Non-isothermal flow of a molten polymer in a coat-hanger die

The non-isothermal flow of a power-law fluid in a coal-hanger flat die is studied. Equilibrium and thermal equations are solved by using an iterative finite difference method. The pressure distribution, the flow lines, the residence time distribution, the temperature distribution, and the flow uniformity at the end of the die are obtained, with a stress on the effect of thermal regulation and of temperature dependence of the viscosity.     

Computer-aided geometric design of the preform dies for flat film extrusion through 3-D finite element flow analysis

A rational computer-aided design procedure is presented for determining the optimum flow channel geometry of a flat film die, which yields a minimum pressure drop and produces a uniform transverse flow rate distribution. The three-dimensional die surface is generated by analytic expressions that represent a dumbbell-like contour. The die surface may be specified by several geometric parameters. The length of the transition zone turns out to be the controlling parameter. Because of the complicated geometric boundary, it is not possible to optimize the flow channel geometry explicitly; instead, a computer trial procedure is employed. The numerical computation is based on an isothermal three-dimensional flow model, which assumes power law behavior for the polymer melts. The calculated results indicate that for a particular polymer and a particular aspect ratio of slit, there may exist an optimum transition length from which the flow channel geometry of a flat film die may be uniquely defined.     

管道泡状流相分布模式和分布机理研究进展

对管道泡状流的相分布模式和分布机理进行了详细的回顾和介绍。从前人研究的结果发现,相分布与流动条件有关,对于小管径泡状上升流,相分布主要表现为壁面峰值分布、中间峰值分布、中心峰值分布、过渡分布和扁平分布模式;而对于小管径泡状下降流,相分布主要表现为偏离中心峰值分布、钟形分布和中心峰值分布模式。然而对于大管径泡状流,相分布与流向无关,主要表现为壁面峰值分布和中心峰值分布两种模式。除此之外,还存在双峰分布模式和双鞍分布模式。影响相分布的主要因素有气泡尺寸、管道尺寸、气液相速度、气泡的注入位置和注入方法、重力水平,而气泡尺寸为关键因素。调查发现,到目前为止仍未形成一个可以解释所有相分布模式的通用机理。部分物理现象仅通过分析升力、湍流扩散力、壁面斥力以及其他力的平衡给予定性分析。未来应进一步研究相间作用力模型、湍流相干结构对气泡输运机理等问题。     

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.     

The measurement of thermal stress distributions along the flow path in injection-molded flat plates

Internal stresses in injection-molded parts are the result of thermal, flow, and pressure histories. Internal stresses can be roughly divided into thermal and flow-induced stresses. In this paper, a modified layer-removal method is presented to determine thermal stress distributions in injection-molded flat plates. With this method, the curvature of a rectangular specimen is determined after the removal of a layer from one surface. This curvature is converted into a stress via a mathematical relation, originally derived by Treuting and Read. By determining the local curvatures after successive layer removals, stress distributions along the flow path were obtained within a single specimen. Validation of this modified layer-removal method is described. A good reproductibility was obtained. The method can be regarded as semi-quantitative. Flat plates were injection-molded from three amorphous polymers: polystyrene, polycarbonate, and a polyphenylene ether/high-impact polystyrene blend. In general, the flat-plate cross-section shows a three-region stress distribution with a tensile stress region both at the surface and in the core of the flat plate and an intermediate region with compressive stresses. The modified layer-removal method was used to determine influences of mold temperature, annealing treatment, and pressure history on the thermal stress distributions. Increasing mold temperature results in a decreasing overall stress level, while the compressive stress region shifts to the surface. An annealing treatment significantly reduces the overall stress level, without affecting the stress pattern. Stress distributions along the flow path were influenced by the varying pressure histories from the entrance to the end of the mold cavity. The various features of the stress profiles are explained by the influence of the pressure decay rate in the injection-molding process.     

Uniformity of flow from sheeting dies

A numerical method for analyzing the uniformity of flow from sheeting dies is presented. The method assumes that the flow is isothermal and that the material is a power law fluid. A uniformity index is defined and methods are presented which enable die dimensions to be established which will result in a specified uniformity at particular flow rates and pressure drops. The analysis shows that the flow index “n” of the power law is the key parameter determining the uniformity of flow from a sheeting die.     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part I: Modeling

The multilayer stratified flow of several polymers in a flat coat-hanger die was modeled using a finite element method. The problem was formulated using the lubrication approximation theory. A solution procedure in decoupling pressure and streamlines was developed. This new method is very powerful in comparison with more classical approaches, permitting the solution of flow problems involving a great number of layers in a complex industrial geometry. It allows us to obtain, among other things, pressure field, streamlines, residence times, and the values of the interface positions in the whole die.     

Two directional coextrusion flow of two molten polymers in flat dies

A theoretical study has been carried out of the two directional isothermal flow of two molten polymers in a flat die. The viscous behavior of each fluid is described by a power-law. Using an iterative finite difference method, a numerical program predicts the influence of geometrical and Theological parameters on the variations of the interface position. Theoretical values are in good agreement with experimental results obtained on a fish-tail die. In the case of a coat hanger-die, the mean value of the interface position is correct, but the general shape may be quite different.     

A flow model for non-newtonian liquids inside a slot die

A one-dimensional flow model for non-Newtonian liquids inside a dual-cavity slot die is presented. The model is capable of analyzing slot dies of any cavity shape, cavity taper, slot-length variations, and slot-gap variations. The proposed model incorporates a truncated-power-law model for the viscosity of non-Newtonian liquids. According to flow models with power-law approximation for liquid viscosity, the distribution of non-Newtonian liquid through a slot die depends on the slot Reynolds number only. With our model, we find that the zero shear viscosity and the relaxation time of a non-Newtonian liquid have large effects on its distribution. For non-Newtonian liquids which are expected to experience shear-thinning over portion of a slot die, it is concluded that a flow model with a truncated-power-law approximation for liquid viscosity be used to predict the liquid distribution from the die.     

Flow,pressure distributions,and internal forces in stacked-disc filters

A mathematical model is described for isothermal flow of Newtonian liquids through stacked-disc filters. Dimension-less flow rates, velocities through filter media, pressure distributions, and internal forces are shown as functions of resistance ratios and reduced dimensions. The distribution of velocities through the media is a strong function of the ratios of the resistances to flow through the gaps between discs and through the spaces inside the discs to the resistance to flow through the filter media. Internal forces compress the discs and can, in exceptional cases, impair the media and open up leakage passages.     

Three-dimensional finite element analysis of polymeric fluid flow in an extrusion die. Part I: Entrance effect

The Galerkin finite element method has been applied to study the three-dimensional flow field of power-law fluids inside an extrusion die. Two inlet designs, i.e., center-fed and end-fed, have been considered. The effects of inertial force as represented by the Reynolds number Re, inlet geometry, and the power-law index n on lateral flow uniformity and vortex formation in the entrance region have been examined. A flow visualization technique has been carried out to experimentally verify the theoretical prediction of the three-dimensional flow field inside a die. It has been found that increasing Re or decreasing n will deteriorate flow uniformity. Depending on the direction of the inlet jet stream, the inertial force may create a flow peak in the central region of a center-fed die, or the maximum flow rate will appear close to the end of the die for an end-fed die. For highly shear-thinning fluids, lower flow rates are always observed close to the end of the dies. It is concluded that creating a plug flow in the inlet tube of the extrusion die is advantageous for both center-fed and end-fed designs.     

The flow distribution of molten polymers in slit dies and coathanger dies through three-dimensional finite element analysis

The isothermal flow of power-law fluids in slit dies and coathanger dies is studied. A general three-dimensional finite element code is developed for the purpose of flow analysis. The pressure distribution, the velocity distribution, and the transverse flow rate distribution are obtained. The effect of the die geometry on the flow distribution is critically discussed. It is found that a die channel with cross section of dog bone profile produces a flatter transverse flow rate distribution.     

Effect of wall slip on the uniformity of flow from sheeting extrusion dies

A theoretical study for analyzing the uniformity of flow from sheeting extrusion dies is presented. In this study it is assume that a slip condition exists at the wall of the die, the magnitude of slip velocity is proportional to the shear stress at the wall, the flow is isothermal and steady state, and a power law model is valid for viscosity. Two extrusion dies, T-dies and coat-hanger dies, are examined. The flow uniformity at the exit of the die is calculated and compared with that for a nonslip analysis. The discrepancies between the slip and nonslip models imply that the wall slip condition induces a significant nonuniform flow distribution. Traditional design criticism based on the nonslip model are invalid for flow with the wall slip condition, and it is necessary to increase the length of the die land to even the flow distribution at the exit of the die.     

Estimation of void boundaries in flow field using expectation–maximization algorithm

Phase distribution in the flow field provides an insight into the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase boundaries. Electrical impedance tomography (EIT), which has high temporal characteristics, has been used as an imaging modality to estimate the void boundaries, using the prior knowledge of conductivities. The voids formed within the process vessel are not stable and their movement is random in nature, thus dynamic estimation schemes are necessary to track the fast changes. Kalman-type estimators like extended Kalman filter (EKF) assume the knowledge of model parameters, such as the initial states, state transition matrix and the covariance of process and measurement noise. In real situations, we do not have the prior information of the model parameters; therefore, in such circumstances the estimation performance of the Kalman-type filters is affected. In this paper, the expectation–maximization (EM) algorithm is used as an inverse algorithm to estimate the model parameters as well as non-stationary void boundary. The uncertainties caused in Kalman-type filters, due to the inaccurate selection of model parameters are overcome using an EM algorithm. The performance of the method is tested with numerical and experimental data. The results show that an EM has better estimation of the void boundary as compared to the conventional EKF.     

A rotating two-phase gas/liquid flow regime for pressure reduction in underwater plasma arc welding

Plasma arc welding processes are used in the off-shore industry for construction and maintenance of underwater structures and pipelines in a wet environment. At greater water depths the density of the plasma gas increases because of the greater hydrostatic pressure. This causes conductive heat losses to the wet environment to increase. To maintain the energy flux to the workpiece to be welded, the plasma arc has to burn in a local dry area with an inside pressure of 1 bar. This requirement can be fulfilled by a rotating cylinder with a liquid film flowing down the inner wall. The flow around the rotating cylinder is experimentally investigated. The rotating cylinder is placed above the work surface which is simulated by a flat plate. Because of the centrifugal forces of the rotating flow inside the gap between the lower end of the cylinder and the flat plate the water is forced out of the cylinder. The velocity distribution in the flow is measured by laser Doppler anemometry. The phase distribution in the two-phase flow in the gap is measured by local electrical probes. The static pressure inside the gaseous atmosphere is reduced in comparison to the hydrostatic pressure of the surrounding water. The pressure reduction is given by the void fraction, the phase distribution and the volume flow rates of both phases in the gap as well as by the speed of revolution and the design of the cylinder and the work surface. The influence of these parameters on heat transfer from the workpiece to the two-phase flow regime is also investigated.     

制冷剂在微通道扁平T型管内的气液两相流相分配特性研究

气液两相流在常规T型管内的相分配特性已得到充分研究,但少有文献关注微通道扁平T型管内的两相流分配特性。以两相制冷剂R134a为工质,对扁平T型管内的相分配特性进行了实验研究。实验结果表明,气液两相流在扁平T型管内的液相进口流速增加会使液相分离比减小,气相分离比增大;进口干度增加使液相分离比增大,气相分离比减小;气相进口流速对扁平T型管内泡状流的相分配影响较小。由相分配模型预测值与实验值对比可知,现有的相分配模型还无法准确预测扁平T型管内泡状流的气液相分离比。在进口干度为0.45~0.5时扁平T型管内制冷剂R134a气液相分配比较均匀。     

Polymer flow through capillaries of variable diameter

A polystyrene melt has been extruded through successive capillaries arranged to produce converging and diverging flow patterns through the twin orifices. Applied pressure at fixed mass flow rate through the combined dies is equal to the sum of the pressure drops in the single capillaries in both flow modes. The Bagley end correction was found to apply to each die in the sequence. Bagley plots were linear with a particular upper capillary at given apparent shear rate in the lower die. No effect of shear history could be detected on the viscous behavior of the polymer, but preshearing in converging flow produced a slight reduction in die swell.     

Development of freeze flow apparatus to study filled polymer melts

A novel method to study the distribution of filler particles and polymer orientation of a polymer melt within a capillary die has been developed. Material within the die is quench‐cooled and then removed to provide information about the flow regime at the instant it was frozen. The equipment has been used to examine calcium carbonate‐filled high density polyethylene under high shear. The samples were examined using Energy Dispersive X‐ray Spectrometry (EDS) as well as being studied using X‐ray Diffraction (XRD). The distribution of filler particles across the radius of the capillary has been studied at high and low wall shear rates using EDS. A constant particle distribution across the radius of the die was observed for both flow regimes. The arrangement of crystalline structures within the specimens was examined by XRD. An increase in crystalline order was noticed with increasing wall shear rate. POLYM. ENG. SCI., 47:1937–1942, 2007. © 2007 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.