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.     

Numerical simulations of annular extrudate swell using various types of viscoelastic models

In this study, numerical simulations of annular extrudate swell of high density polyethylene (HDPE) were carried out. Some important viscoelastic models, such as the Larson, the PTT and the K-BKZ model, were employed for the swell calculation through various types of dies. These numerical results were compared with the experimental ones. The numerical results of the swell behaviors were very different in each viscoelastic model, while their simple shear flow characteristics were almost the same. As a result, the uniaxial elongational viscosity for large deformation as the steady state region is not important, but the property for relatively small deformation has remarkable effects on the numerical results for the die that have a uniaxial contraction region. Both reversible and irreversible types were tried for the Larson model. It was found that there was a difference between the irreversibility assumption of the K-BKZ model and the Larson model. While there was a serious difference in the response for reversing strain among these viscoelastic models, the response was very important to predict annular extudate swell behavior.     

Numerical simulations of annular extrudate swell of polymer melts

Numerical viscoelastic simulations were carried out using a K-BKZ type of separable integral constitutive equation. Both reversible and irreversible models were tried for several types of damping functions to calculate the annular extrudate behavior of high-density polyethylene (HDPE). There are two aims in this study; first, to clarify the properties of these dumping functions, and second, to investigate the influence of rheological characteristics on annular extrudate swell. In these numerical simulations, relaxation spectrum and shear viscosity were fixed, and the other characteristics were varied. The reversional response of the damping function mainly has an effect on the magnitude of the area swell even if the die is straight. The irreversible model expresses the experimental results of annular extrudate swell better than the reversible model. The accurate fitting of N1 by the damping model is important for predicting it. The magnitude of N1 predicted from the Wagner exponential model is lower than that of the PSM model, and the area swell shows the same tendency as N1. A modified PSM model that allows the N1 curve to shift can fit the magnitude of area swell. The relationship between the diameter and thickness of the extrudate depends on N2/N1, and it was estimated by simple linear elasticity of solids. The time dependent viscosity varies with the type of damping function, and it influences the time-dependent swell.     

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.     

Swell of extrudate from an annular die

Diameter and thickness swells have been measured as functions of time and wall shear rate for three high density polyethylenes at 170°C and one polypropylene at 190°C. By extruding into an oil having the same temperature and density as the extrudate, it was possible to measure isothermal swell in the absence of drawdown. Seventy to 80 percent of the swell occurs in the first one or two seconds, while several minutes are required to reach an equilibrium state. Relationships between various swell parameters, including parison weight swell and capillary extrudate swell, are examined. Important differences between the behavior of the polyethylenes and that of the polypropylene are noted.     

Measurement and simulation of low‐density polyethylene extrudate swell through a circular die

BACKGROUND: Extrudate swell is a common phenomenon in polymer processing. The investigation of its mechanism is of both scientific and industrial interest. RESULTS: The rheological parameters of a material described by the viscoelastic PTT (Phan‐Thien–Tanner) constitutive model are obtained by fitting the distributions of material functions detected with a strain‐controlled rheometer. The swelling ratios of low‐density polyethylene (LDPE) under different volume flow rates are indirectly obtained using a photographic technique. A mathematical model of extrudate swell is established and its finite element model is derived. A penalty method is employed to solve the extrudate swell problem with a decoupled algorithm. Computation stability is improved by using the discrete elastic‐viscous split stress algorithm incorporating the inconsistent streamline‐upwind scheme. CONCLUSION: The swell phenomenon of LDPE through a circular die is investigated using both experimental measurement and numerical simulation. The swelling ratios obtained from the simulation are compared with those measured: they agree well with each other. The essential flow characteristics of polymer melts are predicted and the mechanism of the swell phenomenon is further discussed. Copyright © 2009 Society of Chemical Industry     

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.     

The effect of extrudate swell on modeling the film blowing process

The extrudate swell effect has not received sufficient attention in modeling the film blowing process. This effect is addressed in this paper, and as an ab initio study, only viscous fluids were considered. The problem region was separated into two zones; the extrudate swell zone and the film blowing zone. The annular extrudate swell problem was solved using a finite element method. The film blowing process was modeled following Pearson and Petrie's (4) work. Although only viscous fluids were considered, the simulation results show a remarkable difference when swelling was included in the modeling. Viscoelastic fluids, which are more realistic for polymer melts, were not investigated here because of the so called high Weisenberg number problem. This is an open area still under investigation.     

A three-dimensional finite element analysis of the effect of reynolds number on extrudate swell of newtonian liquids from square dies

The effect of Reynolds number upon the extrusion of a Newtonian fluid exiting a square die is examined. It is shown that the extrudate swells at low Reynolds number but contracts at high ones. At zero Reynolds number, the maximum die swell ratio of 1.2 occurs. A swell ratio of one occurs at a Reynolds number of about 24. At large Reynolds numbers, the extrudate contracts to a circular cross-section with a swell ratio of 0.9611.     

Effect of filler content and additives on the extrudate swell of polyethylene pipe resin

In certain extrusion operations, particularly the production of plastic pressure pipe, it would be desirable to be able to control the degree and direction of molecular orientation. While dies can be designed to generate various types of orientation, most of this is lost at the die exit due to extrudate swell. It is known that substantial loadings of nonreinforcing filler can inhibit swell, and the objective of this study was to examine the effects of particle size and loading and of the use of coupling agents on extrudatee swell of CaCO₃-filled medium-density polyethylene pipe resin. Swell was measured as a function of time by extruding into oil having the same density and temperature as the extrudate. In addition, the storage and loss moduli of all samples were measured, and, the relaxation spectra were calculated. The maximum degree of swell suppression was observed for a compound containing 30 wt. percent of 0.4 micron particles treated with stearic acid. Surprisingly, the use of coupling agent increased the degree of swell.     

Effect of molecular structure on extrudate swell behavior for different thermoplastic melts in an electro‐magnetized die

The extrudate swell ratio of five different thermoplastic melts flowing in a constant shear rate rheometer having a capillary die with and without application of magnetic field was studied. The effects of the magnetic flux direction and density, die temperature, and wall shear rate on the extrudate swell and flow properties were investigated. The experimental results suggested that an increasing wall shear rate increased the swelling ratio for the polystyrene (PS), LLDPE, and PVC melts, but the opposite effect was observed for the ABS and PC melts. The extrudate swell ratio for the PS, ABS, PC, and LLDPE melts decreased with increasing die temperature, the effect being reversed for the PVC melt. Thermoplastic melts having high benzene content in the side‐chain and exhibiting anisotropic character were apparently affected by the magnetic field, the extrudate swell ratio increasing with magnetic flux density. The effect of the magnetic field on the extrudate swell ratio decreased in the order of PS → ABS → PC. The extrudate swell ratio for the co‐parallel magnetic field system was slightly higher than that for the counter‐parallel magnetic field system at a high magnetic flux density. POLYM. ENG. SCI., 47:270–280, 2007. © 2007 Society of Plastics Engineers.     

Die design for rigid PVC—the effect of die land length on extrudate swell

PVC profile extrusion compounds have a unique morphology. While other polymers gradually decrease in extrusion die swell with increasing length/thickness (L/D) ratio, PVC profile extrusion compounds have a low die swell, quite independent of the die's L/D ratio in the range of 5 to 20. The fact that the die land length can be changed without changing the extrudate swell is an important consideration, which makes die design and balancing dies simpler and easier for PVC profile extrusion compounds. While other polymers substantially increase extrudate swell with increased shear rate, the swell of the PVC profile compounds is not much affected by shear or extrusion rate. This unique behavior allows wider processing latitude in profile extrusion and faster extrusion rates than with other polymers. Another unique factor in the rheology of PVC profile extrusion compounds is that extrusion die swell increases with increasing melt temperature, while other polymers have decreasing die swell with increasing melt temperature. The unusual rheology of PVC profile extrusion compounds is attributed to its unique melt morphology, where the melt flow units are 1 um bundles and molecules that have low surface to surface interaction and entanglement at low processing temperatures but increased melting and increased entanglement at higher processing temperatures. Other polymers, unlike PVC, have melt flow at the molecular level.     

The influence of state-of-mix on the extrudate swell of a carbon black-filled styrene–butadiene rubber compound

The factors which govern the extrudate swell of a styrene–butadiene rubber compound filled with 30 phr of N330 carbon black at various states-of-mix were investigated. The state-of-mix is quantified by an effective filler volume fraction, based on an estimate of the amount of rubber immobilized in the carbon black agglomerates. The swell has been found to be dominated by recoverable strain and relaxation time, which are both controlled by the effective filler volume fraction. In contrast, shear rate, wall slip, and the rubber–carbon black network have not been found to have a significant effect on the extrudate swell. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:305–315, 1997     

Experimental studies on radial extrudate swell and velocity profiles of flowing PS melt in an electro‐magnetized die of an extrusion rheometer

This article investigates the radial extrudate swell and velocity profiles of polystyrene melt in a capillary die of a constant shear‐rate extrusion rheometer, using a parallel coextrusion technique. An electro‐magnetized capillary die was used to monitor the changes in the radial extrudate swell profiles of the melt, which is relatively novel in polymer processing. The magnetic flux density applied to the capillary die was varied in a parallel direction to the melt flow, and all tests were performed under the critical condition at which sharkskin and melt fracture did not occur in the normal die. The experimental results suggest that the overall extrudate swell for all shear rates increased with increasing magnetic flux density to a maximum value and then decreased at higher densities. The maximum swelling peak of the melt appeared to shift to higher magnetic flux density, and the value of the maximum swell decreased with increasing wall shear rate and die temperature. The effect of magnetic torque on the extrudate swell ratio of PS melt was more pronounced when extruding the melt at low shear rates and low die temperatures. For radial extrudate swell and velocity profiles, the radial swell ratio for a given shear rate decreased with increasing r/R position. There were two regions where the changes in the extrudate swell ratio across the die diameter were obvious with changing magnetic torque and shear rate, one around the duct center and the other around r/R of 0.65–0.85. The changes in the extrudate swell profiles across the die diameter were associated with, and can be explained using, the melt velocity profiles generated during the flow. In summary, the changes in the overall extrudate swell ratio of PS melt in a capillary die were influenced more by the swelling of the melt around the center of the die. Polym. Eng. Sci. 44:2298–2307, 2004. © 2004 Society of Plastics Engineers.     

Experimental investigations of the influence of molecular weight distribution on melt spinning and extrudate swell characteristics of polypropylene

An experimental study of the influence of molecular weight distribution on the melt spinning and extrudate swell of a series of polypropylenes of varying molecular weight and distribution is reported. Emphasis is given to effects of variations of molecular weight distribution. Narrowing the molecular distribution increases the slope of the elongational viscosity–elongation rate curve, stabilizes the spinline relative to both random disturbances and draw resonance, and decreases both instantaneous and delayed extrudate swell. These results are interpreted in terms of viscoelastic fluid mechanics and earlier experimental studies by the authors of the influence of molecular weight distribution on rheological properties. The influences of these rheological factors on spinline structure development is discussed.     

The application of an integral type constitutive equation to numerical flow analyses of viscoelastic fluid in unsteady flow

The applicability of the Wagner model to numerical flow analyses of the injection molding process is investigated under the following approximations: the strain and stress histories of the molten polymer before the injection is negligible, and the flow field in a mold cavity is treated as Hele‐Shaw flow. A comparison between the results for simple step‐strain‐rate flow calculated with the Wagner model and that calculated with the Leonov model suggests that the Wagner model is superior to the Leonov model for unsteady flow because of its stability and accuracy. Therefore, numerical flow analysis software of a viscoelastic fluid in the injection molding process is developed using the Wagner model. For the analysis, the velocity profile of a Newtonian fluid is used instead of that obtained through iterative calculation. The validity of the developed program is confirmed through a comparison of the results of the computation for two simple flow velocity histories with the analytical results from the Wagner model. Furthermore, the computation time of the developed software is only 1.4 times greater than that of the previous numerical flow analysis of a viscous fluid.     

A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell

A general-purpose finite element program has been used to simulate the flow of a typical polystyrene melt in the entry and exit regions of a slit die. Instead of using a general viscoelastic constitutive equation, simplified models were used that include correlations based on experimental data available in the literature for the shear and elongational viscosities and the normal stresses. With such simple models convergence of the iterative scheme is extended to relatively high Deborah numbers (De ≈ 5). The models predict vortex growth in the entry region and an increase of extrudate swell at the exit in qualitative agreement with experimental observations. It was found that the normal stresses are primarily responsible for these phenomena, while the elongational viscosity tends to increase the end (Bagley) correction and decrease the swelling.     

Finite element modeling of the flow of a rubber compound through an axisymmetric die using the CEF viscoelastic constitutive equation

This work is devoted to the simulation of the flow of a high viscosity NR/SBR rubber compound through the die of a single screw extruder with axisymmetric geometry. An in-house developed computer code based on the use of continuous penalty finite element method was employed. Three constitutive equations including two generalized Newtonian models namely; power-law and Carreau and an explicit viscoelastic model named CEF (Criminale-Ericksen-Fillbey) were used to reflect the rheological behavior of the material. Using the parameters of the rheological models determined by a slit die rheometry technique, the flow of the compound was simulated through the die and results were compared with experimentally measured mass flow rates. It is shown that for high viscosity rubber compounds the use of generalized Newtonian models which do not take the normal stress in simple shear flow into consideration gives rise to significant errors in prediction of mass flow rates. On the other hand, comparing the simulations results using the CEF equation with experimental data revealed that this model is the best compromise between generalized Newtonian and full viscoelastic models which need high computational costs and effort. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

An investigation of frictional and collisional powder flows using a unified constitutive equation

This is an experimental and numerical study of dry, frictional powder flows in the quasi-static and intermediate regimes using the geometry of the Couette device. We measure normal and shear stresses on the shearing surface and extract from the data, constitutive equations valid in the slow frictional, quasi-static and the intermediate (dense), collisional regimes of flow. This constitutive equation is then used in a new, specially developed FEM solver (FeatFlow—Ouazzi et al., 2005 [18]) to obtain solutions of the continuum equations of motion as well as stress and velocity distributions in the powder. While the measurements to obtain the constitutive equation are performed in a concentric Couette device, the numerical scheme is used to predict the torque and stresses in two additional geometries. These geometries are an eccentric Couette where the inner, rotating cylinder is placed off-center with different eccentricities and a more complicated geometry where a cylindrical body is introduced in the middle between the rotating and stationary cylinders and obstructs part of the shearing gap. The purpose of these calculations is to show the versatility of the numerical solution.     

Quantitative validation of the discrete element method using an annular shear cell

The discrete element method (DEM) is often used as the “gold standard” for comparison to continuum-level theories and/or coarse-grained models of granular material flows due to its derivation from first-principal constructs, like contact mechanics. Despite its prevalence, the method is most often validated against experiment in only qualitative ways - comparison of mixing rates, gross features of concentration profiles, etc. - for exactly the reason it has found its popularity; detailed experimental measurements are difficult and often expensive. In this paper, we outline work aimed at using detailed, particle-level experimental measurements to quantitatively validate DEM simulations. Specifically, we examine the flow in a horizontally-aligned annular shear cell. Measurements are performed using digital particle tracking velocimetry (DPTV) so that the velocity, granular temperature, and solids fractions profiles may be extracted. Computationally, we attempt to match the experimental measurements as closely as possible and study the impact of a variety of contact mechanics-inspired force laws as well as perform sensitivity analysis on device and particle geometry and material properties employed.