Theoretical analysis of residence time distribution functions and strain distribution functions in plasticating screw extruders

The residence time distribution (RTD) function in a single screw plasticating extruder was theoretically calculated. The calculation is based on the solids conveying, melting, and melt conveying models in extruders. The screw channel is divided into small axial increments and the path of each exiting fluid particle is followed from hopper to die. In addition to the residence times the total shear deformation or strain imposed on the fluid particles was also calculated. This together with the RTD function has led to the definition and calculation of the strain distribution function (SDF). This function is proposed for quantitative characterization of the mixing performance of screw extruders as well as other laminar mixers. Some simple idealized batch and continuous laminar mixers are analyzed in terms of the SDF. Finally, the effect of extruder operating conditions and screw design on the RTD and SDF were investigated by computer simulations.     

Dependence of solids conveying on screw axial vibration in single screw extruders

In the single‐screw extruder, the vibration force field is applied to the solids conveying process by the axial vibration of the screw and the novel concept on the solids conveying process being strengthened with the vibration force field has been brought forward in this study. We establish the mathematical model that describes the solids conveying process with the vibration force field and obtain the approximative analytical solutions of the pressure and velocity of the solids conveying in the down‐channel. In the new theory, if the screw has no axial vibration the solids conveying pressure is the same as that of the Darnell and Mol theory, but the density and velocity of solids conveying along the screw channel is variable, which has modified the Darnell and Mol theory in which the density and velocity of the solids conveying along the screw channel was considered invariable. The results reveal that the axial vibration of the screw can increase the average pressure of solids conveying, decrease the channel length of the solids conveying section and increase the solids conveying angle. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2998–3007, 2006     

动态成型注塑螺杆熔体输送能力的研究

根据动态注射成型时螺杆的工作特点，采用自行修正的Tanner本构方程研究了聚合物熔体在螺槽中的等温流动。同时，近似地给出了振动力场下注塑螺杆熔体输送能力的表达式，理论分析了振动参数对沿程压力降及动态成型熔体输送能力的影响。结果表明，振动力场使塑化过程中聚合物的粘度降低，流动阻力减小。沿螺槽方向的平均压力降减小，在保持成型条件不变的情况下，施加振动可以提高熔体输送能力。     

Analysis and experimental evaluation of twin screw extruders

Twin screw extruders can he classified according to their geometrical configuration. The main distinction is made between intermeshing and nonintermeshing extruders. Another distinguishing characteristic is the sense of rotation. The most important characteristics of the various twin screw extruders are examined, with particular emphasis on the effect of screw geometry on the conveying characteristics. A brief review is given of the state of the art in theoretical analysis of twin screw extruders. Experiments with two lab scale, intermeshing twin screw extruders are described, one co- and one counterrotating. Results are presented on power consumption, residence time distribution, and mixing characteristics of the two extruders. The counterrotating extruder exhibits a narrower residence time distribution and better dispersive mixing capability. The corotating extruder showed a better distributive mixing capability. These results can be explained in terms of the conveying and mixing mechanisms in both extruders. The overall extruder performance seems to be dominated by the effect of the intenneshing region. Any realistic, theoretical analysis of twin screw extruders should be centered around the flow behavior and mixing characteristics of the intermeshing region. The corotating extruder appears to be best suited for melt blending operations, while the counterrotating extruder seems to be preferred in operations where solid fillers have to be dispersed in a polymer matrix.     

Residence time distribution in a real single screw extruder

The residence time distribution in an industrial single screw extruder was investigated experimentally in the case of melt and plasticating extrusion. The investigations performed proved that the extrusion parameters influence strongly the residence time distribution in the extruder. It was found that the resistance to flow through the die-head of the extruder is very important from this point of view, as well as other parameters like rotational speed of the screw and the screw channel depth. Variation of these parameters can change the residence time distribution over a broad range between the extreme idealized cases of plug flow and flow with perfect mixing. In order to obtain quantitative dependences three moduli were used and a correlation equation was obtained. This equation enables an estimation of residence time distribution on the basis of experimental characteristics of the extruder and the actual extrusion parameters.     

振动力场作用下聚合物熔体单螺杆挤出过程数值模拟

根据塑料电磁动态塑化挤出过程中熔体输送的实际情况，对三维模型进行简化，利用大型有限元软件ANSYS模拟了叠加轴向振动力场作用下聚合物熔体在螺槽中的流动情况，求解出周期性变化的速度，压力场分布，结果表明，与稳态挤出过程相比，振动力场的引入在进出口压力差恒定的情况下，可以提高熔全输送流率。采用有限元模拟方法可以为确定和优化工艺参数，产品质量控制提供指导。     

Investigations on the extrusion of rigid PVC on twin screw extruders

The processing of rigid-PVC is mainly performed on twin screw extruders. For a thermal sensitive material, such as rigid PVC, this implies certain advantages. They consist primarily in the fact that intermeshing counter-rotating twin screw extruders are axially closed pump systems, whereas single screw and co-rotating twin screw extruders represent axially open mixing systems, conveying by means of friction forces. This fundamental difference leads to totally different flow rate and shearing force distributions of the axial flow, which in turn affects the residence time distribution and the thermal dynamics of the process. Investigations have been carried out to determine the influence of screw speed, die resistances, barrel wall temperatures and different compounds on the melt temperature and its homogeneity. It could be shown that the melt temperature can be essentially influenced by heating the barrel wall and the screw. This even applies to the most diverging degrees of mechanical power consumption resulting from different compounds. The homogeneity of the melt temperature thus depends on the relationship between the barrel wall temperature and the melt temperature within the respective heating zone. The possibility is shown to establish a model theory based on energetic and rheological similarities, which can be employed in the construction of machines of different diameters. For this purpose the geometrical and operational data of an optimal operating machine serve as a basis.     

间断副螺棱结构对挤出机内混沌混合影响的数值模拟

建立了混沌单螺杆挤出机计量段展开螺槽的物理模型及数学模型,根据流体符合Carreau定律,借助Ployflow软件,采用网格叠加技术,对聚合物熔体在插有间断结构副螺棱螺槽内的流动进行了数值模拟分析,从统计学的角度结合粒子示踪技术以停留时间分布、分离尺度、混合效率及累计混合指数为指标来表征螺杆的混合性能。结果表明,当副螺棱间断次数多且高度略低于螺槽高时混沌单螺杆混合性能更好。     

Modelling of polymer fluid flow and residence time distribution in twin screw extruder using fictitious domain method

Abstract

The flow behaviour of a polymer melt in the conveying region of an intermeshing corotating twin screw extruder was studied using the combination of mixed finite element and fictitious domain method. The model was a combination of the governing equations of continuity and momentum with Carreau rheological model in a three-dimensional Cartesian coordinate system. The equations were solved by the use of a mixed Galerkin finite element technique. The Picard’s iterative procedure was used to handle the non-linear nature of the derived equations. The particle tracking technique was used to obtain residence time distribution and analyse distributive mixing in conveying region. The shear rate distribution was investigated as a criterion for dispersive mixing. The applicability of this model was verified by the comparison of experimentally measured pressure and simulation results for high density polyethylene melt. This comparison shows that there is a good adequacy between experimental data and model predictions.     

振动力场作用下的单螺杆挤出机固体输送理论

在单螺杆挤出机中,通过螺杆的轴向振动将振动力场引入聚合物固体输送过程,提出振动力场强化固体输送过程的新概念.以螺槽中运动的物料为对象建立了振动力场强化固体输送过程的数学模型,并获得了物料沿螺槽方向输送的压力（密度）、速度的近似解析解.传统固体输送过程就是当螺杆轴向振动的振幅为零时的特例,此时的压力降与Darnell and Mol 理论一致,但不同的是物料速度及密度沿螺槽方向是变化的,从而修正了Darnell and Mol 固体输送理论.螺杆的轴向振动提高了固体输送平均压力,缩短了固体输送的长度,增加了固体输送角.透明料筒全程可视化实验挤出机证明了螺杆轴向振动确实缩短了物料固体压实输送所需的螺槽长度.     

Analysis of mixing during melt-melt blending in twin screw extruders using reactive polymer tracers

Mixing during melt-melt blending of segregated polypropylene melt streams in a co-rotating twin screw extruder was experimentally investigated. The mixing limited reaction between two polymer reactive tracers, which are terminally functionalized polyolefin oligomers, was used to determine the mixing performance of a kneading block section. The selected functional groups were succinic anhydride and a primary amine, and Fourier-Transform Infrared Spectrometry (FT-IR) was used to determine the anhydride conversion. In the absence of interfacial tension, the reaction conversion was directly related to the amount of interfacial area generated. Experiments were completed to study the effects of operating conditions, kneading block design, and polymer material properties. The screw speed effect was observed to be non-linear because of competing contributions from shear rate, residence time, channel fill, and viscous heating. The mixing performance of kneading blocks backed by a reverse conveying element was observed to follow the trend of: forward > reverse > neutral. For each kneading block design, the mixing performance decreased with an increase in polymer viscosity.     

Relationship between local residence time and distributive mixing in sections of a twin‐screw extruder

Local residence time and distributive mixing were measured in conveying sections and kneading blocks of a twin screw‐extruder. The residence time measurements were completed using carbon black as the tracer and an infrared temperature probe to detect the temperature decrease caused by the changing surface emissivity. The validity of this experimental technique was extensively evaluated. A mixing limited interfacial reaction between polymer tracers was used to directly measure the distributive mixing in the twin‐screw extruder. Possible relationships between mixing and residence time in the sections of the twin‐screw extruder were investigated by combining these two measurements. Distributive mixing in conveying sections was related to the local average residence time and the fill. In contrast, distributive mixing in kneading blocks was related to the local average number of screw revolutions experienced by the polymer. Forward stagger kneading discs achieved the greatest amount of distributive mixing, which was attributed to a combination of local stagnant flow regions and more frequent interfacial reorientation.     

Influence of the melt viscosity and operating conditions on the degree of filling,pressure, temperature,and residence time in a co‐kneader

The effect of the melt viscosity and operating conditions on processing parameters in a co‐kneader with a discharge die was experimentally investigated. Filling ratio, pressure, temperature, and residence time distribution were measured. Experiments were performed with polypropylene resins. The viscosity of the melt was varied either by changing the regulation temperature of the kneader or the molecular weight of the polymer. The filling pattern in the co‐kneader shows the conveying capability of the various elements without any effect of the melt viscosity. Experimental residence time distributions remain the same at a given feed rate and screw speed, regardless of the viscosity of the material. The global degree of filling in a zone combining conveying elements, kneading elements, and restriction ring was found to be nearly constant in the conditions of this study and therefore a simple relation exists between the mean residence time and the feed rate. Beside expected variations of the die pressure and melt temperature when the viscosity, screw speed or feed rates change, a model based on heat equation and experimental data demonstrate the high capability of the co‐kneader for heat exchange and for the control of self‐heating during mixing. POLYM. ENG. SCI., 58:133–141, 2018. © 2017 Society of Plastics Engineers     

The effects of kneading block design and operating conditions on distributive mixing in twin screw extruders

A mixing limited interfacial reaction between polymer tracers was used to directly measure the distributive mixing performance of a co‐rotating twin screw extruder during melt‐melt blending of polypropylene. The reaction between the polymer tracers, which are low molecular weight succinic anhydride and primary amine terminally functionalized polymer chains, was followed using Fourier‐Transform Infrared Spectroscopy (FT‐IR). Experiments were completed to determine the effects of flow rate, screw speed, and kneading block design on the distributive mixing performance and the residence time distribution (RTD). The only RTD variable that was significantly affected by the experimental factors was the average residence time. Distributive mixing with neutral and reverse kneading blocks was controlled by the average residence time, the fully filled volume, and the shear rate. Conversely, the mixing performance of a forward kneading block did not follow the same trends.     

振动力场对高密度聚乙烯固体物料输送压力的影响

在自行设计的动态固体物料压实试验机上,对高密度聚乙烯固体物料分别做了稳态和动态压实试验,研究了振动力场对固体物料输送过程的影响。结果表明:有振动力场存在时,螺槽中固体物料的压力明显高于稳态压实时的压力;在振动力场作用下,在一定范围内,增大振幅或者提高振动频率,都能明显提高螺槽中固体物料的压力,且压力随时间增加上升得更快;振动力场的引入可以加速固体物料的压实,使螺槽中提早建立固体物料的输送压力,且使压实效果更好。     

On the scale-up of plasticating extruder screws

In the most commonly used scale-up method of plasticating extruder screws, the screw channel depth is increased by the square root of the diameter ratio while the screw RPM is decreased by the square root of the diameter ratio such that the output rate increases proportionally to the square of the diameter ratio. This scale-up method, largely based on the pumping function of the screw, often leads to a higher melt temperature, a higher screw horsepower consumption per unit output rate and an inferior melt quality from the larger diameter screw. Analysis of the common scale-up method reveals that, although the shear rate in the melt is kept constant, the average residence time and the peripheral screw speed are increased for the larger diameter screw. Our recent study on the melting mechanism also reveals that the melting capacity increases less than the pumping capacity. A detailed examination of the common scale-up method in this paper shows that the pumping capacity and the solid conveying capacity increase more than necessary while the melting capacity increases insufficiently.     

Developments in the analysis of steady screw extrusion of polymers

A review is undertaken of theoretical and experimental work which has advanced the understanding of the single screw extrusion process for polymers. Detailed consideration is given to the many published theoretical models of solids conveying, melting and melt flow in the channel of a plasticating extruder. Development of such models is traced in terms of the gradual relaxation of simplifying assumptions to provide methods of analysis which give realistic predictions of machine performance. Comparisons between the results of such analyses and observed machine behaviour are also discussed.     

A composite model for an intermeshing counter‐rotating twin‐screw extruder and its experimental verification

A composite simulation model of solids conveying, melting and melt flow in a closely intermeshing counter‐rotating twin‐screw extruder has been developed. The model is based on combining new melt conveying models with melting and solids conveying models, and the die is included into considerations. A general approach is applied using fully three‐dimensional non‐Newtonian FEM modeling for melt conveying to develop screw pumping characteristics which are implemented into the composite model. Several screw configurations are considered including non‐classical elements. Computations are made for axial fill factor, pressure, temperature, and melting profiles. The results are validated experimentally. POLYM. ENG. SCI., 55:2838–2848, 2015. © 2015 Society of Plastics Engineers     

幂律流体三维脉动流场数值模拟

利用ANSYS软件，模拟了振动诱导单螺杆挤出机熔体输送段中非牛顿幂律流体的三维脉动流场，得到了三维脉动流场的瞬时速度分布及螺槽中物料的流动轨迹。结果表明，在脉动流场作用下，非牛顿流体的瞬时速度响应与在驱动壁面上所施加的正弦形式的脉动驱动形式不同，横螺槽方向的环流中心位置受幂律指数影响，且发生周期性改变。振动的引入使得在相同的时间内，物料的流动路程增加，且可增大物料的平均停留时间，有利于改善混合效果。     

Mixing and residence time distribution in melt screw extruders

The residence time distribution (RTD) functions were derived for screw extruders, based on the “parallel plate” and curved channel flow models. The results indicate a relatively narrow distribution, and they explain several characteristics of screw extruders. The strain distribution in the fluid across the channel was also derived. With the aid of these two functions an average strain of the fluid leaving the extruder was defined. The resulting weighted-average total strain (WATS) provides a quantitative criterion to the “goodness of mixing” in extruders.