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     

Interface determination in bicomponent extrusion

The unidirectional flow of two immiscible fluids with different viscosities in a long die of arbitrary shape is considered. Mathematically, the problem has a continuum of solutions corresponding to arbitrarily prescribed interface shapes, but experimental evidence indicates the existence of a unique interface shape with the less viscous fluid encapsulating the more viscous fluid. With the introduction of the minimum viscous dissipation principle, which postulates that the amount of viscous dissipation is minimized for a given flow rate, the problem becomes a nonlinearly constrained optimization problem. A generalized reduced gradient/finite element method combination is used to predict the interface shape when two inelastic fluids are considered. The effect of the viscosity ratio and flow-rate ratio on the interface shape is examined for different die geometries. Inner layer breakup phenomena are predicted and explained for complex die geometries.     

Modeling of complex parison formation in extrusion blow molding: Effect of medium to large die heads and fuel tank geometry

This work presents the effect of die geometry and die gap opening on the extrudate swell phenomenon, in complex parison formation using the vertical wall distribution system (VWDS) and partial wall distribution system (PWDS). The BlowParison^© software from IMI is used to predict the parison formation for a combined VWDS/PWDS system, accounting for swell, sag, and nonisothermal effects. This software couples a fluid mechanics approach to represent the die flow, with a solid mechanics approach to represent the parison behavior outside the die, and a mathematical swell model to account for the pronounced elongational and shear stresses at high Weissenberg numbers. The emphasis is placed on experimental validation of the predicted parison dimensions using four diverging die geometries and different sets of VWDS/PWDS profiles. The experimental and predicted weight profiles for a dissected fuel tank are also presented. Both experimental and simulation results suggest a strong dependence of extrudate swell to the die geometry in the die land zone. The results also demonstrate the validity of the numerical predictions for part design purposes given the multitude of experimental validations presented in this work. POLYM. ENG. SCI., 2009. Published by the Society of Plastics Engineers     

Rheological behavior and fiber orientation in slit flow of fiber reinforced thermoplastics

The flow behavior and fiber orientation in slit flow of a short fiber reinforced thermoplastic composite melt are investigated. A slit die with adjustable gap and interchangeable entrance geometries was designed and built. The slit die is fed by a single screw extruder. The bulk viscosity is calculated from the axial pressure profiles measured using three flush mounted pressure transducers. The effect of entrance geometry and gap dimensions on the fiber orientation and bulk flow behavior is specifically considered. A skin-core composite fiber orientation is observed in the thickness direction. Fibers are oriented in the flow direction and parallel to the walls in the skin region irrespective of the entrance geometry. Different fiber orientation distributions in the core region can be realized by using different entrance geometries. However, the changes in the core fiber orientation are not fully reflected by the measured viscosities, due to highly oriented skin layer. Exit pressures obtained by extrapolation of linear pressure profiles are found to be all positive, but dependent on the die geometry and entrance conditions, even for the unfilled melts.     

Isothermal swell of extrudate from annular dies; effects of die geometry,flow rate,and resin characteristics

An experimental study was made of the effects of die geometry and extrusion velocity on parison swell for three high-density-polyethylene blowmolding resins. Four annular dies were used: a straight, a diverging, and two converging dies. Diameter and thickness swells were measured as functions of time under isothermal conditions and in the absence of drawdown. This was accomplished by extruding into an oil having the same density and temperature as the extrudate. It was observed that 60 to 80 percent of the swell occurs in the first few seconds and that equilibrium swell is attained only after 5 to 8 minutes have elapsed. The diameter and thickness swells appear to be independent phenomena, as the relationship between them depends strongly on die design. The ranking of the resins in terms of the magnitude of the swell was found to be the same for all die geometries and extrusion rates used.     

Die geometrical effect on annular die swelling

Die geometrical effect on Newtonian annular jet swelling was studied using a finite element method. Numerical result shows what we expected in the limiting cases of die swelling with annular die geometries, i.e., variation of the die gap for straight dies follows the limiting behavior of capillary and planar die swellings. Also the effect of upstream die geometry was investigated. The result shows that final extrudate dimensions are generally influenced by its previous history in the die, i.e., not only by shearing action but also by elongational effect caused by narrowing die gap.     

Measurement of stress birefringence patterns in molten polymers flowing through geometrically complex channels

Measurements were taken of stress birefringence patterns in molten polymers flowing through geometrically complex channels. Six different flow channels were constructed for experiment, some representing the flow geometries of spinnerettes encountered in fiber spinning, and others representing mold cavities encountered in injection molding. All the flow channels had two glass windows, which permitted one to take photographs of the flow birefringence patterns of molten polymers with the aid of a polariscope. Quantitative information on the stress distributions in a flow channel was obtained, with the aid of the stress-optical laws, from the pictures taken of both isochromatic and isoclinic fringe patterns. The significance of flow birefringence measurement is discussed from the standpoint of die design for extrusion operation and mold design for injection molding operation.     

Design of extruder dies using thermoplastics melt properties data

The procedures developed in this paper enable the die designer to estimate the dimensions of the die at the exit and to define a flow channel within the body of the die appropriate to the required dimensions and output rate of the extruded product. Design procedures are given for predicting die swell (and hence die exit dimensions) from a knowledge of product dimensions, output rate and the basic shear, elasticity, and viscosity data. Within the body of the die the length and included angle of a convergent tapered section should be such that the critical tensile deformation rate is not exceeded. At the die entry the taper angle is related to the tensile and shear viscosities. Analytical expressions based on flow data are given for predicting pressure drops resulting from flow through circular and slot dies of constant cross-section and through conical and wedge-shaped dies. A numerical example shows how the theory may be applied to the design of a die for a thin-walled tube. For the resultant die design, the likely effects are predicted to changes in output rate and melt temperature for the chosen material, of changes in grade of the same type of polymer, and of changes in polymer type.     

A general non-isothermal model for one-dimensional multilayer coextrusion flows

A general computation of multilayer coextrusion flow in a flat die geometry is presented. For any given number of layers of different polymers, characterized by their thermal and rheological behaviors, the model permits computation of velocity and temperature fields along the flow in constant or slightly varying geometries. The influence of different operating parameters (wall regulation temperature, flow rate, initial temperatures) on the interface positions and temperature evolutions is evaluated. Theoretical predictions of interface positions are in agreement with experiments carried out on an industrial multimanifold flat die.     

Extrudate swell from slit and capillary dies: An experimental and theoretical study

A comparative experimental study of extrudate swell from long slit and capillary dies is reported for rheologically characterized polystyrene and polypropylene melts. Generally extrudate swell from a slit is greater than that from a capillary die. At low die wall shear rates it goes to a value of about 1.2 as opposed to about 1.1 found for capillary dies. The onset and character of extrudate distortion have been studied. The experimental results are compared with theories of swell based on unconstrained recovery from Poiseuille flow in these geometries. A detailed analysis of such theories of extrudate swell based on the original work of Tanner has been carried out. The analysis is placed in a more general form which should be valid for a range of die cross-sections.     

Additive Manufacturing in Fluid Process Engineering

Additive manufacturing describes technologies that translate virtual computer‐aided design data into physical models in a fast process. While industries such as automotive and aerospace adopt this manufacturing technique rapidly, it is little applied within process engineering. Additive manufacturing offers freedom of design which gives access to novel shapes and geometries with fast production times. This review analyses the most important layer fabrication principles first and shows applications of additive manufacturing in fluid process engineering second. The review focuses on applications where liquids and gases are involved and it showcases the potential of additive manufacturing within process engineering of functional devices. Examples of current research projects show the potential of the technology for advances process engineering.     

共挤出的影响因素

本文介绍了共挤物料的粘度比、模具温度和流道几何形状几个因素对共挤出的影响规律的实验观察结果，并对其产生原因进行了分析。     

Fiber orientation in multilayer tubes processed by a conical extruder

A new extruder design has been developed for the coextrusion of two-layer annular sections. The extruder consists of a conical stator-rotor-stator assembly, which performs extrusion from each side of the rotor. Flow within this assembly is fully three-dimensional, with helicoidal streamlines in the vicinity of the rotor and the die entry region. Fiber orientation is created in a circumferential direction by these helicoidal streamlines; close to the inner and outer surfaces of the tube, the fibers are parallel to the main extrusion direction, whereas in the mid-thickness, they are oriented in the circumferential direction. It is demonstrated that the amount of orientation depends on rotor speed and die design. When using a short die and high rotor speed, an increased fraction of fibers are oriented in the circumferential direction. Polym. Compos. 25:331–341, 2004. © 2004 Society of Plastics Engineers.     

A systematic approach for the design of a spiral mandrel die

An effective design strategy is presented for the determination of optimal flow channel geometry of a spiral mandrel die, which can produce annular, thin, and uniform products of polymer melt. This strategy includes two steps: First, a two-dimensional flow simulation associated with the Taguchi approach is applied to search several sets of die geometric parameters, from which process the flow uniformity is assessed. Second, the optimum one parameter set selected by further considering total pressure drop, mixing degree and residence time distribution (RTD). The strategy is illustrated through the design of a spiral mandrel die with four spirals traveling a full 360°, and the viscosity of polymer melt is assumed to be power law model. The results indicated that the design criteria such as high flow uniformity, low pressure drop, good mixing degree and narrow RTD are difficult to attain simultaneously. For a particular polymer melt, there exists a design window for the geometric parameters; within the window the geometric parameter set may satisfy most of the design criteria.     

Microlayer and nanolayer tubing and piping via layer multiplication coextrusion. I. Validation

Layered annular structures produced with layer multiplication coextrusion, utilizing both a standard in-line “spider” die, and a custom annular die, are compared in structures up to 129 layers. One multilayered system, of a Dow LDPE 5004I was utilized in generating experimental results to validate the custom die design performance. It was found that the custom design demonstrates successful extrusion of high layer number annular structures with substantial benefits over the standard spider die. Moreover, a design method incorporating angular rotation was implemented within the custom die to eliminate weld lines and attain concentric layer structures to further enhance commercial viability and mechanical integrity. Results indicate angular rotation may be utilized to generate idealized annular products with concentric layer structures. Additionally, exploration of flow through the annular die land was conducted with ANSYS Polyflow in under several conditions of angular rotation. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 137, 48683.     

Effect of die geometry on the structural development of a thermotropic liquid crystalline polymer in a thermoplastic elastomer matrix

This study investigates deformation of a thermotropic liquid crystalline polymer (TLCP) in different die geometries. Blends of aTLCP with a thermiplastic elastomer of EPDM were made in a twin-screw extruder. Morphological observation of the extruded blends demonstrates the complimentary effect of shear in the die exit on dispersed phase deformation and fibril formation. Shear strain can affect fibril formation for a relatively large dispersed phase in the region close to the die wall. However, the main role of shearing is in breaking up the larger particles and initial polydomain structure. A strong elongational deformation on the blended melt after the die exit is required, and fine microfibrils normally obnserved in in situ composites were not easily formed by shear deformation only in the die.     

Transverse orientation dies for solid-state extrusion of polymers. Part I: Process mechanics

Solid-state extrusion of crystalline polymers is a well-known technique to produce monoaxial orientation in filaments and films. This is essentially achieved by extruding or drawing the polymer through a convergent die at temperatures below its melting point. Biaxial orientation in die drawing processes has been achieved by adding extensional forces in the transverse direction at the die exit, as in the case of tubular products. In the present study, billets of poly(tetrafluoropolyethylene) (PTFE) and ultrahigh-molecular-weight polyethylene (UHMWPE) were subjected to simultaneous deformations in the longitudinal and transverse directions, by means of dies featuring converging and diverging walls perpendicular to each other, to produce extrudates exhibiting a predominant orientation in the transverse direction. Two geometries, producing a nominal state of pure shear deformations, by maintaining constant the cross-section area at entry and exit, were examined to determine the relationship between die geometry, yielding and frictional properties of the polymer and extrusion forces. The effects of die geometry and processing conditions are analyzed in Part 2.     

Effect of die gap width on annular extrudates by the annular extrudate swell simulation in steady-states

We calculated the steady-state annular extrudate swell of polymer melts through flow geometries encountered in processes used to control parison thickness. A streamline-upwinding finite element method with an under-relaxation for the rate of deformation tensor was used. The Giesekus model was employed as the constitutive equation. An operation that widens the die gap is appropriate for the control of parison thickness corresponding to the change of die gap width. However, a control process that decreases the die gap width is not useful, because the parison thickness does not correspond to the die gap width. Furthermore, thickness swells change strikingly with the Weissenberg number. It is difficult to control the parison outer diameter in the case of a converging die, because the change of the outer diameter swell becomes large with increasing Weissenberg number. In the case of a diverging die, the changing value of the outer diameter swell is smaller than that in the case of a converging die.     

Roll compaction of maize powder

This paper presents a study of a roll compaction process as a dry granulation method for typical food materials such as maize powder. This process is widely applied in industry as it can continuously produce large quantities of granular product at comparatively low cost. The objectives of this work were to predict the roll compaction performance from a simple measurement involving uniaxial die compaction using the classical Johanson model. This involved determination of the optimum operating conditions for the production of granules as evaluated by apparent density.In the current work, a smooth counter-rotating rolling mill with a roller diameter of 0.08 m and a roller width of 0.20 m was used. The operating conditions for the rolling mill are shown to be influenced by parameters such as the roll gap, the roll speed, the feed powder amount, and the friction ratio. Material properties such as the compressibility factor and the angle of wall friction were investigated using uniaxial die compaction. The angle of wall friction was analysed using both contact mechanical and continuum mechanical approaches.The results indicated that this simplified approach can be used to provide a quantitative prediction of the extent of the roll compaction performance, and can be used to design optimal roller geometries and operating conditions.     

Flaring dies to suppress die drool

Die lip build‐up is the unwanted material accumulation on extrusion die lips. Here, flared dies are shown experimentally to suppress die lip build‐up. A semiempirical method for flared die design is also provided. Nonlinear viscoelastic constitutive equations are used to calculate the wall shear stress and first normal stress difference in flared dies. By incorporating melt memory, a promising design method for die flaring is presented. The stress history upstream of the die exit governs the die design. The upstream gap is selected to maximize undershoot of the first normal stress difference N₁ at the die wall caused by flaring. The flare length, on the other hand, is selected to ensure a steady N₁ at the die lips.