基于拉格朗日的单螺杆销钉挤出机混沌混合分析

Chaotic Mixing Analysis of Single Screw Extruder Based on Lagrangian Viewpoint

从拉格朗日理论的新视角,分析了高分子聚合物熔体在单螺杆销钉挤出机内的流型结构以及流动行为,揭示了销钉强化聚合物熔体输运和混沌混合的机理。使用有限元软件Polyflow计算了流场的速度分布和混合指数;借助Matlab数学软件进行自主编程对速度场进行积分得到了三种不同销钉挤出机模型的有限时间李雅普诺夫指数。结果显示,在加入销钉之后,单螺杆销钉挤出机流域中出现了圆柱绕流现象,绕流产生的尾迹将撞击螺棱,销钉和螺棱的这种相互作用将加剧聚合物熔体的拉伸作用。每个销钉都将产生尾迹,随着销钉数量的增加,导致流域中产生了更多的尾迹。尾迹与销钉相互作用得到了增强,导致流域中产生了更多的涡结构,说明流域中的大部分熔体处于混沌混合的状态。混沌混合使销钉挤出机内的流体拉伸作用得到了增强,流体的混合指数得到增加,混合效率也逐渐增大。

The flow pattern of high molecular polymer fluid in a single screw extruder was analyzed from the new viewpoint of Lagrange theory, which revealed the mechanism of the pin strengthing polymer melt transport and chaotic mixing of the flow field.The velocity distribution and mixing index of the flow field were calculated by the finite element software Polyflow. Besides,with the help of Matlab software,autonomous programming was used to intergrate the velocity field and then the finite time Lyapunov exponent of three pin screw extruder models was obtained. The results show that after the pin is added,the flow around the circular cylinder appear in the basin of the extruder of the single screw pin. The wake generated by the flow will impact the spirial,and the in-teraction between the pin and the screw will aggrarate the tensile effect of the polymer melt. Each pin will generate the wake and with the increase of pin number,more wakes will be generated in the basin. The interaction between the wake and the pin is enhanced, re-sulting in more vortex structure in the basin which suggest the polymer melt is in a state of chaotic mixing. Chaotic mixing enhances the fluid stretching effect,mixing index and the mixing efficiency in the pin screw extruder.