圆管内上随体Maxwell流体流动的谱方法逼近

Numerical Simulation of Upper-convected Maxwell Fluid Flow in a Pipe by Spectral Method

给出了[0,1]区间上的广义Chebyshev多项式及其相关性质。应用Chebyshev Tau方法高精度地模拟了上随体Maxwell流在水平圆管内的流动。通过管中心和其它管线的速度变化趋势,以及圆管径向的速度分布,描述了流场的整体流动特性,揭示了非牛顿流体管道流的速度过冲和振荡现象。计算结果表明:流体弹性对管中心流体的影响最大;且流体弹性越大,流动的不稳定性越强,松弛时间越长。

In order to simulate the rheological behaviors of upper-convected Maxwell fluid flow in a horizontal circular pipe accurately, both the Chebyshev polynomials in a wider sense which is defined on the interval from zero to one and some qualities of them are given. The curves of the velocity at the axes parallel with the centre axis of the cube as well as the cutaway view of it on the whole pipe are obtained using Chebyshev Tau method which is one of spectral methods. They can easy show the behaviors of the flow in the whole cube, reveal the phenomenon of locity overshooting and damping oscillation of the flow. At the same time, the results display that the elasticity of the fluid influenced the velocity at the centre axis most; The velocity becomes more unsteady and the time of laxity becomes longer with the increase of the elasticity of the fluid.