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.     

Three-dimensional flow modeling of a self-wiping corotating twin-screw extruder. Part I: The transporting section

A three-dimensional modeling of the transporting elements in a self-wiping corotating twin-screw extruder has been carried out by using the finite element package Sepran (1). This simulation uses the 3D geometry of the channel rolled over the twin-screw, which consists of the intermeshing and normal areas. The flow profile, the backflow volume, the pressure buildup, the shear and elongation rates, and the adiabatic axial temperature gradient have been calculated by solving the Navier-Stokes equations and the continuity equation for a Newtonian fluid. These results are given for different extruder parameters such as the throughput of the extruder, the rotation speed of the screws and the helix angle of the screws to better understand the influence of different extruder configurations. This study belongs to a program of research on the self-wiping corotating twin-screw extruder that also includes the modeling of the kneading elements (Part II) and, in the future, the study of scale-up and heat transfer.     

Pumping characteristics of self-wiping twin-screw extruders—A theoretical and experimental study on biopolymer extrusion

The flow of Newtonian and non-Newtonian fluids which obeys a power law relationship between shear stress and shear rate has been modeled in the melt conveying section of a self-wiping co-rotating twin-screw extruder using a finite element analysis of an unwound channel section. Predictions of throughput against pressure gradient are compared with experimentally obtained results for maize grits which is represented as a power law material. Rheological data applicable to extrusion simulation were obtained from capillary rheometry. Comparisons are reasonable with predicted characteristic showing similar behavior.     

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.     

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（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。     

Transport in a twin-screw extruder for the processing of polymers

The fluid flow and heat transfer in polymer extrusion in a twin-screw extruder was studied numerically by using the finite volume method. In the mathematical model, the coordinate system is fixed to the screw so that it is held stationary and the barrel is moved to simplify the complicated geometry. The screw channel of a twin-screw extruder is approximated as two regions: translation and intermeshing. The flow in the translation region is similar to that in a shallow single screw extruder and is treated by the numerical methods given in the literature. In the nip or intermeshing region, strong mixing effects are expected, along with the diffusion of energy and momentum. The full governing equations are solved in this region to determine the velocity components in all the three coordinate directions. The energy equation is coupled with the equations of motion through viscosity, since the viscosity of the polymeric, non-Newtonian, fluids considered here is dependent upon the shear rate and temperature. There is no clear physical demarcation between the nip region and the translation region. Therefore, a domain matching was employed at an arbitrary location that was varied numerically to ensure that the results were independent of this location. The variation of pressure and bulk temperature along the helical channel of the twin-screw extruder is obtained, along with the shear rate. An experimental investigation of the velocity profiles in the translation region of a self-wiping twin-screw extruder, which is often used in practical applications, was carried out using a Laser Doppler Anemometer. The numerically predicted velocity profiles are compared with those from the experiments, yielding fairly close agreement.     

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。     

啮合盘元件中粉体聚集体分散混合的数值模拟

采用有限元方法对啮合同向双螺杆挤出机的啮合盘元件流场进行了三维等温模拟计算，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啮合盘元件中的三维流动路径,结合粉体聚集体的分散模型和三维流动路径，计算得到了粉体聚集体在啮合盘元件出口的平均直径及其分布。     

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。     

Resin distribution along axial and circumferential directions of self-wiping co-rotating parallel twin-screw extruder

A self-wiping co-rotating twin-screw extruder (TSE) is operated in a starved state in which the screws are partially filled with resin. Understanding the resin distribution on the screw surface of a TSE in this state is essential for the design, operation, and maintenance of the twin-screw extrusion process. Accordingly, in this study, the circumferential and axial distribution of resin in a TSE were simulated using a novel method combining the mathematical formulation of Hele–Shaw flow, the finite element method, and a newly developed down-wind pressure updating scheme. The results of the simulation were found to be in good agreement with experimental measurements. The proposed simulation method enables the detailed visualization of resin distribution in the entire axial and circumferential directions over the length of a TSE, improving the ability to determine both the devolatilization and fiber attrition during the extrusion process.     

Processing of reinforced plastics using multi-screw compounders

Polymer modification by addition of reinforcing agents represents a popular means of increasing physical property values. The polymer matrix has been forced to accept up to 55 percent by weight of fibrous reinforcement and 80 percent by weight of powdered types in order to meet application requirements. These materials demand sophisticated mixing equipment which must provide extensive intake and conveying capabilities, polymer wetting of reinforcement, and dispersion of reinforcement. This process must also be conducted with controlled shear intensity and excellent temperature and residence time control in order to respect polymer thermal sensitivity and product requirements. The extrusion process is a proven economical method for incorporating reinforcements into polymer resins. Co-rotating intermeshing twin-screw extruders are particularly suited for these tasks. Positive conveying, self-wiping, and shear intensive mixing characteristics provided by the screw mechanism satisfy requirements of reinforcement compounding. This mechanism allows interruption of streamline flow which is needed to disperse both high and low aspect ratio reinforcing agents into a polymer matrix. Mathematical representation of the benefits of twin-screw extrusion (relative to single-screw) related to pumping and mixing capability have been developed based on the classical pressure flow continuity equation with proper selection of boundary conditions.     

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。     

Numerical study of twin-screw extruders by three-dimensional flow analysis—development of analysis technique and evaluation of mixing performance for full flight screws

We have developed a method for predicting the three-dimensional flow field in the melt conveying zone in counter-rotating and co-rotating twin-screw extruders. We applied this technique to the full flight screws with thin flight width and open C-shaped channels in both rotating type extruders having the same screw configurations. We compared the details of velocity and stress fields, the flow rates of transportation, and various kinds of leakage flows for both rotating type extruders. Also, we obtained the spatial distribution of tracer particles and residence time distribution using a numerical tracer experiment. The flow rate in the transport direction in the co-rotating twin-screw was larger than that in the counter-rotating twin-screw, and this suggested that the latter has higher transport performance when the screws have thin flight width and open C-shaped channels as used in this study. As for the distributive mixing, it was found that the co-rotating twin-screw excels in the area of fluid rearrangement between the two screws and distribution in the rotational direction, while the counter-rotating twin-screw has the desirable characteristic of wide distribution in the axial direction. With regard to dispersive mixing, there was no considerable difference between calculated stress fields in both rotating type extruders.     

回流对不相容体系共混物分布混合效果的影响

对啮合同向双螺杆挤出机熔体输送段6种不同螺杆构型所形成的流场进行了数值模拟,并进行了实验研究。结果表明,增大回流系数能增强共混物的分布混合效果,并且回流系数越大,分布混合效果越好。     

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。     

双螺杆挤出机螺杆组合对聚丙烯/纳米CaCO3复合材料在线流变性能的影响

采用啮合型同向旋转双螺杆挤出机制备聚丙烯(PP)/纳米碳酸钙(nano-CaCO3)复合材料,制备过程中在双螺杆挤出机末端连接Haake在线流变仪进行在线流变性能测试。研究了两种螺杆组合结构、纳米CaCO3含量对PP/纳米CaCO3复合材料在线剪切黏度的影响,比较了在不同聚合物加工流场下PP/纳米CaCO3复合材料的在线流变性能。结果表明,引入分布混炼有利于降低复合材料的剪切黏度,复合材料剪切黏度随纳米粒子的加入先呈下降趋势,当达到某一含量后,再提高纳米粒子含量会使黏度提高。     

啮合异向双螺杆挤出过程轴向循环流道三维流场分析——轴向循环流场分析(Ⅲ)

介绍了作者在啮合异向双螺杆某一轴向位置设置一非啮合段 (且该段其中一根螺杆是反向输送元件 ) ,从而将轴向循环流动的概念引入到啮合异向双螺杆挤出过程中 ,并利用ANSYS有限元分析软件对啮合异向双螺杆挤出过程轴向循环流道中的非牛顿流体等温流动进行的三维模拟分析 ;在得出速度场和压力场的基础上 ,对剪切速率、剪切应力及剪切粘度进行了模拟 ,并将各模拟结果与未引入轴向循环段的啮合异向双螺杆挤出过程常规螺纹元件流道的模拟结果进行了比较。     

Modeling of the conveying of solid polymer in the feeding zone of intermeshing co-rotating twin screw extruders

In this paper, a model for the conveying of solid polymer in the feeding zone of intermeshing co-rotating twin screw extruders is proposed. The theoretical model uses an approach that is similar to that commonly used in single screw extruders; however, it takes into account the particular geometry of the screw channel, the partially filled channel, and the special configuration of the two self-wiping screws. The model thus considers two conveying mechanisms: the first one in the channel, which is analyzed in terms of polymer-metal friction, and the second one, which is mainly an axial transport in the intermeshing zone. The theoretical predictions of the model are compared with the experimental results obtained on a laboratory extruder with a polymer in powder form, and satisfactory agreement is observed. The model enables the prediction of the evolution of the filling of the screws towards the geometry and the operating conditions. This is an important key to analyzing the thermal aspects in this zone, which can lead to a prediction of the melting capacity of the extruder. Indeed, the filling of the feeding zone defines the heat transport that occurs between the hot barrel and the solid polymer.     

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.