矩形收敛流道内聚合物熔体三维等温幂律流动的数值模拟

Numerical Simulation of Three Dimensional Isothermal Power-law Polymer Melt Flow within a Rectangular Convergent Channel

本文利用罚有限无法 ,采用幂律本构模型 ,对聚合物熔体在矩形收敛口模内的三维等温流动进行了数值模拟。对于幂律模型 ,即使流量非常大 ,经过有限次迭代 ,计算都能够收敛 ,并得到合理的结果。流量越大 ,则主流动方向的流速从流道入口至出口加速上升的趋势越明显。在流道中心呈现拉伸流动 ,而壁面附近则为剪切流动。流道的中心部位存在比拉伸应力更大的第一法向应力差。在同一横截面上压力并不相同 ,因此以往关于在同一横截面上的压力恒定的假设是不恰当的。采用罚有限元法 ,速度场很小的误差就可能导致压力求解较大的误差 ,而且在流道壁面附近这种误差表现得特别显著 ,因此用罚有限元方法求解压力场有较大的局限性。

In this paper, the numerical simulation was implemented for the three dimensional isothermal power-law polymer melt flow within a rectangular convergent channel by means of penalty finite element method. When the power-law constitutive model is used, even though the flow rate is rather high, the computation can be finished and yield rational results only after finite times of iteration. The melt flow speeds up with increasing acceleration from the channel entrance to exit and the higher the flow rate the greater the acceleration. Near the channel wall renders a shear flow but at the central area of the channel exits an elongational flow and over there the first normal stress difference is larger than the elongational stress. The pressure is not identical at the same cross section of the channel so that such a assumption that the pressure keeps uniform at the same cross section is incorrect. Penalty finite element method has some drawbacks when it is utilized to compute the pressure distribution because only a little error of velocity can result in substantial error of pressure and such phenomena is more obvious near the channel wall.