,给出了一种统计的二阶双尺度分析方法,并针对典型问题进行了数值模拟。建立了考虑辐射项的统计二阶双尺度计算公式,给出了统计意义下热流密度极值的预测算法,并通过与理论解的比较对算法进行了验证,利用本文中方法研究了孔洞体分比和空间分布状态对陶瓷多孔材料热传导系数、辐射传导系数和热流密度极值的影响。结果表明:孔洞体积分数的增加将导致有效热传导系数下降;热流密度极值随孔洞体积分数的增加而变大,并且在高温时辐射的作用明显增大;数值试验表明,使用统计二阶双尺度方法及其有限元算法预测孔洞随机分布复合材料结构的热性能是有效的。
A mathematical model of radiative heat transfer coupling calculation for porous materials, namely the Rosseland equation, is presented, and a statistical second-order two-scale analysis method is given. The typical problems are numerically simulated. The statistical second-order double-scale calculation formula considering the radiation term is established. The prediction algorithm of heat flux density under the statistical significance is given. The algorithm is verified by comparison with the theoretical solution. Effect of Ratio and Spatial Distribution on Thermal Conductivity, Radiative Conductivity and Heat Flux Density of Ceramic Porous Materials. The results show that the increase of void fraction leads to the decrease of effective heat transfer coefficient. The extreme value of heat flux density increases with the increase of void volume fraction, and the effect of radiation increases obviously at high temperature. Numerical experiments show that using the statistical second- The method and its finite element algorithm are effective in predicting the thermal properties of randomly distributed holes in composite structures.