Ti e m -a e v ra e g d f E ifc e i c n a I s n a o Ef ifc e i c n y 249

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1 2018 International Conference on Computational, Modeling, Simulation M amatical Statistics (CMSMS 2018) ISBN: D Numerical Simulation of Flow Mixing Performances in Novel Four-sc rew Extruders * Chong- xin W ANG Xiang- zhe Z HU S chool of Mechanical Engineering, Liaoning Shihua University, Fushun, , China * Corresponding author K eywords: Four-s crew e xtruder, m esh superposition technique (MST), mixing efficiency. A bstract. Two kinds of novel four screw extruders, namely square- layout four screw extruder ( SFSE) rhombic- layout four screw extruder (), were selected to study ir flow m ixing performances. Based on finite element method mesh superposition technique ( MST), two- dimensional flow characteristics in SFSE at cross sections were studied b y using Polyflow software. Moreover, measurements of mixing efficiency, such as mixing index, time- averaged efficiency, instantaneous efficiency logarithm stretching rate, were calculated in SFSE, respectively. The c omparisons of mixing efficiencies in SFSE a nd were employed in order to better underst effect of screw layout on mixing performances in four screw extruders. The results show that mixing efficiency of is higher than that of SFSE. For square-layout of four screws, counter- rotating SFSE has higher mixing efficiency than co- r otating SFSE. I ntroduction With development of polymer processing industry, extrusion molding is an important process. Polymer materials by extrusion barrel heating under condition of screw rotation will by p owder or granular materials continuously push forward, compaction gradually molten plastic into a viscous flow. The polymer melt after plasticizing under shear compression of s crew is continuously pushed into shunt plate of extruder a certain shape of die. The final cooling is finalized to obtain desired finished product or semi- finished product. Compared with or forming methods of polymer melt, extrusion molding process has many outsting a dvantages. For example, continuous production process, high production efficiency, wide application scope, strong practicability, simple equipment structure. Extrusion molding process is widely used in processing of rubber, plastic fiber, especially plastic products, almost most t hermoplastic s ome rmosetting. The screw extruder as one of main equipment has been widely used in polymer processing. In recent years, multi- screw extruder has been developed widely. With its unique advantages, multi- s crew extrusion technology has made up for shortcoming of single double screw extrusion, has attracted more more attention in field of extrusion. The multi- screw extruder mainly consists of three-screw extruder four-screw extruder. The research of three- s crew extruder is more common, but research on four- screw extruder is less. In this paper, flow rules of polymer melt in four- screw extruder are analyzed by using meshing conventional thread element of four-screw extruder[ 1-2]. This paper compares characteristic parameters of S FSE, provides some reasonable solutions for optimization design of multi- s crew extruder. T heoretical Physical Model M odel 1 shows square-l ayout four screw extruder ( SFSE). The extruder screw in structure of basin can choose different relative motion forms. It is called Co-rotating square- layout four screw extruder Counter-rotating square- layout four screw extruder. Square layout is discussed 245

2 in this paper same as four pillars of counter-r otatin g screw co-rotatin g screw two k inds of operating conditions, corresponding to flow field of material transport properties, a nd comparing two kinds of working conditions of mixing efficiency. The sizes of two types of extruders are as follows, barrel radius is 18.5mm (R1), screw root radius is 13mm (R2), screw h ead radius is 17mm (R3), screw center is 33mm (R4). 2 is geometrical structure of rhombic-l ayout four screw extruder (), screw is rotating counterclockwise. There are similar geometrical structure characteristics between square-layout four screw extruder rhombic- layout four screw extruder. With periodic r otation of screw, central region of two triangles in basin presents corresponding p eriodical changes. F igure 1. Geometry of square- l ayout four screw extruder (SFSE). 2. Geometry of rhombic-l ayout four screw extruder ( ). N umerical simulation using finite element model of SFSE all by quadrilateral grid cell, in order to capture basin edge screw root small changes in fluid flow velocity near end. This article on inner wall of screw meshing zone, barrel screw around roots o f mesh refinement, adopts three layer boundary refinement grid localized encryption processing. Finally, finite element model of square- layout four screw extruder (SFSE) is shown in 3, w hich contains elements, finite element model of extruder finite element model of rhombic- layout four screw extruder () is shown in 4, which contains e lements. 246

3 3. F inite element model of SFSE. M amatical T he Model 4. F inite element model of R FSE. form of continuity momentum equa tions c an b e expressed by: β v + P = 0 η ( 1) H T he ( - v) + ( 1- H )(- P + Τ + ρg - ρa) = 0 v ( 2 ) stress tensor is described as: 0 ( γ) T = 2η D ( 3) The Bird- C arreau equation can be described by: ' ' 2 ( n 1)/2 + ( η0 η )[1+ ( λγ) ] η = η ( 4) Where λ 2 = D, w hich is a property of a given material [ 3]. In this study, simulation p arameters of this blend melts at 160 C are as follows: λ = 0.049s, n η = 0.5, 0 = 5520p a s, η =0. In order to minimize High Weissenberg Problem potential 3D effects, small r otational speeds of screws with 0.5 rpm were used in simulations. Convergence accuracy level is set at i n all simulations. 247

4 M easurements of M ixing Efficiency It is important to quantify mixing equipment by using relevant mixing s egregation scale, S (t), is a significant tool to evaluate distributive m ixing. parameters. The ( t) R( r, t) dr S = ξ 0 ( 5) W here R(r,t) is a correlation coefficient for concentration. The segregation s cale is a measure of size of h omogenous concentration in some regions it decreases when mixing improves [ 4-8]. A mixing index λm z, is widely used to evaluate dispersive mixing. D λ mz = D + W ( 6) The fluid in screw extruder will be in rotational simple shear conditions with λ mz=0 λ mz= 0.5, respectively. When λm z is 1.0, it means that fluid is in pure elongation condition f or screw extruders. R esults V elocity Discussions F ield M ixing Index F igure 5 is velocity vector diagram of melt flow in square array extruder. F igure 6 shows t he velocity vector diagram o f melt flow in S FSE, respectively. It can be seen from figures that maxima l v elocity magnitude of melt in square array extruder t he rhombic arranged extruder is 1.516m/s 1.782m/s respectively. Rhombic- l ayout four screw e xtruder melt maximum speed of higher than that of square arrangement in maximum speed of melt in extrusion machine, rhombic-l ayout four screw extruder mixed zone rotor m aterial exchange between extruder are more frequent than square arrangement, illustrate a rrangement of rhombic extruder mixing efficiency is higher. 7 8 show mixing index distributions in SFSE relative to i nitial position, corresponding to typical rotational angles of 0. The fluid mixing index in two kinds of extruders is most widely distributed between It shows that material p article experience is stronger elongational flow is more favorable to mixing of extruder m aterial. In addition, re is a floating dead zone near rotor wall in two arranged extruders, so re is a small blue area in figure. However, blue area of rhombic- layout four screw extruder is obviously smaller than square-l ayout four scr ew extruder. 5. V elocity field of SFSE. F igure 6. Velocity field of R FSE. 248

5 7. Mixing index distribution of R FSE. Time- a veraged E fficiency 8. Mixing index distribution of S FSE. I nstantaneous Efficiency T his section compares different screw combination conditions of different screw to screw extruder time-averaged efficiency instantaneous efficiency. The higher time- averaged e fficiency, higher mixing efficiency of screw extruder. The comparison of time average mixing efficiency of different screw extruder is shown in 9. The time- averaged efficiency is greater than 0 flattening is necessary condition for effective mixing of screw extruder. According to figure, time-averaged efficiency of four-s crew rhombic extruder is larger than square- l ayout extruder, indicating that rhombic layout is more efficient than square one. It can be seen that effect of counter-r otating screw on mixing efficiency. In square layout, time- a veraged efficiency is higher than that in different direction. 10 shows instantaneous efficiency in three models of four- screw extruder, i t is found that instantaneous efficiency of all models is at initial time, it increases sharply. And n, with mixing time moves in a certain range. Particles in a complex due to special geometric configurations, stretching compression state, as shown in figure causes i nstantaneous mixed average efficiency of cyclical fluctuations. It can be seen that instantaneous mixing efficiency of square arrangement is higher than instantaneous mixing efficiency of t he or two models Time-averaged efficiency Time/s Comparison of time-a veraged efficiency between three models. 249

6 0.30 Instantaneous efficiency L ogarithmic S tretch F igure Time/s 10 C omparison of instantaneous efficiency between three models. M ixing Index M any literatures show that elongational flow is more effective than shear flow in mixed effect. So logarithmic stretching is an important tool for comparing efficiency. From 11, it can be seen that with increasing of time, elongation of screw extruder gradually increases, showing exponential growth. Logarithmic stretch of rhombic- layout four screw extruder () as shown to significantly greater than square arrangement. Under condition of same configuration, counter-rotation value is higher than co-r otation one, mixing of counter- rotating extruder has higher efficiency. It is concluded that mixing efficiency of rhombic- layout f our screw extruder is better. 12 shows mixing index probability distribution curve of screw in different configuration an d different steering. Mixing index between 0 to 0.5, flow form of shear flow mixing index greater than 0.5, flow form of elongational flow, elongational flow in polymer is b etter than shear flow. This shows that shear elongational flows of three models are s lightly enhanced, dispersion is better better. The probability that co- rotating square- layout four screw extruder is greater than or two models, mixing effect of co- rotation extruder is better. The probability of rhombic- layout four screw extruder is greater than counter-rotating extruder, effect is better than counter- r otating extruder stretch Length of Time/s 11. Compariso n of logarithmic stretch Probability Mixing index 12. C omparison of mixing index between three models. 250

7 25 Segregation scale Segregation S cale F igure Time/s 13 C omparison of segregation scale between three models F igure 13 variation curves of segrega tion scale of material melt in section of screw extruder under different screw layout conditions. It can be seen from figure that, wher S FSE a nd R FSR is large, s egregation scale is rapidly decreasing in first 200 seconds due to large scale value of initial s egregation. After 200 seconds, s egregation scale values of material melt in two types of screw extruder are at a certain value. However, s egregation scale of counter- rotating SFSE s hould be lower than that of two or models. It is shown that mixing effect of square- l ayout screw extruder is best. C onclusions Rhombic- layout four screw extruder is much bigger than maximum speed of extruder melt flow i n a square layout maximum flow of melt in extrusion machine speed, rhombic layout of extruder speed of material flow in mixed zone faster, material exchange more frequent. Moreover, mixed dead zones of rhomboid extruder are less than mixed dead zones a rranged in square. Therefore, rhombic layout of extruder has higher dispersion m ixing efficiency. The counter-rotation square-layout four screw extruder has highest time- averaged efficiency a nd instantaneous efficiency efficiency of rhombic array extruder mixing efficiency is higher than square layout of extruder with co- rotation, so square layout of extruder with counter- r otation has higher efficiency. It can be seen from curve of separation scale that mixing effect of counter- rotation square- layout four screw extruder is better than or two models. The mixing effect of rhombic-layout screw extruder is better than square- layout extruder, but if we change d irection of rotation about rotor of a square layout, mixing efficiency of extruder is higher. A cknowledgement T his w ork was supported by National Natural Science Foundation of China (grant No , ) ; Program for Liaoning Excellent Talents in University (grant N o. L R ). R eferences [ 1] X.Z. Z hu, Y.J. X ie, H.Q. Y uan, Numerical simulation of ex trusion characteristics intermeshing co-rotating tri-sc rew extruder, P olym. M ater. S ci. E ng. v ol. 24, pp , [ 2] X.Z. Z hu, H.Q. Y uan, Y. M iao, Numerical simulation of temperature distributions power consumptions in conveying element of tri-sc rew extruders, P olym. M ater. S ci. E ng. v ol. 25, pp , of 251

8 [ 3] W.D. X u, X. Q ian, Numerical experimental study on concentration distribution of PE- L LD/SBS blending process C h ina. P las. Vol. 23, pp , [ 4] P. V. D ankwertz, The definition measurement of some characteristics of mixtures, Appl. S ci. Res. v ol. 3, p p , [ 5] Z. Tadmor a nd. C G. G ogos, P rinciples of polymer pr ocessing, Wiley- I nterscience, [ 6] R.K. C onnelly a nd J. L. K okini, 2D numerical simulation of differential viscoelastic fluids in a single- screw continuous mixer: ap plication of viscoelastic finite element methods, Adv. P olym. T ech. V ol. 22, pp , [ 7] Y. N akayama, E. T akeda, T. S higeishi T. K ajiwara, Melt- mixing by n ovel pitched- tip k neading d isks in a co- rotating twin- screw ex truder, C hem. Eng. Sci. v ol. 66, pp , [ 8] V. K iran, B. K. A. V yakaranam a nd L. K. J ozef, E valuation of effect of paddle element stagger angle on local velocity profiles in a twin- screw continuous mixer with viscous flow using Finite E lement Method simulations, J. Food Eng. v ol. 108, p p ,