A theoretical treatment of die swell in a Newtonian liquid

A finite-difference technique is used to calculate the die swell of a Newtonian liquid emerging from a capillary at zero Reynolds number. There is semi-quantitative agreement with experimental results. The experimental die swell is 13·5%; this theory predicts a die swell of 6·3%.     

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.     

Die swell in elastic and viscous fluids

Measurements of die swell have been made on an elastic liquid and a Newtonian liquid of similar viscosity (～ 10⁴ N s m^?2). The Reynolds number was about 10^?8. The Newtonian liquid has a die swell of 13.5% which was independent of shear rate. The die swell of the elastic liquid increased with shear rate and seemed to be asymptotic to the Newtonian die swell at low shear rates.     

Finite difference simulation of die swell for a newtonian fluid

The phenomenon of die swell for Newtonian fluids has been successfully simulated using a finite difference numerical method. The calculations predict the surface shape of Newtonian jets over a range of Reynolds numbers from 4.2 to 92.3 for both rectangular slits and cylindrical tubes. The calculated die swells for tubes compare favourably to experimental data. Velocity profiles and pressure distributions in jets exiting from slits or tubes are also predicted. The numerical data were incorporated into a momentum balance expression to demonstrate factors influencing this phenomenon. Other solutions were calculated to predict the effect of gravity and a sudden perturbation in flow on the resulting jet shape.     

Finite difference simulation of die swell for a newtonian fluid

The phenomenon of die swell for Newtonian fluids has been successfully simulated using a finite difference numerical method. The calculations predict the surface shape of Newtonian jets over a range of Reynolds numbers from 4.2 to 92.3 for both rectangular slits and cylindrical tubes. The calculated die swells for tubes compare favourably to experimental data. Velocity profiles and pressure distributions in jets exiting from slits or tubes are also predicted. The numerical data were incorporated into a momentum balance expression to demonstrate factors influencing this phenomenon. Other solutions were calculated to predict the effect of gravity and a sudden perturbation in flow on the resulting jet shape.     

FINITE ELEMENT ANALYSIS OF THE FREE EXTRUSION FLOWS OF BOGER FLUIDS

The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.     

Compensating for die swell in the design of profile dies

Because of the effects of die swell, the final shape of an extrudate is often substantially different from that of the exit opening of the die. As a result, the design of profile dies producing complex shapes often involves more than just “balancing” the die but also compensating for the effects of die swell. Typically, a successful design of such dies is achieved only through much “cut and try,” However, with the use of a fully three‐dimensional finite element flow algorithm along with quick mesh generating capabilities, the usual cut and try involved in the design of many profile dies can be greatly reduced, if not eliminated. This paper demonstrates how the effects of die swell can be compensated for in the design of profile dies. For profiles with one plane of symmetry, this includes compensating for the sideways translation of the extrudate as well as the change in shape that the extrudate experiences. Completely asymmetric profiles undergo a “twisting” downstream of the die. This twisting, which appears not to have been reported in the literature (at least for isothermal extrusion), is also accounted for here, along with the change in shape that the extrudate undergoes. The translation or twisting of profiles downstream of a die is often attributed to non‐Newtonian or non‐isothermal effects. Only isothermal Newtonian examples are considered here. These results clearly show that asymmetry of the profile will result in a translation and twisting of the extrudate even in the isothermal Newtonian case.     

Velocity profiles at the exit of circular tubes

An investigation has been carried out on velocity profiles of Newtonian liquids at the exit of circular tubes for Reynolds numbers from about 50 to 1000. A simple expression which asymptotically approaches a Poiseuille parabolic distribution for higher Reynolds numbers is obtained. Experimental measurements of extrudate swell ratios were used as criteria for convergence to the solution. Comparison with jet shapes from previous experimental and theoretical studies supports the obtained results. The work also illustrates a straightforward method for simplifying and solving the governing equations for laminar flows of thin liquid layers.     

Numerical simulation of entry and exit flows in slit dies

A general-purpose finite element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in the entry and exit regions of a slit die. It was found that shear-thinning increases the entrance correction while it decreases the exit correction. Shear-thinning reduces the size of the small corner vortex that forms in the entry flow of a Newtonian fluid. The swelling ratio had a value of 1.196 for Newtonian fluids and decreased as the value of the power-law index decreased. Viscoelastic calculations were performed using the Criminale-Ericksen-Filbey (CEF) constitutive equation. Convergence of the iterative scheme was unattainable for Deborah numbers above 1.0. The results showed a decrease of the entrance correction and an increase of the exit correction with elasticity. Extrudate swell first decreased slightly and further increased with the Deborah number.     

Finite difference solution for flow from a slit die

A finite difference solution for an isothermal viscoelastic liquid flowing through a film forming die is investigated. The fluid is described by a Maxwell model in which the time derivative has been replaced by an Oldroyd's convective derivative and the numerical technique used combines features of the Solution Algorithm (SOLA), Simplified Marker and Cell method (SMAC), and SOLASMAC. The numerical scheme was tested with a Newtonian fluid and high density polyethylene (HDPE). Two slit dies with gap-to-length ratios 4 and 16 were used. In the two cases, die swell has occurred: A maximum of 4.5% swell was observed for the Newtonian fluid, while up to 77% swell was attained with HDPE. The simulated flow behavior of HDPE exhibited high amplitude oscillations at dimensionless time greater than 0.18. These oscillations are thought to be related to the nature of sheet flow, which can be unstable. This study shows that with some improvement the finite difference method can be used for studying the extrusion of polymer through slit and capillary dies.     

Extrudate swell of newtonian liquids from rectangular dies

Extrudate swell from square and rectangular dies was studied for glycerol solutions. Experiments were performed for a wide range of viscosities 75 < μ < 464 mPa · s, with small changes in surface tension and density. Dies with aspect ratios of 3:1 and 2.25:1 and a wide range of length to hydraulic diameter ratios, i.e., 24 < l/D_h < 62, were used. Results were obtained in the range of Reynolds number 1 < Re < 50. Swell ratios for the short and long faces of a die are below the swell ratio of a plane slit. Swell ratios for the short face are consistently higher than those for the long face for lower Reynolds numbers. Liquid contracted at the corners, while swelling along faces.     

高粘度聚酯熔体出喷丝孔口膨化行为

采用实验方法研究不同特性粘度的聚酯物料在纺丝状态下的挤出膨化行为。实验装置为Brabender挤出纺丝实验台。喷丝头具有不同孔径和长径比。出口膨化程度用挤出膨化比Ψ来度量。根据实验结果讨论了物料的特性粘度、喷丝孔直径、喷丝孔长径比、挤出温度和剪切速率等与出口膨化比的关系。所发现的规律对高粘度聚酯纺丝实际生产工艺条件的制订和喷丝板的设计是有价值的。     

Predictions of flow behaviors and entrance pressure drop characteristics of a rubber compound in a capillary die using various rheological models

Rubber compounds have highly viscoelastic properties. The viscoelastic behaviors that have been exhibited during die extrusion include die swell and vortices in regions of sudden contraction. In this study, the application of rheological models to the capillary die extrusion process is investigated. Experiments and simulations were conducted using a fluidity tester and finite element analysis, respectively. The velocity distributions, velocity profiles, pressure drops, and vortices at the capillary die entrance were analyzed through computer simulations for various viscoelastic models [i.e., Phan‐Thien and Tanner (PTT), Giesekus, POMPOM, simplified viscoelastic, and generalized Newtonian models]. Different models exhibited different pressure drops and different velocity profiles in the capillary die. Only the full viscoelastic models (PTT, Giesekus, and POMPOM) predicted the vortex at the corner of the reservoir that is the capillary die entrance. However, the simplified viscoelastic and generalized Newtonian models did not predict the vortex. All the viscoelastic models studied in this article predicted the die swells in various ways, and these were compared with the experimental results. The PTT and simplified viscoelastic models exhibited good agreement with the experimental results of the die swells. POLYM. ENG. SCI., 54:2441–2448, 2014. © 2013 Society of Plastics Engineers     

熔纺聚氨酯流变性能的研究

研究了熔纺聚氨酯熔体的流变性能.结果表明:熔纺聚氨酯熔体为切力变稀流体,随温度升高其非牛顿指数增大,胀大比减小,表观剪切粘度随温度升高下降明显,且低于常规熔纺成纤高聚物,为避免纺丝时产生自重引伸大于喷丝头拉伸比而导致并丝,纺丝温度不应大于210℃;水分存在会导致熔体粘度下降,胀大比减小.     

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.     

A method for approximate prediction of extrudate swell

The extrudate swell problem is modeled as the stratified flow of two Newtonian isothermal fluids with differing viscosities. If the viscosity of the thin outer layer is the greater of the two, then enhanced swelling relative to the case of equal viscosity is observed. By suitable selection of the the viscosity ratio, this model can be used to represent thermal, shear-thinning, and elastic effects in extrusion. The stratified flow problem is solved using an efficient boundary element method. The model then provides a means of studying and predicting complex geometrical effects in profile extrusion without the burden of a full viscoelastic solution, which may yield a practical aid to the die design process.     

Swell and distortions of high-density polyethylene extruded through capillary dies

The effect of varying the die entrance angle and the die length on extrudate swell and on the onset of extrudate distortion in capillary extrusion has been studied. Using theory from the literature, we have analyzed the contribution to the total pressure drop from the elongational and shear deformation in the entrance region, and from the capillary pressure drop in the land region of the die. From the contribution of the elongational deformation, we obtained an estimate for the elongational viscosity of the polymer. The same analysis was used to study the influence of the die geometry on the stick-slip instability. It is found that the elongational component at the inlet region mainly influences the extrudate distortions. The onset of the stick-slip instability occurs within 10% at a wall stress τ_w of 0.3MPa, where τ_w is calculated from expressions assuming fully developed flow. The variation around this average value is systematic with changes in die geometry, and the observed variations are probably due to the non-homogeneous pressure field in the die. We also propose a model for predicting extrudate swell. Input to the model are material parameters obtainable from oscillatoric measurements of the loss and storage modulus and residence times calculated from the geometry of the die. The swell model includes a fitting parameter that sets the overall scale of the swell.     

An experimental study of the relationship between rheological properties and spinnability in the dry spinning of cellulose acetate–acetone solutions

The elastic and viscous properties of five cellulose acetate–acetone solutions, varying from 19.9% to 28.6% solids concentration, are independently determined at 60°C by capillary rheometry techniques. The viscous flow behavior of the solutions is determined over four decades of shear rate. The Bagley analysis is used to determine the entrance pressure drop and the true shear stress at various shear rates. A plot of the entrance pressure drop at the maximum experimental shear rate versus solution concentration undergoes a rapid increase in slope at 24.0% solids concentration, the significance of which is discussed with respect to the development of an elastically deformable chain entanglement network. The die swell behavior of the solutions at 60°C is determined on a commercial-type dry-spinning apparatus. When the die swell ratio is plotted versus volumetric flow rate, all five solutions are found to possess a characteristic curve with a distinct maximum. Photographs illustrating the variation of die swell with volumetric flow rate are shown. Die swell measurements are also shown to correlate well with entrance pressure drop measurements. The degree of spinnability of each cellulose acetate–acetone solution at 60°C is found by determining first godet speed at which one or more threads break abruptly. Spinnability is found to go through a maximum at 24.0% solids concentration. The rheological measurements and spinnability results are discussed through the aid of a single rheological parameter incorporating both elastic and viscous solution responses.     

气辅挤出过程中挤出胀大的实验和模拟研究

气体辅助挤出是一种新型挤出工艺,可以显著减小挤出胀大,减小口模压力降。对气辅挤出过程中的挤出胀大现象进行了实验研究和数值模拟,在实验研究中,对传统挤出和气辅挤出进行了对比实验,分析了螺杆转速、辅助挤出气体压力和流量对挤出胀大的影响,并采用CFD有限元通用软件FIDAP分析了气辅挤出过程中口模内的速度场和压力场。     

Extrudate swell of high density polyethylene. Part III: Extrusion blow molding die geometry effects

Two high density polyethylene resins—801 and 802— are examined with regard to their isothermal, time-dependent, and nonisothermal swelling properties when emerging from two annular and three diverging dies. The short time swelling characteristics of samples 801 and 802 are very important for these dies, resulting in a lower diameter swell for the latter, independent of the die geometry or flow rate. Output variations have much less impact on the swelling behavior than small changes in the geometry of the die mandrel. Accordingly, shear stress and shear rate parameters alone cannot be used to explain the swelling properties of a HDPE resin in the different die geometries. Straight annular dies induce higher diameter swelling than diverging dies.