膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动，基于二阶矩模型在演化方程中引入表征介质阻力的作用力项，求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量，通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析，通过比较发现结果与孔隙尺度的解析解十分吻合，并且收敛较快，表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响，研究结果表明，膨胀性流体的多孔介质流动不符合达西规律，压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时，流道中的速度呈现均匀分布，并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加，Da越大幂律指数对压力降的影响越明显．

Simulation Analysis of Expansive Non-Newtonian Fluid Flow Through Porous Media

The flow of expansive non-Newtonian fluid through porous media is analyzed by the Lattice Boltzmann Method on representative elementary volume scale. Based on the second order moment model, the force term describing the medium resistance is introduced into the evolution equation to solve the generalized Navier Stokes equation which describes the percolation flow model. The deformation rate tensor is calculated by the local method. The non-Newtonian viscosity and relaxation time are calculated by iteration. The Poiseuille flow in porous media is analyzed, and the results are compared with the analytical solution of pore scale. The results are in good agreement with the analytical solution of pore scale, and the convergence is fast, which shows that the proposed method is reasonable and effective. The effects of permeability and power-law index on velocity and pressure drop are analyzed. The results show that the porous media flow of expansive fluid does not comply with Darcy's law, and the increase of pressure drop is less than the decrease of permeability. When the dimensionless permeability Da is less than 10-5, the velocity becomes uniformly distributed, and the profile of velocity distribution becomes more uniform as the power-law index decreases. The pressure drop increases with the increase of power-law index. With the increase of Da, the influence of power-law index on pressure drop is more obvious.