Analysis Of Mixing Mechanism Of Four-screw Extruder Based On Lagrange Method

As an important extrusion equipment for polymer processing and mixing,screw extruder is widely used in key industries such as petroleum,food and medicine.Due to the structural limitations of conventional screw extruder,in order to meet the processing requirements under different working conditions,four-screw extruder appeared as a new type of processing equipment.The advantages of the four-screw extruder are as follows: multiple meshing areas,small aspect ratio,compact structure and good mixing effect.As a new equipment,the four-screw extruder has a good development prospect,but its popularization is limited due to its short time and immature related theory.In this paper,we will take four-screw extruder as the research object,enrich the relevant theoretical research,and provide theoretical basis for the design and optimization of the four-screw extruder.Based on the chaotic dynamics theory,we discussed the two-dimensional flow field of a four-screw extruder with screws rotating in the same direction and different directions from the Lagrangian point of view,and analyzed the material transport mechanism and flow mixing characteristics in the flow field.Four-screw extruder is used as the main calculation model,Polyflow is used for two-dimensional transient simulation,and Matlab is used for post-processing analysis.With the help of lyapunov exoponent,Lagrange coherent structure,Poincaré cross section and particle tracing technology,the chaotic mixing mechanism under two-dimensional end face of the same-direction/different-direction four-screw extruder is comparatively analyzed,the hyperbolic invariant manifold in the flow field is determined,and the mixing law is studied.Particle tracer technique and lyapunov exoponent diagram is used to analyze the local mixing ability of different flow fields.Through particle visualization analysis,the trajectory of particles released at screw engagement and flow field center is analyzed,and the trajectory of single particles is analyzed.Combined with shear rate,logarithmic of stretching rate,instantaneous efficiency,time-averaged efficiency and mixing index,the mixing ability of four-screw extruder with screw rotating in the same/different direction and traditional twin-screw extruder was compared and analyzed.Afterwards,we took four-screw extruder as the basic model,the influence of screw structure(including the number of screw threads and the tip angle of three-screw threads)on the mixing characteristics is studied,and the chaotic differences caused by the structural differences are comprehensively analyzed from multiple angles.The flow and mixing characteristics in a four-screw extruder with meshing block structure are analyzed in three dimensions.The results show that the four-screw extruder with co-rotating or counter-rotating screws can produce a complete Lagrangian coherent structure,and the images of the four-screw extruder with co-rotating screws are more regular,forming a "lobes" structure which can enhance the material exchange.The location of KAM was found by Poincaré section,and then the consistency of fluid movement was revealed by combining coherent structure and particle visualization,and the characteristics of flow,mixing and material transport ability in different systems were revealed.Structural differences lead to the orderliness and randomness of particle motion,and the mixing curves of screw extruders with different structures are different.The research results show that the counter-rotating four-screw extruder has the best local and overall mixing ability.And the smaller the angle of the screw tip,the better mixing effect particles experiences.