Chaotic Manifold Analysis of Four-Screw Extruders Based on Lagrangian Coherent Structures.

Xiang Zhu,Ying Tong,Yue Hu

doi:10.3390/ma11112272

Abstract

The four-screw extruder (FSE) is a novel equipment for polymer processing. In this paper, from a new viewpoint of Lagrangian coherent structures (LCS), two-dimensional fluid transport and chaotic mixing characteristics within three kinds of novel industrial FSEs are explored based on LCS to better understand the flow and mixing natures in the FSEs. Firstly, based on the finite-time invariant manifold theory, the finite-time Lyapunov exponent (FTLE) and LCS of FSEs are calculated by considering the different initial time. Hyperbolic LCSs from the FTLE maps are adopted to identify chaotic mixing manifolds in FSEs. Moreover, particle tracking and Poincaré sections are used to illustrate the different fluid motions in the above three isolated regions. Finally, the effects of relative rotating directions and layout of four screws on the chaotic manifolds in FESs are discussed in order to enhance local mixing performance. Furthermore, quantitative mixing measures, such as the segregation scale, logarithmic of stretching, and mean-time mixing efficiency are employed to compare the mixing efficiencies in three kinds of FSEs. The results show that the relative rotating directions and positions of four screws can change the chaotic manifolds and increase mixing performance in local poor mixing regions. FTLE and LCS analysis are helpful to better understand the chaotic mixing nature in the novel screw extruders.

Highlights

As a classic piece of mixing equipment, single-screw and twin-screw extruders are widely used in the polymer-processing industry [1]
For the screw equidistance distribute system (SEDS), we explored the relationship between the four screw positions and the hyperbolic Lagrangian coherent structures (LCS) of the flow system, which are relationship the fourmixing screw positions and the hyperbolic LCSs of the flow system, which are responsiblebetween for determining performance
This paper explores the chaotic-mixing and fluid-transport characteristics within three of x at time t, the length of stretch of a material line is defined as: novel industrial four-screw extruders by employing finite-time Lyapunov exponent (FTLE), LCSs, and Poincaré sections

Summary

Introduction

As a classic piece of mixing equipment, single-screw and twin-screw extruders are widely used in the polymer-processing industry [1]. With the development of the polymer industry, some novel screw mixing elements in screw extruders, such as the pin mixing section [2], pitched-tip kneading disk [3], and screw profile with slots [4], are devised to obtain highly efficient mixing and a fine final product. The traditional twin-screw extruder only has two intermeshing regions and without central region. Due to the complicated geometry, the flow and mixing mechanisms in the four-screw extruder are very complex in comparison with the typical twin-screw extruder. It is necessary to study the effects of four-screw extruder’s geometry, screw rotating manner on the flow, and the nature of the mixing in the four-screw extruder. As a dynamic flow system, a fundamental understanding of the flow and mixing mechanisms in the extruders is helpful in controlling the desired

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