Abstract:

As a novel equipment for polymer fluid processing, the tri-screw extruder has very complex mixing mechanism due to periodic change in geometrical structures and stresses at its unique center region. Chaotic mixing in tri-screw extruder was analyzed by Lagrangian system, which is much different from the traditional linear mixing analysis technique. With the finite-time Lyapunov exponent (FTLE), Lagrangian coherent structure (LCS), Poincaré section and particle visualization technology, mechanism of fluid transfer and chaotic mixing in 2D flow field as well as influence of dynamic structure characteristics at the center region to the FTLE's and LCS's distributions were studied in tri-screw extruder and compared to those in single-and twin-screw extruders. The results show that LCS divided the flow field in tri-screw extruder into three regions of different flow characteristics, namely, the near screw region, the far screw region and the center region, where a snarl is mass transfer bridge connecting these three regions. With the increase of mixing time, the degree of bending and folding in the snarls increased gradually, that enhanced chaotic mixing in flow field of tri-screw extruder by increasing transportation of polymer melt across three regions. Three hyperbolic fixing points near the kneading block indicated good mixing capability. The existence of elliptical cycle points in the Poincaré cross-sections implied the presence of non-chaotic spots in the center of flow field. Thus, mixing in the center region of tri-screw extruder was relatively poor.

Key words: tri-screw extruder, finite-time Lyapunov exponent, Lagrangian coherent structure, chaotic mixing, flow, CFD, numerical analysis

摘要：

三螺杆挤出机是一种新型的聚合物流体加工设备，其独有的中心区呈现出几何结构和受力状态的周期性变化，混合机理非常复杂。区别于传统的线性混合分析，从拉格朗日体系的新视角对三螺杆挤出机混沌混合进行拉格朗日拟序结构分析，利用有限时间Lyapunov指数（FTLE）、拉格朗日拟序结构（LCS），结合Poincaré截面和粒子可视化技术研究三螺杆挤出机二维流场的流体输运和混沌混合机理，讨论了中心区动态结构特性对FTLE和LCS分布的影响，并与单螺杆挤出机和双螺杆挤出机进行了对比分析。结果表明，LCS将三螺杆挤出机流域划分为近螺杆区、远螺杆区和中心区3个具有不同运动特性的区域，扭结是连接近螺杆区、远螺杆区和中心区物质交换的桥梁。随着混合时间的增加，扭结的弯曲和折叠程度逐渐增大，增强了3个区域的物质交换，强化了三螺杆流场的混沌混合。三螺杆挤出机啮合区附近存在3个双曲固定点，混合能力较好。Poincaré截面中椭圆周期点的出现说明在流域中心有非混沌区存在，因此三螺杆挤出机的中心区混合能力相对较弱。

关键词: 三螺杆挤出机, 有限时间Lyapunov指数, 拉格朗日拟序结构, 混沌混合, 流动, 计算流体力学, 数值分析