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.     

聚合物熔体挤出胀大的唯象研究进展

介绍了目前国内外对聚合物熔体挤出胀大的研究工作进展,评述了近50年来挤出胀大研究发展情况。从唯象理论出发,应用张量分析方法,研究了短口模的挤出胀大行为;引入了随流坐标系的随流协变度量张量,并利用张量的特性描述了聚合物熔体微元在挤出口模的流动状态;结合流变本构方程,探讨了聚合物熔体对称和非对称的挤出离模后的胀大过程,提出挤出胀大相关研究的发展趋势,为未来研究方向提出了一个新的研究方法。     

Numerical analysis of polymer melt flow in the nipping region

In the extrusion coating process, it has never been revealed how a polymer melt flows near the nipping region and how the cooling process occurs. We created a numerical simulation program for the polymer melt flow near the nipping region using the finite element method. Numerical results showed the effects of many individual factors (e.g. line speed, melt thickness, extrusion temperature, shear‐thinning property, etc.) on the cooling process and polymer melt flow near the nipping region. It was found that a polymer melt buildup that can be observed between two calender rolls in the sheet forming process also formed in the extrusion coating process, and that the amount of polymer melt buildup (bank) depended upon the coating condition. It was found that not only line speed and melt thickness contribute to the extrusion coating process significantly, but also the rheological property has an effect on the process.     

Decoupled Gating and Simulation for Injection Molding

Polymer process control is limited by a lack of observability and controllability of the state of the polymer melt. A new polymer processing system is described that utilizes multiple self-regulating valves to independently and dynamically control the melt pressure at multiple locations in a hot runner injection mold. Concurrently, multiple process simulations are executed in parallel to analyze the flow rates, given the pressure drops between the outlets of self-regulating valves and each mold cavity. The developed simulation utilizes a hybrid finite difference and finite element scheme to simultaneously solve the mass, momentum, and heat equations including juncture losses according to a Cogswell model. Numerical verification indicates that the flow rate predictions of the described simulations compare well with the results from a commercial mold-filling simulation. However, empirical validation indicates that the process simulation is qualitatively useful, but does not yet possess sufficient accuracy for quantitative process and quality control. The most significant sources of variance were the calibration of process data and the modeling of the polymer rheology.     

Finite element analysis of thermoplastic melts flow through the metering and die regions of single screw extruders

This research work is devoted to the development of a mathematical model for the simulation of the flow of polymer melts through the metering and die regions of single screw extruders. The sets of the governing equations (flow and energy) are solved using the finite element method. The power‐law model is used to describe the non‐Newtonian rheological behavior of the fluid. The standard Galerkin technique is used in conjunction with the continuous penalty scheme to solve the flow equations. Due to the low thermal diffusivity of the polymer melts, a streamline upwinding Petrov–Galerkin method is used to obtain convergent and stable results for the energy equation. This method is based on the extension of a previously developed scheme. The overall solution strategy is based on the Picard iterative scheme. Simulation results are obtained for the flow of a polypropylene melt through the metering and die zones of a laboratory scale extruder. To validate the proposed model, the results of the computer simulations are compared with experimentally measured mass flow rate and pressure profile. These comparisons show that there is very good agreement between the model predictions and actual data. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 676–689, 1999     

数值模拟黏弹流体通过椭圆环模具的挤出胀大

The numerical simulation of extrudate swell is significant in extrusion processing.Precise prediction of extrudate swell is propitious to the control of melt flow and the quality of final products.A mathematical model of three-dimensional(3D)viscoelastic flow through elliptical ring die for polymer extrusion was investigated.The penalty function formulation of viscoelastic incompressible fluid was introduced to the finite element model to analyze 3D extrusion problem.The discrete elastic viscous split stress(DEVSS)and streamline-upwind PetrovGalerkin(SUPG)technology were used to obtain stable simulation results.Free surface was updated by updating the streamlines which needs less memory space.According to numerical simulation results,the effect of zero-shear viscosity and elongation parameter on extrudate swell was slight,but with the increase of volumetric flow rate and relax time the extrudate swell ratio increased markedly.Finally,the numerical simulation of extrudate swell flow for low-density polyethylene(LDPE)melts was investigated and the results agreed well with others’work.These conclusions provided quantitative basis for the forecasting extrudate swell ratio and the controlling of extrusion productivity shape.     

A full 3D finite element analysis of the powder injection molding filling process including slip phenomena

A full 3D finite element analysis system has been developed to simulate a Powder Injection Molding (PIM) filling process for general three‐dimensional parts. The most important features of the analysis system developed in this study are i) to incorporate the slip phenomena, the most notable rheological characteristics of PIM feedstock, into the finite element formulation based on a nonlinear penalty‐like parameter and ii) to simulate the transient flow during the filling process with a predetermined finite element mesh with the help of a volume fill factor and a melt front smoothing scheme. The treatment of the nonlinear slip boundary condition was successfully validated via a steady state pipe flow. For the purpose of comparisons, not only the numerical simulations but also experimental short‐shot experiments were performed with two 3D mold geometries using two typical materials of slip and no‐slip cases. The good agreements between the numerical and experimental results indicate that the melt front tracking scheme successfully simulates the transient filling process.     

Wall slip heating

When molten plastic is extruded, the upper limiting throughput is often dictated by fine irregular distortions of the extrudate surface. Called sharkskin melt fracture, plastics engineers spike plastics formulations with processing aids to suppress these distortions. Sharkskin melt fracture is not to be confused with gross melt fracture, a larger scale distortion arising at throughputs higher than the critical throughput for sharkskin melt fracture. Sharkskin melt fracture has been attributed to a breakdown of the no slip boundary condition in the extrusion die, that is, adhesive failure at the die walls, where the fluid moves with respect to the wall. In this article, we account for the frictional heating at the wall, which we call slip heating. We focus on slit flow, which is used in film casting, sheet extrusion, curtain coating, and when curvature can be neglected, slit flow is easily extended to pipe extrusion and film blowing. In slit flow, the magnitude of the heat flux from the slipping interface is the product of the shear stress and the slip speed. We present the solutions for the temperature rise in pressure‐driven slit flow and simple shearing flow, each subject to constant heat generation at the adhesive slip interface, with and without viscous dissipation in the bulk fluid. We solve the energy equation in Cartesian coordinates for the temperature rise, for steady temperature profiles. For this simplest relevant nonisothermal model, we neglect convective heat transfer in the melt and use a constant viscosity. We arrive at a necessary dimensionless condition for the accurate use of our results: Pé?1. We find that slip heating can raise the melt temperature significantly, as can viscous dissipation in the bulk. We conclude with two worked examples showing the relevance of slip heating in determining wall temperature rise, and we show how to correct wall slip data for this temperature rise. POLYM. ENG. SCI., 55:2042–2049, 2015. © 2014 Society of Plastics Engineers     

Finite element analysis for wavelike flow marks in injection molding

Wavelike flow marks are a kind of surface defect that can arise during the filling stage of the injection molding process. In this study, we performed a numerical analysis using a finite element method to predict the conditions under which flow marks are generated. To simplify the analysis, a two dimensional flow through a channel between two parallel plates was considered. The viscosity of the polymer melt was modeled by the Cross‐WLF equation. For the finite element analysis, a velocity–pressure formulation was used to simultaneously solve the continuity and momentum equations. The calculation domain for the numerical analysis keeps changing with time due to the advancing melt front. To handle the free surface more accurately, a moving grid method was employed. A numerical mesh was generated at each time step using an automatic mesh generation scheme. An analytical model was developed to correlate the effects of process variables to the flow mark geometry. Results of the numerical analysis were compared with the available experimental data. The estimated geometry of the flow marks were in good qualitative agreement with experimental observations. Parametric studies have been performed to examine the effects of various processing conditions and the material properties on flow mark size. POLYM. ENG. SCI., 47:922–933, 2007. © 2007 Society of Plastics Engineers     

注塑件残余热应力的数值计算

注塑件残余应力主要有流动残余应力和残余热应力 ,文中主要考虑注塑件的残余热应力 .利用文中建立的二维积分型热黏弹本构方程的递推公式 ,推导了单元的有限元求解公式 .数值算例考察了冷却效率、熔体注射温度对注塑件残余应力的影响 ,得到的结论与文献中结论一致 .     

管壁厚度对微挤出成型的影响分析

基于Bird-Carreau黏度模型,运用有限元方法对三维等温微管挤出成型流动模型进行了数值分析,主要研究了管壁厚度对微管挤出成型过程中挤出胀大、速度分布、剪切速率和口模压降等重要指标的影响。结果表明,当熔体入口体积流率相等时,随着管壁厚度的增大,挤出物挤出胀大率和横截面尺寸变化量增大;口模出口端面上熔体的二次流动增强,但挤出速度和剪切速率减小;熔体在口模内的压力降明显下降;适当增加管壁厚度,有利于提高微管挤出质量。     

Fluoropolymers and their effect on processing linear low-density polyethylene

A comparison is made of flow curves for the extrusion of a LLDPE melt through clean metal capillaries and when overcoated by fluoropolymer (FE) process aids. Characteristics differences between the flow traces include a shear-rate dependent reduction in flow resistance due to the presence of FE at the die surface. The FE preferentially wets high energy die surfaces, but interacts very weakly with LLDPE melts, thus acting as a lubricant at the polymer/stationary phase interface, and promoting the slip of LLDPE melts. Arguments are presented showing that the percent slippage time must attain an equilibrium value at high extrusion rates. Flow curves for extrusion through FE-coated dies are divided into distinct regions and the slopes of these have been rationalized by equations that combined the concepts of molecular dynamics and of adhesive failure at the die wall/polymer interface as the origins of slip-stick flow.     

Thermoplastic extrusion—the mechanism of the formation of extrudate structure and properties

Systems processed by thermoplastic extrusion can be regarded as heterophase polymer melts of incompatible water-plasticized biopolymers. In the process of thermoplastic extrusion, proteins and polysaccharides are melted at high pressure and temperature below the temperature region of their thermal decomposition. Dispersed particles of these systems can be deformed in flow. The mixed-melt anisotropic structure, formed in flow, is fixed by rapid conversion of the melt jet that lets the extruder die from a viscous state to a rubber-like state and then to a glassy state caused by cooling and drying. Incompatibility of proteins and polysaccharides in their water-plasticized melt mixtures impacts on structure formation and texturization during thermoplastic extrusion. Presented at the 20th ISF World Congress and 83rd AOCS Annual Meeting and Expo, May 10–14, 1992, Toronto, Ontario, Canada.     

Finite element analysis of polymer melt flow in cable-covering crossheads

A finite element method is presented for the analysis of isothermal non-Newtonian polymer melt flow in narrow channels of complex shape. The particular application considered is flow in cable-covering crossheads. The geometric flexibility of the finite element method allows a mesh of triangular elements to be constructed to suit the shape of the flow channel. Computed results obtainable from the analysis include the distribution of polymer layer thickness on the finished cable, together with the extrusion pressure required to maintain a given flow rate of melt. Some typical thickness distribution results are presented as an introduction to experimental verification of the method and its application to crosshead design.     

熔体挤出速度对共挤吹塑型坯离模膨胀影响的数值模拟

基于三维非等温黏弹性熔体多相分层流动有限元数值模拟技术,模拟研究了熔体挤出速度对多层共挤吹塑成型环坯离模膨胀和初始温度场的影响规律,揭示了型坯离模膨胀的产生机理。结果表明,多层共挤吹塑成型环坯离模膨胀是由熔体的二次流动诱发而产生,与熔体流出机头进入自由膨胀段的二次流动强度成正比,而其二次流动强度随着熔体挤出速度的增大而增强,因而导致环坯离模膨胀随着熔体挤出速度的增加而增大;多层共挤吹塑成型熔体的二次流动强度与其第二法向应力差成正比关联关系,这与Debbaut的试验研究结论完全吻合,表明二次流动是由第二法向应力差驱动而产生。     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Numerical simulation of polymer foaming process in extrusion flow

Computer simulations of polymer foaming processes in extrusion flow have been carried out in order to improve current understanding of viscoelasticity and bubble growth effects on die-swelling in the production of polymer foam. The linear and non-linear viscoelastic materials functions of a commercial low density polyethylene (LDPE) melt have been extracted by fitting its rheometric data with constitutive models including a simple viscoelastic model (SVM), the exponential Phan-Thien–Tanner (EPTT) model and the double convected pom–pom (DCPP) model. Simulations of LDPE melt under extrusion flow without foaming show that the predictions of the die-swell by the SVM are in reasonably good agreement with the results obtained from the EPTT and DCPP models. By comparison of the simulation results of LDPE foaming in extrusion flow using the Bird–Carreau model and the SVM, a cooperative effect of polymer viscoelasticity and bubble growth on the die-swell has been quantified. The numerical results also show that the density of polymeric foam decreases significantly with the increasing concentration of foaming agent, and that the combination of the SVM and bubble growth model can account for some essential physics of polymer foaming process in extrusion flow.     

A novel unified wall slip model for Poiseuille flow of polymer melt in the circular tube

In this study, to better reflect the slip effect of Poiseuille flow for polymer melt extruded through a circular tube, a novel unified wall slip model and flow equation based on two phase fluid system were proposed via a purely phenomenological approach. According to the different combinations of boundary conditions and flow parameters, the novel slip model was transformed into other models, such as adsorption–desorption model, entanglement–disentanglement model, lubrication layer model, Z–W model, and no‐slip model. The numerical simulation based on computed fluid dynamics was performed to verify the feasibility of the novel slip model. In the simulations, the radial flow velocity profile, shear rate, and viscosity distribution were obtained for six different models. Moreover, the effect of different slip coefficient combinations for the novel slip model on the radial flow velocity, slip velocity, volumetric flow rate error, and viscosity distribution of melt were also investigated and discussed. Results showed that the novel unified slip model not only incorporated the characteristics of other five models above mentioned, but also well interpreted the reason of simultaneously occurring the sharkskin surface defect and gross melt fracture phenomenon when flow rate of melt was extremely large. POLYM. ENG. SCI., 56:328–341, 2016. © 2015 Society of Plastics Engineers     

Melt fracture and wall slip of thermoplastic vulcanizates

Thermoplastic vulcanizates (TPVs) are blends of polypropylene (PP) (thermoplastic phase) and ethylene propylene diene monomer (EPDM) rubber (rubber phase) in which a high content of rubber EPDM is cross-linked and dispersed in a thermoplastic matrix (PP) in the presence of oil (lubricant) and filler. Depending on the molecular characteristics of the constituent polymers, the level of curing and the amount of cross-linked rubber, their processing (extrusion) exhibits various difficulties such as melt fracture (extrudate distortions). In this study, a number of different TPVs with various characteristics, including the degree of curing and amount of cross-linked rubber are examined in capillary extrusion at two different temperatures (190°C and 205°C) relevant to real processing. First, the effect of the temperature on the yield stress is investigated using rheological measurements. Consequently, the flow behavior of the TPVs in capillary flow is studied concluding that TPVs slip massively (nearly plug flow) due to the presence of lubricant and the vulcanized rubber phase. Although there is little slip observed in PP samples, EPDMs themselves exhibit severe slip and melt fracture. As a consequence, the TPV samples essentially follow the slip behavior of EPDMs. Finally, the melt fracture analysis of several TPVs has shown that with increase of temperature and amount of cross-linked rubber, the severity of TPVs' surface defects increases accordingly.     

Modeling of the impregnation process during resin transfer molding

A model has developed for simulating isothermal mold filling during resin transfer molding (RTM) of polymeric composites. The model takes into account the anisotropic nature of the fibrous reinforcement and change in viscosity of the polymer resin as a result of chemical reaction. The flow of impregnating resin through the fibrous network is described in terms of Darcy's law. The differential equations in the model are solved numerically using the finite element technique. The Galerkin finite element method is used for obtaining the pressure distribution. A characteristics based method is used to solve the non-linear hyperbolic mass balance equation. The finite element formulation facilitates computations involving the motion of the polymer resin front characterized by a free surface flow phenomenon.