Conjugate transport in polymer melt flow through extrusion dies

A numerical study is carried out on the conjugate thermal transport in polymer and food melts flowing through extrusion dies. The simulation is performed to determine the influence of conduction through the die wall and of the thermal boundary conditions on the transport in the fluid and on the conditions at the outlet. An extrusion die with a uniform temperature or heat transfer coefficient specified at the outer surface is considered. It is found that, because of conduction in the solid wall, important physical variables such as centerline velocity, pressure drop, bulk temperature of the fluid and shear experienced by the fluid are strongly affected by the boundary conditions, as well as by the wall thermal conductivity and thickness. Channels of different geometries are used for the study. The flow in a circular straight tube with constant wall thickness is studied first. Flow and thermal transport in different, constricted, channels are studied next. Different wall materials are also considered. Comparisons with some experimental results are presented, indicating good agreement. The fluids considered in this study are highly viscous, polymer melts. Due to high viscous dissipation and temperature-dependent viscosity, the flow and heat transfer are coupled and the problem is quite complicated. The results show that, for some operating conditions, the bulk temperature can be high enough to cause significant heat transfer from the fluid to the wall. The downstream variation in the pressure and temperature are calculated. The thermal boundary conditions are found to have a strong influence on the temperature field and thus on the flow. The general dependence of pressure drop on temperature, flow rate, and geometry is investigated. Several other basic aspects of this problem are also discussed.     

Modeling of three‐dimensional flow and heat transfer in polystyrene foam extrusion dies

A three‐dimensional mathematical model was developed to investigate the nonisothermal, non‐Newtonian polymer flow through the dies used in the polystyrene foam extrusion process. The model, based on the computational fluid dynamics (CFD) code, Polyflow, allowed for the shear rate and temperature dependence of the shear viscosity of the blowing agent laden polystyrene melt. The model also accounted for viscous heating. The shear viscosity of the polystyrene‐blowing agent mixture was measured experimentally at several temperatures. The model was used to calculate pressure, flow, and temperature distributions in two different dies used for industrial‐scale extrusion of polystyrene foams. The article presents a selection of computed results to illustrate the effect of die design on uniformity of flow at the die exit, the overall pressure drop in the die, relative magnitudes of pressure drop in the land section versus the rest of the die, and temperature distribution in the die. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

The influence of power‐law rheology on flow distribution in coathanger manifolds

Coathanger dies are effective in delivering uniform flow if a polymer melt; however, when the fluid flow index varies from the design values, the flow is not uniform. Although mechanisms such as die lip adjustments have been effective tools for adjusting flow profiles, the issue of a variable flow index has not been fully addressed at the design stage. An analytical solution, based on the assumptions present in the 1‐D design equation, has been developed for the flow distribution in a coathanger manifold. This solution determines the flow distribution for a power‐law fluid with a flow index n* in a manifold designed for a separate flow index n*. From this solution, a uniformity index and a critical design angle are defined. The critical design angle is the angle at which the local derivative of the uniformity index with respect to n* approaches a maximum (for n* < n) or a minimum (for n* > n) as a function of the design angle. The critical design angle is independent of n and is presented as a function of the manifold aspect ratio.     

Design of dies for the extrusion of sheets and annular parisons: The distribution problem

A systematic design of the classical “coat hanger” die is proposed and tested experimentally. The objectives of the design are 1. distribution of the polymer over the width of the die before it reaches the final lip section for thickness adjustment, 2. invariance of distribution to flow rate, 3. invariance to changes in polymer viscosity, and 4. uniform average residence time. The die design is based on a flow model which assumes power-law viscosity, steady shear flow In each cross-section, uniform temperature, and separation of the flows into a manifold component and a component in a slit section of uniform height. The design corrects for an oversimplification of the pressure gradient that was applied in previous studies; and it differs from previous designs by suggesting a rectangular cross-section for the manifold. Applications to side-fed dies for extrusion blow molding and to a sheet extrusion die achieved uniform distribution and did not require any additional flow corrections (such as choker bars or flexible lips). With the new design, the lip region of the die can freely be used for thickness control, fine tuning, or further shaping of the extrudate.     

导热油进口速度对造粒模板造粒带温度均匀性影响

造粒模板是切粒系统的主要部位之一，造粒模板内部包括加热通道与物料通道，通道内部流动介质分别为导热油和聚乙烯。探究在同等条件下，导热油进口速度分别为0.01、0.05、0.1 m/s的情况下物料挤出速度与造粒带温度分布的均匀性。应用SolidWorks软件对造粒模板进行三维建模，采用ANSYS软件对聚合物与导热油的流动与传热进行数值模拟，获得了造粒模板的温度分布与流体流场分布。结果表明，导热油的进口速度对造粒模板温度场的影响明显，导热油进口速度在0.01、0.05、0.1 m/s 3个条件下，物料的挤出速度变化不大，造粒带的温差分别为14.08、7.14和5.39 ℃。在导热油进口速度为0.1 m/s时，造粒带温度分布最均匀。     

Thermal and hydrodynamic characteristics of constructal tree‐shaped minichannel heat sink

A three‐dimensional thermal and hydrodynamic model for constructal tree‐shaped minichannel heat sink is developed. The heat and fluid flow in the constructal heat sink with an inlet hydraulic diameter of 4 mm are numerically analyzed, taking into consideration conjugate heat transfer in the channel walls. The pressure drop, temperature uniformity, and coefficient of performance (COP) of the constructal tree‐shaped heat sink are evaluated and compared with those of the corresponding traditional serpentine flow pattern. The results indicate that the constructal tree‐shaped minichannel heat sinks have considerable advantages over the traditional serpentine flow patterns in both heat transfer and pressure drop. The strong and weak heat flow can be effectively allocated in tree‐shaped flow structures; hence, the inherent advantage of uniform temperature on the heating surface in the constructal tree‐shaped heat sink is demonstrated. And in tree‐shaped flow structures, the local pressure loss due to confluence flow is found to be larger than that due to diffluence flow. In addition, an aluminum constructal tree‐shaped minichannel heat sink is fabricated to conduct the verification experiment. The experimentally measured temperature distribution and pressure drop are in agreement with the numerical simulation, which verifies that the present model is reasonable. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Flow behavior of polypropylenes with different molecular structures in a coat‐hanger die

An experimental investigation of the flow behavior of three polypropylene melts with different molecular structures during extrusion through a coat‐hanger die is presented. Two linear and one long‐chain branched material, rheologically characterized in shear and elongation, were investigated. Using laser–Doppler velocimeter measurements of the velocity profiles across the gap height were performed at five various locations along the die. The uniformity of the velocity distribution along the die has been assessed using the maximum velocities v₀ of the corresponding velocity profiles across the gap. The velocity distribution along the die changes with throughput and temperature. Regarding the rheological properties, it was found that the power‐law index of the viscosity as a function of shear rate has a decisive influence on the uniformity of flow but that the pronounced strain hardening in elongation typical of the long‐chain branched polypropylene is not reflected by the velocity distribution along the die. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Velocity measurements on a polypropylene melt during extrusion through a flat coat‐hanger die

An experimental investigation of various flow regimes observed during the extrusion of a polypropylene melt through a flat coat‐hanger die by laser‐Doppler velocimetry (LDV) is presented. LDV measurements of the velocity profiles across the gap of the die at various locations along the die reveal three different extrusion regimes. At small wall shear stresses, the velocity profiles can be fitted by symmetrical curves with the velocities becoming zero at the die walls. These profiles are not uniformly distributed along the die. An increase of the wall shear stress reveals a second flow regime characterized by a uniform distribution of the velocity profiles along the die. As the wall shear stress is increased even further, a third flow regime characterized by wall slip on the glass windows is observed. This flow regime is systematically characterized by measurements of the slip velocities at various temperatures and throughputs. The maximum velocities along the die are taken to assess the uniformity of flow which decisively influences the thickness of the extruded film. By measuring velocity profiles, at different throughput, and temperatures, the conditions for constant velocities along the die were determined. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Optimization of the coathanger manifold via computer simulation and an orthogonal array method

A well-designed coathanger die may deliver a polymer melt through the die more uniformly. However, it is difficult to optimize the manifold profile because of the complexity of flow distribution with regard to problems of die geometry, temperature, shear, and viscoelastic effects. The empirical methods have been widely used to design the manifold of a flat slit die. But this approach is time consuming and causes die material waste due to the iterative design process. With computer simulation, die designers can repeat modifications to obtain the optimal manifold shape easily. In this research, the Taguchi method was used to investigate the influences of the materials, die geometry, and processing conditions on optimizing the manifold profile. The comparison of the thickness distributions with and without modified manifold showed that the modified manifold improves the thickness uniformity significantly.     

Mixed convection flow of non‐Newtonian fluid from a slotted vertical surface with uniform surface heat flux

In the present paper, the combined convection flow of an Ostwald–de Waele type power‐law non‐Newtonian fluid past a vertical slotted surface has been investigated numerically. The boundary condition of uniform surface heat flux is considered. The equations governing the flow and the heat transfer are reduced to local non‐similarity form. The transformed boundary layer equations are solved numerically using implicit finite difference method. Solutions for the heat transfer rate obtained for the rigid surface compare well with those documented in the published literature. From the present analysis, it is observed that, an increase in χ leads to increase in skin friction as well as reduction in heat transfer at the surface. As the power‐law index n increases, the friction factor as well as heat transfer increase.     

Optimization‐based design of polymer sheeting dies using generalized Newtonian fluid models

A polymer sheeting die design methodology is presented, which integrates finite element flow simulations, numerical optimization, and design sensitivity analyses to compute die cavity geometries capable of giving a near‐uniform exit velocity. This work extends earlier die design methods to include generalized Newtonian fluid (GNF) models that represent the shear‐thinning behavior of polymer melt. Melt flow computations and design sensitivity analyses are provided using the generalized Hele‐Shaw flow approximation with isothermal power‐law, Carreau‐Yasuda, Cross, Ellis, and Bingham fluid models. The nonlinear equations for die cavity pressure are solved using the Newton‐Raphson iteration method and design sensitivities are derived with the adjoint variable method. The die design method is applied to an industrial coat hanger die, in which a design parameterization is defined that allows for an arbitrary gap height distribution in the manifold of the die. In addition, die performance is assessed and compared for power‐law and Carreau‐Yasuda fluid flow over a range of die operating conditions. Pareto optimal die designs are also considered in this study. POLYM. ENG. SCI., 45:953–965, 2005. © 2005 Society of Plastics Engineers     

Three-dimensional modelling of Non-Newtonian fluid flow in a coat-hanger die

The three-dimensional model of isothermal flow of power-law fluid in a coat-hanger die has been developed using finite element method. The shape of coat-hanger die used in the present model was determined according to the previous analytical design equation which is based on one-dimensional flow model in the manifold and the slot. Because uniform flow rate across the die outlet is most important to achieve uniform thickness of extruded polymer sheet or film, flow rate distribution is mainly examined to determine the valid process condition for the design equation as the design parameters are changed. The effects of fluid property in terms of power-law index and process parameters not considered in one-dimensional design equation such as die inlet size and the presence of land were analyzed. Results show that the manifold angle is the most influencing design parameter on flow rate distribution. When the material of different power-law index from design value is processed, the change of power-law index affects the uniformity of flow rate appreciably.     

U型件的气体辅助挤出成型工艺的数值模拟与实验研究

应用Polyflow软件将气辅挤出成型引入U型件挤出成型过程中,建立了口模?气体?熔体的三相模型,在传热情况下,对口模温度、气体温度对口模内熔体的流动速度、温度及剪切速率等进行数值计算,用origin软件进行分析,通过传统挤出和气体辅助挤出成型对U型件进行挤出成型实验,选用聚丙烯（PP）材料挤出,均能顺利挤出,在达到挤出平衡后,气辅挤出时比传统挤出时更能使试样离膜下垂现象明显减弱。PP/10 %玻璃纤维在传统挤出成型时,有明显的挤出胀大现象,纤维在U型截面的侧壁与底面分布不均匀,在U型件拐角处分层分离现象严重;气辅挤出成型时,可以很好改善挤出胀大和纤维在侧壁与底面分布不均匀的现象,同时在U型件拐角处纤维分层分离的现象也能得到部分缓解。PP/20 %玻璃纤维在气辅挤出成型下挤出的U型件时,U型件壁厚变薄严重,试样中纤维分布比较均匀,拐角处无明显的纤维分层分离现象,但是试样表面有明显的纤维组织,且U型件的开口变形严重。结果表明,气辅挤出成型可以部分的减弱试样挤出后的下垂现象,也可以改善口模内熔体的温度场;传统挤出成型时候,口模内的U型件内外壁温度随着口模的变化而变化,气辅挤出成型时熔体高温区域集中在U型槽截面的中心线位置附近;气辅挤出成型与传统挤出时的剪切速率场分布发生了较大变化,气辅挤出成型时的剪切速率最大值比传统挤出时小很多。     

Study on squeezing flow during nonisothermal embossing of polymer microstructures

A numerical simulation of the hot embossing process with nonisothermal embossing conditions was carried out to observe the flow pattern of poly (methyl methacrylate) into microcavities. The microcavity was isomorphically downsized. The ratio of the cavity width over the cavity thickness was maintained constant at 8:1 throughout the analysis, while the cavity thickness varied from 200 μm to 0.5 μm. It was found that as the microcavity was downsized, the filling mechanism varied. For larger cavity thicknesses (e.g., 100 μm), the polymer flow climbed along the wall of the heated die and was then compressed downward and squeezed outward. In contrast, for a smaller cavity thickness (e.g., 5 μm), the flow was uniform and the wall‐climbing flow was absent. This size effect was correlated with the uniformity (UNF) of the temperature distribution of the polymer substrate during the embossing process. For larger cavity thicknesses, the high temperature zone was localized in the vicinity of the die wall, and consequently localized wall‐climbing flow occurred. The size effect in nonisothermal embossing was also studied experimentally, and localized flow was observed for larger cavities but not for smaller cavities. POLYM. ENG. SCI., 45:652–660, 2005. © 2005 Society of Plastics Engineers     

The application of an extrusion slit die in the rheological measurements of polyethylene composites with calcium carbonate using an in‐line rheometer

This article has reported the results of rheological testing of low‐density polyethylene (LDPE) and its calcium carbonate composites containing 7, 14, 21, and 28 wt% filler, respectively. The polymer composites were produced in a twin‐screw extrusion process. The assessment of the rheological properties of the polymeric materials was made under extrusion process conditions, using an in‐line rheometer with an extrusion slit die (W = 20, H = 2, L = 150 mm), at temperatures of 170°C, 180°C, and 190°C, respectively. The rheological parameters were determined based on the Ostwald‐de‐Waele power law model. The employed testing stand enabled the assessment of the effect of filler addition and slit die temperature on the variations in viscosity, power law index (n), consistency index (K), maximum flow velocity (V_max), and maximum flow profiles (V_z), under the conditions of technological processing (extrusion) of plastics. POLYM. ENG. SCI., 59:E16–E24, 2019. © 2018 Society of Plastics Engineers     

Nonisothermal comprehensive 3D analysis of polymer melt flow in a coat‐hanger die

The nonisothermal flow of Carreau fluid in a coat‐hanger die is studied. A general three‐dimensional finite volume code is developed for the purpose of flow analysis. The isobars, the isotherms, and the velocity distribution are obtained. Simulation results illustrated that the highest temperature occurred by the center of manifold, rather than the die‐lip region because of the combined effects of high shear rate and poor heat conduction, which is important for processing those heat‐sensitive materials. In the regions where die gap is relatively small, the wall temperature plays a key role in deciding temperature distribution in the melt. The validity of simulation results is verified experimentally. POLYM. ENG. SCI., 46:406–415, 2006. © 2006 Society of Plastics Engineers.     

Investigation of the temperature homogeneity of die melt flows in polymer extrusion

Polymer extrusion is fundamental to the processing of polymeric materials and melt flow temperature homogeneity is a major factor which influences product quality. Undesirable thermal conditions can cause problems such as melt degradation, dimensional instability, weaknesses in mechanical/optical/geometrical properties, and so forth. It has been revealed that melt temperature varies with time and with radial position across the die. However, the majority of polymer processes use only single‐point techniques whose thermal measurements are limited to the single point at which they are fixed. Therefore, it is impossible for such techniques to determine thermal homogeneity across the melt flow. In this work, an extensive investigation was carried out into melt flow thermal behavior of the output of a single extruder with different polymers and screw geometries over a wide range of processing conditions. Melt temperature profiles of the process output were observed using a thermocouple mesh placed in the flow and results confirmed that the melt flow thermal behavior is different at different radial positions. The uniformity of temperature across the melt flow deteriorated considerably with increase in screw rotational speed while it was also shown to be dependent on process settings, screw geometry, and material properties. Moreover, it appears that the effects of the material, machine, and process settings on the quantity and quality of the process output are heavily coupled with each other and this may cause the process to be difficult to predict and variable in nature. POLYM. ENG. SCI., 54:2430–2440, 2014. © 2013 Society of Plastics Engineers     

Infrared melt temperature measurement of single screw extrusion

An infrared temperature sensor has been used to provide real time quantification of the thermal homogeneity of polymer extrusion. The non‐intrusive sensor was located in the barrel of a single screw extruder, positioned such that it provided a measurement of melt temperature in the channel of the metering section of the extruder screw. The rapid response of the technique enabled melt temperature within the extruder screw channel to be monitored in real time, allowing quantification of the thermal stability of the extrusion process. Two polyethylenes were used in experiments with three extruder screw geometries at a range of screw speeds. Data generated by the infrared sensor was found to be highly sensitive to thermal fluctuations relating to the melting performance of the extruder screw. Comparisons made with an intrusive thermocouple grid sensor located in the extruder die suggested that the infrared technique was able to provide a similar level of information without disturbing the process flow. This application on infrared thermometry could prove highly useful for industrial extrusion process monitoring and optimization. POLYM. ENG. SCI., 55:1059–1066, 2015. © 2014 The Authors. Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers     

The effect of fin conductance on laminar heat transfer characteristics of internally finned tubes

An analytical solution for the temperature distribution and Nusselt number during fully developed laminar flow in internally finned tubes is obtained taking into consideration the realistic situation of fins with finite thermal conductivities. Axially uniform heat flux and circumferentially uniform temperature are assumed at the outer surface of the tube. For any tube geometry, it was found that the heat transfer characteristics are influenced by a single parameter K, which is directly related to the angle subtended by the fin, and the thermal conductivities of the fluid and the fin material. Nusselt numbers corresponding to different values of K are presented for a range of tube geometries     

Analysis of asymmetric morphology evolutions in iPP molded samples induced by uneven temperature field

Mold surface temperature has a strong effect on the amount of molecular orientation and morphology developed in a non‐isothermal flowing polymer melt. In this work, a well‐characterized isotactic polypropylene was injected in a rectangular mold cavity asymmetrically conditioned by a thin electric heater specifically designed. The cavity surface was heated at temperatures ranging from 80 to 160°C for different times (0.5, 8, and 18 s) after the first contact with the polymer. Asymmetrical thermal conditions have a strong influence on the melt flow, by changing its distribution along the cavity thickness, and final part deformation. The morphology distribution of the molded samples was found strongly asymmetric with complex and peculiar features. Optical and Electron microscopy confirmed the complete reorganization of the crystalline structures along the sample thickness. X‐rays analysis reveals that molecular orientation of the sample surface decreases with the mold temperature and the heating time. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2699–2712, 2016