嵌件平板收缩流支化聚合物黏弹行为的数值模拟

选取基于Doi-Edwards模型发展起来的XPP模型作为聚合物浓厚体系的本构关系，采用同位网格有限体积法结合数值求解的稳定化技术首先对4∶1平板收缩流进行了全域模拟，而后对聚合物成型中常见的嵌件收缩流进行了模拟。得出了4∶1平板收缩流和嵌件收缩流中流函数、拉伸量、第一法向应力差、第二法向应力差等值线的变化趋势，讨论了嵌件对聚合物浓厚体系行为的影响。数值结果表明，随着嵌件中心位置的变化，聚合物宏观信息表征量发生明显的变化，特别是收缩区上游拐角处涡的大小、形状以及嵌件后侧到收缩处拉伸量的变化非常显著。

Numerical simulation of branched polymer melts through planar contraction with inset based on XPP model

The finite volume method in the non-staggered grid was applied to the prediction of the two-dimensional branched polymer melts through a 4∶1 planar contraction and planar contraction with inset.The constitutive equation followed the extended pom-pom model (XPP model), which was developed from the Doi-Edwards model based on the rheology molecular theory.The decoupling about velocity-pressure and velocity-stress was removed by a new interpolation technique inspired by that of Rhie and Chow.Moreover, some numerical terms were added in order to promote the stability of the finite volume schemes.With the help of contour about stream function, backbone stretch, the first normal stress difference and the second normal stress difference, the development tendency of the polymer melts in 4∶1 planar contraction and planar contraction with inset was presented.The influence of inset on viscoelasticity of concentrated liquids was also discussed in detail.The numerical result indicated that the quantities describing viscoelasticity of polymer melts, especially for the size and shape of the salient corner vortex and backbone stretch behind inset, had obvious changes if the central position of inset was different.