分形理论在碳化材料三维烧蚀热防护计算中的应用

烧蚀过程中的传热传质对烧蚀防护工程具有重要意义，准确的温度评估可以为高超声速飞行器的热防护结构和烧蚀材料的设计提供有效的支持.由于材料烧蚀形成的碳化物是一种典型的多孔介质，其结构具有自相似性，可以用分形理论来描述.在烧蚀计算中引入了分形渗透率张量模型进行计算.针对烧蚀过程中热解气体在碳化层中的扩散方程、温度、材料等参数对烧蚀过程的影响，对不同迂曲度分形维数和不同孔径分形维数材料三维球头进行了数值模拟.计算结果表明:材料的孔径分形维数越小，迂曲度分形维数越大，热防护效果越好. 

Application of Fractal Theory on Three-Dimensional Ablative Thermal Response of Charring Composite

The heat and mass transfer in the ablation process are of great importance for the ablation protection engineering. In this work, the effect of permeability on heat and mass transfer and ablation thermal protection of gases produced during ablation were studied. Since the carbide formed by ablation of material is a typical porous medium, its structure has self-similarity and can be described by fractal theory. Taking account into the relationship of global coordinates and local coordinates, fractal permeability tensor was introduced into the ablation equation in this paper. In order to verify the correctness of this method, the simulation results were compared with the classical experiments. To simulate the ablation process, the temperature of three-dimensional spherical head with different pore area fractal dimensions and tortuosity fractal dimensions were simulated numerically. It is found that the higher the tortuosity fractal dimensions, and the lower the pore area fractal dimensions, the better the thermal protection.