Abstract: An improved numerical calculation method for the non-Newtonian fluid flowing through micro tubes is proposed.This method is rapid and stable in calculation and can provide a precise and effective way for a large quantity of numerical experiments.The partial derivative equations for describing flow of 2-D incompressible power-law fluid are transformed,and flow function-turbulence equations of flow are generated.In this way,the number of unknown quantity can be reduced.In the process of discretization of equations,the unsteady solution was used to solve the steady problem,and the up-wind style was adapted to solve the convection term.The velocity was interpolated by the cubic spline,and the over-relaxation iterative solution method with an automatic parameter was used to calculate the flow function.With the help of above methods,a stable and rapid solution style was set up.The derivation theories,formula and program flow charts are given.The calculation result of a practical example is introduced.The possible improvement method for calculating the network models of porous media is presented.

Key words: no-Newtonian fluid, power law fluid, micro-tube flow, porous network, models, numerical calculation

摘要： 提出了一种对非牛顿流体在微观孔道中流动进行模拟计算的改进方法,该方法较以往的方法快速而稳定,从而为进行大量数值实验提供了精确而有效的手段.首先对描述不可压缩幂律流体二维流动的偏微分方程组进行变换,形成流函数-涡度方程组以减少未知量个数.在对微分方程组进行差分离散化的过程中,用不定常解法求解定常问题,对平流项采用迎风格式,用3次样条求解速度场,用自动参数超松弛迭代求解流函数场.利用这一系列改进措施,获得了稳定快速的求解格式.给出了导出方法、计算公式以及程序框图,还给出了实际算例的计算结果,并提出了当前孔隙网络模型计算的改进方向.

关键词: 非牛顿流体, 幂律流体, 微管道流动, 孔隙网络模型, 数值计算