一类非牛顿流体非线性渗流的压力波解析求解方法及波形分析

The analytical method for solving the pressure of non-linear percolation of one non-Newtonian fluid and analysis for pressure wave structures

一类非牛顿流体渗流的视粘度依赖于压力梯度,且在不同的压力梯度区间内变化规律不同。其具有既不同于牛顿流体渗流,也不同于幂律流体渗流和宾汉流体渗流的非线性渗流特征。建立了该流体在多孔介质内部渗流的数学模型并利用行波法推导出了压力波的解析解。通过一系列算例分析了渗流方程控制参数对压力波形的影响,对比了该类流体与牛顿流体渗流的压力波差异。

The apparent viscosity of one kind of non-Newtonian fluid flow in porous media depends on the pressure gradient, and the characteristics of its changes are different in different intervals of pressure gradients. The characters of non-linear percolation of the fluid are neither completely same as Newtonian fluids nor completely same as power law fluids and Bingham Fluids. A mathematical model of the special non-Newtonian fluid flow in porous media is presented and its analytical solution for pressure is obtained by the method of traveling wave. By the runs of examples, the effect of the control parameters of percolation equation on pressue wave structures is analyzed and the difference between the non-Newtonian fluid flow and Newtonian fluid flow in porous media is compared.