非牛顿流体在渐变管中压力和剪切应力的二次摄动解

本文利用双摄动方法求解缓慢变化管道中Johnson-Segalman(J-S)流体流动的渐近解．将管道的扩张（或收缩）角度和粘弹性参数分别作为双摄动的参数，由流函数和涡量函数的形式，推导出压力和壁面剪切应力的渐近解．在此基础上，分析了管道角度，粘弹性参数和雷诺数等参数对压力以及剪切力影响．主要结论如下：(1) 管道扩张角度增加时，流向同一位置处径向压力以及壁面剪切应力随扩张角度减小；(2) 在同一扩张管道中，径向压力随着流向位移减小，收缩管与之相反；(3) 扩张角度与雷诺数对流场起主导作用，粘弹性系数起次要作用．

Double Asymptotic Solutions of Pressure and Shear Stress of Non-Newtonian Media Fluid in Gradient Tube

In this paper, we utilize the double perturbation strategy to construct the asymptotic solutions for Johnson-Segalman (J-S) fluid through a slowly varying pipe. The expanding (or shrinking) angle of the pipe and the viscoelastic parameter are taken as the parameters in double perturbation successively. By applying this method to the stream and vorticity functions, the asymptotic solutions are derived. On this basis, the influence of the parameters such as the expanding angle, viscoelastic parameter and Reynolds number on the flow are investigated in detail. The conclusions are as follows. (1) With the increasing expanding angle, the pressure at the wall decreases with the angle. (2) In the same angle of the pipe, the radial pressure in the expansion pipe is constantly decreasing with the flow direction, and the situation in the shrink pipe is opposite. (3) Compared with the expanding angle and the Reynolds number, the viscoelastic parameter has less influence on the flow fields.