Non-Isothermal Free-Surface Viscous Flow of Polymer Melts in Pipe Extrusion Using an Open-Source Interface Tracking Finite Volume Method

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated.

Numerical Study of the Effect of Thixotropy on Extrudate Swell

The extrusion of highly filled elastomers is widely used in the automotive industry. In this paper, we numerically study the effect of thixotropy on 2D planar extrudate swell for constant and fluctuating flow rates, as well as the effect of thixotropy on the swell behavior of a 3D rectangular extrudate for a constant flowrate. To this end, we used the Finite Element Method. The state of the network structure in the material is described using a kinetic equation for a structure parameter. Rate and stress-controlled models for this kinetic equation are compared. The effect of thixotropy on extrudate swell is studied by varying the damage and recovery parameters in these models. It was found that thixotropy in general decreases extrudate swell. The stress-controlled approach always predicts a larger swell ratio compared to the rate-controlled approach for the Weissenberg numbers studied in this work. When the damage parameter in the models is increased, a less viscous fluid layer appears near the die wall, which decreases the swell ratio to a value lower than the Newtonian swell ratio. Upon further increasing the damage parameter, the high viscosity core layer becomes very small, leading to an increase in the swell ratio compared to smaller damage parameters, approaching the Newtonian value. The existence of a low-viscosity outer layer and a high-viscosity core in the die have a pronounced effect on the swell ratio for thixotropic fluids.

Testing the PTT Rheological Model for Extrusion of Virgin and Composite Materials in View of Enhanced Conductivity and Mechanical Recycling Potential

One of the challenges for the manufacturing processes of polymeric parts is the dedicated control of composite melt flow. In the present work, the predictive capability of the Phan-Thien-Tanner (PTT) viscoelastic model is evaluated in relation to the extrudate swell from slit dies at 200 °C, considering polypropylene and graphite filler, and applying ANSYS Polyflow software. It is shown that for sufficiently low filler amounts (below 10%; volumetric) the PTT accurately reflects the viscoelastic interactions, but at higher filler amounts too large swellings are predicted. One can although obtain insights on the swelling in the height direction and consider a broader range of swelling areas compared to virgin materials. Guidelines are also provided for future experiments and model development, including the omission of the no-slip process boundary condition.

An Effective Interface Tracking Method for Simulating the Extrudate Swell Phenomenon

The extrudate swell, i.e., the geometrical modifications that take place when the flowing material leaves the confined flow inside a channel and moves freely without the restrictions that are promoted by the walls, is a relevant phenomenon in several polymer processing techniques. For instance, in profile extrusion, the extrudate cross-section is subjected to a number of distortions that are motivated by the swell, which are very difficult to anticipate, especially for complex geometries. As happens in many industrial processes, numerical modelling might provide useful information to support design tasks, i.e., to allow for identifying the best strategy to compensate the changes promoted by the extrudate swell. This study reports the development of an improved interface tracking algorithm that employs the least-squares volume-to-point interpolation method for the grid movement. The formulation is enriched further with the consistent second-order time-accurate non-iterative Pressure-Implicit with Splitting of Operators (PISO) algorithm, which allows for efficiently simulating free-surface flows. The accuracy and robustness of the proposed solver is illustrated through the simulation of the steady planar and asymmetric extrudate swell flows of Newtonian fluids. The role of inertia on the extrudate swell is studied, and the results that are obtained with the newly improved solver show good agreement with reference data that are found in the scientific literature.

Effects of gas-assisted extrusion on slip in the cable coating process

The isothermal viscoelastic finite element method is used to simulate and analyze the process of cable coating extrusion, in which the Navier slip model is adopted. The Phan–Thien–Tanner differential viscoelastic constitutive equation is used to describe the flow characteristics of the polymer melt. The polymer material used for simulation is polypropylene. The extrudate swell, velocity field, pressure field and shear stress field are calculated by finite element method. The influences of the gas-assisted extrusion and traditional extrusion on wall slip of cable coating extrusion are compared. The results indicate that the extrudate swell ratio is the largest under the condition of the complete slip between core wire and melt during traditional extrusion process. The increase of core wire dragging velocity can lead to the increase of slip velocity, the decrease of pressure and the increase of shear stress of melt. Gas-assisted extrusion can eliminate the negative effects caused by the slip of core wire or the increase of core wire dragging velocity. Therefore, gas-assisted extrusion can reduce the energy consumption, improve the cable coating layer quality and increase the production efficiency during extrusion process.

Effect of extrudate swell on extrusion foam of polyethylene terephthalate

The effect of extrudate swell on extrusion foam of thermoplastic polymers is presented using an experimental approach supported by a modelling of the phenomenon. Its understanding is fundamental in designing the geometry of a die for extrusion foam and to predict foaming. The extrudate swell is the swelling of a viscoelastic material due to a fast elastic recovery after being subjected to stresses. We show that there exists a link between the extrudate swell and foaming, performing experiments with simple and complex extrusion dies to measure the expansion ratio. It was found that the expansion ratio is anisotropic and the anisotropy in the expansion of the foam is due to the extrudate swell that affects strongly the final shape of the product and it cannot be neglected in standard application for extrusion foam. A simple heuristic model was developed to predict the extrudate swell from geometrical parameters and rheological characterization of the fluid. It was found that the foaming mechanism of polyethylene terephthalate, blown with cyclopentane, changes as function of extrudate swell and the lowest density foam is achieved using the die that has the bigger extrudate swell.