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

Célio Fernandes,Ahmad Fakhari,Željko Tukovic

doi:10.3390/polym13244454

Célio Fernandes, Ahmad Fakhari + Show 1 more

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https://doi.org/10.3390/polym13244454

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Abstract

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.

Highlights

The extrudate swell flow is a well-known benchmark problem in the polymer processing field, where a free-surface and a boundary stress singularity at the die exit are present
The effects of inertia and yield stress on the extrudate swell ratio computed by the newly developed algorithm were studied and compared with results found in the scientific literature for the range of the dimensionless Reynolds (Re) and Bingham (Bn) numbers as follows: 1 ≤ Re ≤ 10 and 0.001 ≤ Bn ≤ 10
For the isothermal Bingham flows, the extrudate swell ratio was found to vary by approximately 13% from the lowest to the highest Re number when the yield stress effects are negligible (Bn = 0.001)

Summary

Introduction

The extrudate swell flow is a well-known benchmark problem in the polymer processing field, where a free-surface and a boundary stress singularity at the die exit are present. There is increasing research effort on non-isothermal free-surface flows, these studies are limited to academic purposes and problems. Phuoc and Tanner [11] developed a finite element scheme based on the Galerkin method to explore the effects of thermally induced property changes in extrusion. Karagiannis et al [12] developed a three-dimensional (3D) non-isothermal code to study viscous free-surface flows with exponential dependence of viscosity on temperature. The code was based on Galerkin’s finite-element formulation, and, apart from the phenomenon of thermally induced extrudate swelling, the bending and distortion of the extrudate due to temperature differences and/or geometric asymmetries were confirmed numerically and experimentally. Spanjaards et al [13] developed a 3D transient non-isothermal finite element code to predict the extruded shape of viscoelastic fluids emerging from an asymmetric keyhole-shaped die. A systematic study was carried out to decouple the effects of shear-thinning, elasticity, and temperature in the shape of the extrudate

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