Scale-up rules for mixing in a non-intermeshing twin-screw extruder

Various scale-up rules and theories have been presented for extrusion, including both single- and twin-screw extruders. Until now, however, most of these theories have concerned fully-filled channels, not only for twin screw extruders of the co-rotating fully intermeshing type (COTSE) or non-intermeshing counter-rotating type (NITSE), but single screw extruders as well. As the demand for distributive mixing and devolatilization devices increases, more and more nonintermeshing twin screw extruders with regions of partially-filled channels are being used. Therefore, developing scale-up rules for such screw extruders is imperative. In this paper, scale-up rules are developed, theoretically and experimentally, by examining the relationship between distributive mixing and important flow parameters. Two partially-filled NITSE's, with screw diameters of 0.8 and 2 inches, have been studied by using a flow visualization technique entailing a dye tracer to study the effects of distributive mixing by varying such parameters as: percentage of drag flow, screw stagger, and screw velocity. Qualitative evaluation of the spread of the dye with the number of screw revolutions was obtained from videotape of the experiments. Factorial experimental design method has been applied for evaluating these results. Finally, new scale-up rules were developed and compared with rules in the literature.     

Numerical simulation of fluid flow and heat transfer in twin-screw extruders for non-Newtonian materials

A new simplified approach has been proposed for the numerical simulation of the thermal transport in corotating, tangential, and self-wiping twin-screw extruders. It is assumed that the flow domain in a twin-screw extruder can be divided into (i) the translation region (T-region), which represents a flow similar to that in a single-screw channel and (ii) the intermeshing region (I-region), which is located between the two screws. The two regions are simulated separately and then coupled for each screw section to model the overall transport in tangential and self-wiping twin-screw extruders. A finite difference method is employed for the developing flow and temperature fields in the T-region, in order to minimize the computing effort, while a finite element method is employed for determining the interchannel flow mixing and the thermal transport in the I-region. Results are obtained in terms of temperature, velocity, and pressure variations along the screw channels and mixing between the two screws.     

双螺杆挤出中聚合物熔体混合状态的统计学分析

利用POLYFLOW对啮合同向和异向双螺杆挤出机中的三维等温流场进行了数值模拟，在获得大量粒子轨迹的基础上，运用统计学指标-分配尺度和分散指数对聚合物熔体在两种挤出机中的混合状态进行了定量描述。     

啮合同向三螺杆挤出机中三维等温流动的数值模拟

Three-dimensional isothermal flow of polymer melt in the kneading-disc element of an intermeshing co-rotating tri-screw extruder was simulated by using finite element package POLYFLOW. Based on the velocity fields calculated, flow patterns of the melt were analyzed, and particle trajectories were visualized. The numerical results indicated that, in intermeshing co-rotating tri-screw extruders, particles went through three intermeshing regions during one cycle around the screws, thus achieving better plasticating and mixing than intermeshing co-rotating twin-screw extruders. Flow in the central region was also studied by using particle tracking technique, and residence time distribution (RTD) and trajectories for particles in this region were presented. The simulation results showed that there was no stagnation in the central region. This study provided a clear insight into the flow mechanism of tri-screw extrusion. It also provided a new method for studies of flow mechanisms in other complicated mixers.     

高分散混合元件设计及混合性能的研究

根据啮合同向双螺杆挤出机的啮合原理,设计了一种高分散混合双螺杆元件。运用Polyflow有限元分析软件对该双螺杆元件的3种螺杆构型的流场进行了模拟分析,并且对这3种螺杆构型进行了实验研究。研究表明,错列角为150°的元件的分散混合性能最好,其次是错列角为30°的元件,错列角为90°的元件的分散混合性能最差。     

The effect of axial pressure gradient on extruder mixing characteristics

Many twin screw extruders are operated in the starve-fed mode with the majority of the extruder having partially-filled channels. There will always be regions of totally filled channels due to the presence of the die or reverse elements. The authors experimentally show the effect of the change of percent drag flow on the rate of distributive mixing in the co-rotating and counter-rotating twin screw extruder. Optimum operating conditions for distributive mixing are identified experimentally and verified theoretically.     

啮合同向双螺杆挤出机中组合螺杆性能的数值研究（Ⅰ）瞬态流场分析

采用聚合物流动分析软件POLYFLOW,数值模拟了聚合物熔体在组合式啮合同向双螺杆挤出机ZSK60的组合螺杆中的三维等温流动。在计算所得速度场和压力场的基础上,全面分析并讨论了由不同厚度和不同错列角的捏合块元件组成的组合螺杆的流场分布规律;研究了组合螺杆的输送性能和挤出稳定性;并分别采用平均剪切速率、平均特征剪切应力以及平均拉伸流动指数等瞬态混合指数表征了组合螺杆的瞬态混合特性。此外还考察了两种不同流变性质的聚合物熔体在组合螺杆中的瞬态流场分布规律。所得结论可为双螺杆挤出的数值模拟研究提供一定的方法指导,并为其工程实践提供一定的理论指导。     

啮合同向双螺杆挤出过程停留时间分布实验研究

通过对啮合同向双螺杆挤出过程常规螺纹元件螺杆组合及引入轴向循环段的螺杆组合停留时间的实验研究，分析了轴向循环段的引入对啮合同向双螺杆挤出过程停留时间及其分布的影响。     

啮合同向双螺杆挤出机中组合螺杆性能的数值研究（Ⅱ）混合特性分析

采用有限元软件POLYFLOW,对组合式啮合同向双螺杆挤出机ZSK60中不同构型的组合螺杆进行了混合分析。通过计算螺杆转过不同角度时的拟稳态流场,采用粒子示踪分析(PTA)方法,对组合螺杆中聚合物熔体的动态混合过程进行了可视化模拟;在此基础上通过对大量粒子运动轨迹的统计处理,分别采用停留时间分布、分布混合指数、分离尺度等累积混合指数表征了组合螺杆的轴向混合性能、分布混合性能以及分散混合性能。此外还研究了不同工艺条件下组合螺杆的混合特性。并将部分数值模拟结果与前人实验研究进行了对比。     

啮合同向双螺杆挤出机普通螺纹元件中物料停留时间计算

采用有限元方法对啮合同向双螺杆挤出机的普通螺纹元件流动进行了三维等温非牛顿模拟计算，根据流场计算所得到的速度场通过编程计算得到了物料在螺纹元件中的三维流动路径，利用物料的三维流动路径计算结果分析了普通螺纹元件中物料的停留时间分布和平均停留时间随螺杆转速和挤出机产量的变化规律。     

Solid transportation in the feeding zone of intermeshing co-rotating twin-screw extruders

A mathematical model was proposed for the characteristics of solid transportation in the feeding zone of an intermeshing co-rotating twin screw extruder. The model was based on the observations made from a “transparent” extruder. The analysis considered optimal solid conveyed with maximum throughput rate, i.e., when the upper and lower intermeshing zones, and the two sides of the screws were all partially filled with solid resin to an extent that a slight increase in the solid filling would immediately cause blocking of the solid transportation. Because of these starve-fed characteristics, the conventional approach for analysing solid feeding used in single-screw extruders was inadequate for twin-screw extruders. This paper also suggests a solution for the mathematical expressions describing the stress and velocity fields in the solid feeding zone of a twin-screw extruder. Finally, the predicted values are compared with our experimental findings.     

Study of mixing efficiency in kneading discs of co-rotating twin-screw extruders

Co-rotating twin-screw extruders are widely used for compounding and blending in polymer processing. In a modular machine, the dominant elements determining dispersive mixing efficiency are the kneading discs. A fluid dynamics analysis package - FIDAP, using the finite element method was implemented to simulate the 3-D isothermal flow patterns in the kneading disc region of a Werner & Pfleiderer ZSK-53 co-rotating twin-screw extruder. The kneading discs simulated are three-lobe discs. The flow field characteristics relevant for dispersive mixing are shear stresses generated and elongational flow components. We compare these flow characteristics for the three-lobe kneading discs of the ZSK-53 with the two-lobe discs of a ZSK-30 machine. We also discuss the influence of processing parameters on the flow field mixing efficiency.     

波状双螺杆元件混合性能的研究

对同向波状双螺杆元件和常规螺纹元件的分散混合性能进行了数值模拟,分析了2种元件流场的平均剪切应力、最大剪切应力分布、最大拉伸应力分布等混合性能参数,并对其进行了实验研究。模拟结果与实验结果基本吻合。结果表明,波状双螺杆元件有较强的分散混合能力。     

新型同向双螺杆元件——S型元件研究（Ⅰ）——流场数值模拟

对一种作者设计的新型同向双螺杆元件－S元件进行了流场计算。建立了三维非牛顿等温流场模型。利用ANSYS软件和自行编程计算了元件流场中的压力场，挤出量，回流量，速度场，剪切速率和拉伸速度，并对S形元件的流场与常规螺纹元件的流场作了一定的比较。在后续的文章中将对S形元件的流场及常规螺纹元件的流场计算结果进行实验验证。     

A 2-d numerical study of intermeshing self-wiping screws in biopolymer extrusion

A knowledge of flow behavior is important in the study of laminar flow in twin-screw extrusion processes to predict the velocity distribution and to understand the mixing process. The flow of a power law fluid in self-wiping twin-screw extruders is examined using a two-dimensional finite element analysis of a mid-channel section of intermeshing screws. Theory is compared with experiment using food biopolymer and plastic materials. Comparisons showing overprediction of throughputs, but similarities in behavior, suggest that this model could provide an upper limit for melt conveying. For most of the throughput range examined, pumping of intermeshing self-wiping screws appears to be almost independent of the power law flow index of the melt extruded, but the value of the flow index determines the degree of influence intermeshing has on the overall pressure gradient generated in the extruder.     

3‐D numerical analysis on the mixing performance for assemblies with filled zone of right‐handed and left‐handed double‐flighted screws and kneading blocks in twin‐screw extruders

We have calculated and visualized numerically the mixing performances of four kinds of assemblies in twin‐screw extruders that were composed of right‐handed or left‐handed double‐flighted full flight screws and neutral or left‐handed stagger angle kneading blocks, taking into consideration industrial usage. We have found that the mixing performance of a kneading block interposed between full flighted screws is strongly influenced by the flow of full flighted screws, in particular that of a neutral kneading block. Furthermore, we have proposed the simple mixing indices, which could describe both uniform mixing and heterogeneous mixing, and also applied them to our marker tracking results of four kinds of assemblies. We found that more uniform mixing is obtained for the assembly that has a neutral kneading block before the right‐handed full flight screw, and a more enhanced heterogeneous mixing is obtained for the assembly that has a left‐handed kneading block before the left‐handed full flight screw. The reason for the latter mixing ability will relate to the quasi‐channels of the left‐handed kneading block, through which marker clusters flow while elongating.     

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.     

Numerical simulation and experimental verification of nonisothermal flow in counter‐rotating nonintermeshing continuous mixers

We have developed non‐Newtonian and nonisothermal flow simulation codes in twin screw extruders using the finite element method. These codes can simulate the fully filled part of several kinds of screw elements, such as full flight screws, kneading discs, rotors, and their combinations. In this paper, we describe how we applied them to simulate a counter‐rotating nonintermeshing continuous mixer, LCM100G, by Kobe Steel, Ltd. The LCM100G is a Farrel‐type continuous mixer that has two mixing stages. We focused on the second mixing stage, since the flow domain of this stage is almost filled by polymer melts. Numerical simulations at various flow rates were performed. We also carried out experimental observations to verify the numerical simulations. Pressure and temperature profiles from the simulations were found to be in good agreement with the experimental results.     

Simulation of flow in compounding machinery: Internal mixers and modular corotating intermeshing twin-screw extruders

Hydrodynamic lubrication theory has been applied to analyze flow in internal mixers and twin-screw extruders. Fluid motions in mixing regions are interpreted as being due to coupling of drag flow and pressure gradients. Pressure fields and mean flow patterns have been computed. Distributive and dispersive mixing are interpreted in terms of computed fluid fluxes in the processing machinery.     

Measures of mixing in laminar flow

The general domain in which this work resides is that of mixing in creeping flows. Mixing, in this context, refers to the stretch of an interfacial line, or area in a strain field. The advancement of mixing technology is applied to the design of continuous mixers used in polymer processing. The geometric designs included single screw extruders, static motionless mixers, and co- and counter-rotating twin screw extruders. The co-rotating twin screw extruder was chosen to be studied in detail since it enjoys wide applications and, for which, little understanding of the contribution to mixing in the different screw geometries is known. In order to evaluate the rate of mixing for the non-uniform strain history flows, the method for measuring mixing had to be reexamined and broadened. An automated method has been developed which incorporates a digital camera and a computer to analyze the cross-sections of interest. Two measures of mixing—the correlation function and the distribution function—are developed to describe mixing in these regimes. These measures are applied successfully to the mixer geometries revealing subtle differences as to the nature of mixing in each.