Maxwell流体管内起动流的研究 　

A STUDY OF START-UP PIPE FLOW OF MAXWELL FLUID

对Maxwell流体管内起动流的振荡特性进行研究,得到了描述振荡特性的解析解,研究了黏弹性参数对各时刻速度剖面的影响,获得了轴心速度、平均速度和壁面摩擦力随时间的变化规律以及它们的频率特征.结果表明振荡的基频成分决定了流动的主要特性,给出并分析了基频频率与振幅和黏弹性参数之间的关系.

The characteristics of damping oscillation in start-up pipe flow of Maxwell fluid are studied. The analytical solutions, which is applied to the range of dimensionless elastic constant λ > 0.0432, are obtained using the method of variable separation. Based on the analytical solutions the effects of λ on the start-up pipe flow are studied. It is shown that the characteristic of damping oscillation in start-up pipe flow of Maxwell fluid is very obvious when the elastic constant is over a critical value. The oscillations of velocity and wall shear stress, frequency of fluid oscillation are dependent on the elastic constant.Time-history curve of the velocity at the axis as well as that of the average velocity of the cross-section is obtained. The results show that the phenomenon of velocity overshooting happens only when the value of λ is big enough. During the rebound process of Maxwell fluid adverse flow appears near the pipe wall at first. In the situation of positive velocity of the pipe axis, it is possible that the adverse flow near the wall results in the negative average velocity.The spectrum analysis reveals that despite a series of frequency in oscillating flow, the base frequency occupies the most of the total flow energy. The base frequency of velocity oscillation firstly increases then decreases with increasing λ. The maximum of the base frequency appears when λ = 0.08645. But the base frequency of wall shear stress decreases with increasing λ.