粘弹性聚合物溶液微观渗流的有限体积法

Finite volume method of the microfiltration of viscoelastic polymer solution

针对残余油的微观存在形式,应用收缩流道模型并结合非线性上随体Maxwell本构方程、动量方程、连续性方程及收缩流道的边界条件建立了完整的数学模型。采用有限体积法求解了由UCM本构方程、动量方程、连续性方程和流道的边界条件构成的非线性耦合方程组。为了解决流场计算中的关键问题——不合理压力场的检测,同时保证计算的准确度及对压力的物理特性模拟,在对整个计算域采用交错网格的同时采用乘方格式对动量方程进行离散,进而得出控制方程组的离散方程式。选择交替方向隐式迭代法,并补以块修正技术促进收敛,最终得到了粘弹性流体在收缩流道内流动时的速度场、流函数场。

In viewpoint of microscopic existing form of residual oil, by applying flow channel contracting model and integrating non-linear upper converted Maxwell constitutive equation, momentum equation, continuity equation and the boundary conditions of contracted flow channel, the perfect mathematic model is established. Through adopting finite volume method, the non-linear coupled equation set that is composed of UCM constitutive equation, momentum equation, continuity equation and the boundary conditions of contracted flow channel has been resolved. In order to work out the key problems in the calculation of flow field, that is the test of unreasonable pressure field and at the same time making sure of the accuracy of the calculation and the modeling to the physical properties of the pressure, at the time of using cross network in the whole calculation domain, involution mode is produced to discretize momentum equation simultaneously, finally the discrete equation form of controlling the equation set is obtained. By choosing ahernative-direction implicit iterative method and adding block-correcting technique, makes the convergence improve, in the end the velocity field and steam function field can be obtained for the viscoelastic fluid flowing in contracted flow channel.