分形多孔介质传热传质过程的格子Boltzmann模拟

Lattice Boltzmann simulation for heat and mass transfer in fractal porous media

针对自然界中实际多孔介质具有的分形特性和随机性,利用中点替代算法和二值化处理构造统计上具有分形特性的随机多孔介质。分析了所构造的多孔介质盒维数与Hurst指数之间的关系。基于随机分形构造的原理,对二维实际多孔介质图像进行了重构。利用两点相关函数,分析了重构图像的结构相关性,并与实际目标多孔介质的结构特征进行比较。在与解析解对比验证的基础上,将基于二元混合理论的格子Boltzmann模型(LBM)用于模拟多孔介质内流体扩散过程。通过计算不同分形特性的二维多孔介质的有效扩散系数,研究了重构多孔介质的分形维数与有效扩散系数的关系。利用热耦合LBM模型计算多孔介质内传热过程,分析了不同的分形特性对多孔介质蓄热过程的影响。

According to stochastic and fractal features of real porous media in nature,the reconstructed stochastic porous media with fractal features were generated by random midpoint displacement algorithm(RMD)and binaryzation processing.The relationship between Hurst exponent of fractal Brown surface and box dimension of reconstructed porous media was presented.Based on the fractal reconstructed theory,the reconstruction process of porous media was carried out based on a real porous media image, and the two-point correlation function was implemented to compare the structure characteristics between real porous media image and reconstructed porous media image.A lattice Boltzmann model(LBM)which was derived from the binary gas mixture theory was introduced to simulate the gas diffusion process in stochastic porous media.The feasibility of this model was validated by comparing with the analytical solution of unsteady diffusion process.The effective diffusivity of stochastic fractal porous media reconstructed by RMD with different Hurst exponent was calculated in this paper.For a given porosity, the positive correlation between the effective diffusivity and Hurst exponent was proposed.Using thermal lattice Boltzmann model,the heat conduction process in stochastic porous media was studied,and the effect of fractal features on effective diffusivity of porous media was presented.