Maxwell流体管内振荡流的壁面摩擦力分析

Analytical study on wall friction in a pipe induced by oscillatory Maxwell flows

研究了Maxwell流体对管内振荡型Poiseuille流动的管壁摩擦力特性。由Bessel方程控制速度振幅 ,用分离变量法求出了解析解。由振荡频率对管壁摩擦力的影响的研究中发现 ,管壁摩擦力存在类共振特性 ,即在某些临界频率位置 ,振荡流体在管壁上产生的摩擦力会急剧增大。流体的弹性参数、管径和振荡流频率对壁面摩擦力的影响可用两个无量纲参数 ω和 R表示。在确定的 ω范围内 ,当 R取值较小时 ,壁面摩擦力振幅与 ω变化关系曲线的共振峰较少 ;随着 R的增大 ,共振峰的位置在 ω轴上左移 ,幅值下降 ,个数增多 ;在 R >12之后 ,该曲线变成一条单调下降的曲线 ,与牛顿流体的曲线一致 ,且不再有任何共振现象。

The wall friction induced by oscillatory Maxwell flow in a pipeline was studied.The oscillation of velocity was controlled by Bessel equations,and the analytical solution was obtained using the variable separation method.The effect of oscillatory frequency on the wall friction was analyzed.The results show that the resonance_like characteristic of wall friction is revealed.For some critical values of oscillatory frequency,the wall friction increased dramatically.The effects of the elastic parameters of Maxwell fluids,pipe diameter and oscillatory frequency on the wall friction can be expressed by two dimensionless parameters ( and ).In a certain region of parameter ,there are less numbers of resonance peaks for smaller parameter in the correlative curve of wall friction with .With the increase of ,the positions of resonance peaks move towards left,the number of peaks increased,and the amplitude of peak decreased.When the value of is over 12,the curve becomes a monotone decreasing curve without any peaks and just like that of Newtonian fluids.This resonance_like characteristic of the wall friction is very useful for increasing the efficiency of oil displacement in the cores.