Non-Newtonian tangential flow in cylindrical annuli. IV

Tangential flow of a “power law” model fluid between two concentric cylinders is analyzed. A constant angular pressure gradient is imposed and one of the cylinders is rotating at a constant angular velocity. This type of flow is of interest in screw extrusion theory. The error in the superposition, i.e., linear addition of tangential pressure and drag flows, for a “power law” model fluid, is quantitatively calculated and plotted in the form of a correction factor. Tangential pressure flow is compared to a pressure flow between parallel plates and additional correction factor to account for the curvature is derived and plotted. The applicability of the “power law” model for flow of polymer melts in extruders is also discussed.     

Theoretical model for intermeshing twin screw extruders: Axial velocity profile for shallow channels

Positive displacement intermeshing twin screw extruders have been analyzed by a simple model for flow in the channel formed by the screw root and screw flights. The model considers the down channel flow to be a combination of drage flow resulting from the relative motion of the barrel and screw and pressure flow resulting from the positive displacement action of the device. The pressure flow in this situation is distinguished from pressure flow in a single screw extruder in that the pressure forces induce flow toward the die for the twin screw model rather than away from the die as in a single screw extruder. Comparison of the down channel shear rate profile of apositive displacement twin screw extruder with that of a single screw extruder with no net flow reveals that they are identical but inverted with respect to channel depth. The model presented does not consider leakage between the twin screws or the rotational motion of the second screw.     

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.     

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.     

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.     

Residence time distribution in twin-screw extruders

Twin screw extruders are finding increased usage in reacting and devolatilizing applications. Using self-wiping profiles, the twin screws fulfill the requirement that there be no “dead” or “unmixed” zones. Agitator design must be chosen with care so that a reasonable balance can be obtained between forwarding rate, surface-generation rate, vapor passageway, power, and axial mixing. Techniques have been developed for measuring residence time distributions and characterizing axial flow behavior. The method also permits direct determination of the holdup in starved barrel applications. Data on residence time distribution are presented for 4-in. diameter twin screw equipment with a variety of rotor configurations.     

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.     

双锥型螺杆挤出机固体输送离散元分析

利用EDEM软件对一种普通锥形和两种双锥型螺杆挤出机固体输送段进行模拟.分析了高密度聚乙烯(PE-HD)颗粒在锥形双螺杆挤出机内的运动状态和分布规律.对比分析了3种锥形螺杆挤出的质量流速率、填充率、平均速度、平均压力、平均剪切应力和力矩等参数,给出了普通型和双锥型螺杆挤出机固体输送机理以及主要影响因素.结果表明,相比于...     

Comparison of scale‐up methods for dispersive mixing in twin‐screw extruders

Twin‐screw extrusion processes are commonly refined on laboratory‐scale extruders then scaled‐up to manufacturing systems. When using twin‐screw extrusion to compound filler into a polymer, the dispersion of the filler must be considered during scale‐up. In this work, two scale‐up methods are evaluated for how accurately they scale dispersion as measured by the Residence Stress Distribution, an experimental method that quantifies stress developed in a twin‐screw extruder. The first scale‐up method evaluated is the industry‐standard scaling based on maintaining equivalent volumetric flow rate across extruder sizes. Volumetric scaling is compared to a second, novel scale‐up method, the percent drag flow rule, which maintains the same degree of fill in the strongest dispersive screw elements on all extruder sizes. Both scale‐up rules have been used to scale between three extruder sizes and have been evaluated for how accurately the larger extruders recreate the dispersive mixing of the smallest machine. Results indicate that the percent drag flow scale‐up more accurately maintains dispersive mixing behavior than the volumetric scaling. Furthermore, percent drag flow scale‐up resulted in all three extruder sizes behaving similarly to changes in operating conditions. These results indicate that percent drag flow scale‐up is a valid technique to scale real industrial processes. POLYM. ENG. SCI., 57:345–354, 2017. © 2016 Society of Plastics Engineers     

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.     

Mixing mechanism of three‐tip kneading block in twin screw extruders

In recent years, twin screw extruders have been applied to various kinds of polymer processing. It has been important to find their optimum geometrical configurations and operational processing conditions for the best performance of extrusions and products. Many engineers have been evolving numerical and the experimental methods to characterize the mixing performance for twin screw extruders. We have carried out three‐dimensional flow simulations of kneading blocks in intermeshing co‐rotating twin screw extruders by using the finite element method to quantify their ability in distributive and dispersive mixing. We discuss their performance in distributive mixing for three different type of kneading blocks in terms of the residence time distribution and the nearest distance between markers at various periods of time, by using the marker tracking method. Those numerical techniques and applications of mixing indices have enabled us to quantify and evaluate their abilities in distributive mixing of kneading blocks in twin screw extruders.     

Isothermal flow of viscous liquids in corotating twin screw devices

A mathematical model is derived for isothermal flow of a Newtonian liquid through corotating twin screw equipment. Two different flow regimes are studied. In the first, channels of twin screw equipment are completely filled with liquid, generate a pressure gradient, and provide a discharge pressure at the end of the pump. Equations are given for drag flow rate, pressure backflow rate, and flow rate through the nip zone. It is shown how the analysis of single screw pumps can be modified for twin-screw pumps. In the second regime channels are partly full, which is the case with extraction equipment. Equations show how the degree of fill in the equipment changes with flow rate, speed, and dimensions.     

Melting model for modular self wiping co-rotating twin screw extruders

A model for the melting process in a self wiping co-rotating twin screw extruder is described. Self-wiping co-rotating twin screw extruders are modular and starve fed. This leads to melting mechanisms that are different from single screw extruders. The melting process in the modular screw configurations generally occurs in specialized sections such as kneading disk blocks. The model, based on our previous experimental observations, considers the formation of two stratified layers of melt in contact with the hot barrel and solid pellets in contact with the relatively colder screw. In the kneading disk blocks, a part of the solid bed is blocked because of the relative stagger between successive disks. The model predicts both the location of melting and melting lengths in a screw configuration. Calculations for individual screw elements and kneading disc elements are presented first. Melting in a modular configuration of these elements is then considered. The effect of operating variables such as mass flow rate and screw speed on melting is then studied. The model is put in a dimensionless form and the effect of various dimensionless groups is discussed. We make a comparison to the experiment and agreement is good.     

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.     

Mechanisms of mixing in single and co-rotating twin screw extruders

Previous experimental studies have revealed that the mixing efficiencies of widely used continuous processors such as the single and twin screw extruders depend on the types of screw elements, which are utilized. It is generally recognized that the basic single screw extruder and the fully-fighted sections of the fully-intermeshing co-rotating twin screw extruders are not efficient mixers, in contrast to the specialized mixing elements such as the kneading discs used in co-rotating twin screw extruders. However, no simulation techniques were available to characterize quantitatively and rigorously the mixing efficiencies of continuous processors. In this study, we have solved the three-dimensional equations of conservation of mass and momentum, and utilized various tools of dynamics to analyze the mixing occurring in single and co-rotating twin screw extruders. It is shown that simulation methods can indeed capture the relative differences in the mixing mechanisms of continuous processors like the single and twin screw extruders. The ability to distinguish quantitatively between the distributive mixing capabilities of various continuous processors should facilitate numerical testing of new continuous mixer designs, optimization of operating conditions and geometries of existing mixers and the material-specific design of new mixers.     

Modeling heat transfer in screw extrusion with special application to modular self‐wiping co‐rotating twin‐screw extrusion

This paper proposes two important models useful for describing heat transfer and temperature profiles in single and modular self‐wiping co‐rotating twin‐screw extruders. One model predicts heat transfer coefficients. Calculations of the barrel and screw heat transfer coefficients are made for various modules in different diameter extruders. We compare the values of the heat transfer coefficients from the model with those from literature. The second model predicts the axial screw temperature profile when the barrel, but not the screw, is heated, Example calculations of the cup mixing and screw temperature profiles are also made for different diameter extruders.     

螺杆挤出技术加工火炸药的研究进展

从螺杆挤出技术加工火炸药的安全性分析、所加工物料类型以及物料性能改善三方面综述了火炸药螺杆挤出技术的研究进展,指出单螺杆挤出技术存在内摩擦力较高和双螺杆挤出技术建压不足等问题,说明了锥形双螺杆挤出机加工火炸药的适应性。     

Residence time in a single screw free helix extruder using a new solution to the biharmonic equation

A new analytical solution for the biharmonic equation was developed for single screw extrusion cross-channel fluid mechanical flow. This analysis led to a quantitative model for residence time distribution when combined with the historic solutions of the drag and pressure flow in the rectangular channel in the single-screw extruder. The focus of the theoretical and experimental investigation here was to examine how closely the new analytical solution correlated with experimental residence time data for a free-helix extruder. This new extrusion device was operated as both a conventional extruder and a more positive displacement device by using only helix rotation as the pump. The Moffatt eddies that occur in the quiescent corners of the rectangular channel with screw rotation were found to have a strong effect on the residence time of the extruder. Because there were no quiescent corners for the free-helix flow there was essentially no residence time tail for this mode of extruder displacement. The theoretical results for a sheet of dye spanning the screw channel width and dye “blobs” were compared with experimental results for both modes of operation. In all cases, the experiments and the theory predictions were essentially consistent.     

Flow field analysis of the kneading disc region in a co-rotating twin screw extruder

Co-rotating, intermeshing twin screw extruders are widely used in polymer compounding and blending. Among the different modules of the co-rotating twin screw extruder, the kneading discs are the dominant ones in determining mixing efficiency. The major difficulty in solving the flow problem in the kneading disc region arises from the complex geometry and the time-dependent flow boundaries as the discs rotate. In this work, a fluid dynamics analysis package—FIDAP—using the finite element method was employed to simulate the flow patterns in the kneading disc region of a Werner & Pfleiderer ZSK-30 co-rotating twin screw extruder. The problem of time dependent flow boundaries was solved by selecting a number of sequential geometries to represent a complete mixing cycle. The flow field was characterized in terms of velocity profiles, pressure distributions, shear stresses generated and a parameter λ quantifying the elongational flow components. The last two parameters are the most important ones in analyzing mixing efficiency. The influence of design variables (stagger angle, right or left handed configuration) and processing conditions (rpm, axial pressure gradient) on the flow characteristics was analyzed.     

Steady and transient flow of a non‐Newtonian chemically reactive fluid in a twin‐screw extruder

The flow of chemically reactive non‐Newtonian materials, such as bio‐polymers and acrylates, in a fully intermeshing, co‐rotating twin‐screw extruder is numerically investigated. A detailed study of the system transient behavior is carried out. The main transient aspects, including response time, variation of system variables, and instability of operation, are studied for both single‐ and twin‐screw extruders, since single‐screw extruder modeling closely approximates the region away from the intermeshing zone in a twin‐screw extruder. The effect of a time‐dependent variation in the boundary conditions is studied. The coupling due to conduction heat transfer in the screw barrel is found to be very important and is taken into account for single‐screw extruders. In the absence of this conjugate coupling, the response time is much shorter. Several other interesting trends are obtained with respect to the dependence of the transient response on the materials and operating conditions. Steady state results are obtained at large time. The calculated velocity distributions in the screw channel are compared with experimental results in the literature for steady state flow and good agreement has been obtained. The calculated results for transient transport agree with the few experimental observations available on this system. Chemical reaction, leading to chemical conversion of the material, is also considered and the resulting effects on the flow and transport determined. These results will be useful in the design, control and optimization of polymer extrusion processes.