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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: M. Papadrakakis, B.H.V. Topping
Chapter 5

Finite Element Modelling of Two- and Three-Dimensional Viscoelastic Polymer Flows

R. Tenchev1,3, O. Harlen2, P.K. Jimack1 and M.A. Walkley1

1School of Computing, University of Leeds, United Kingdom
2School of Mathematics, University of Leeds, United Kingdom
3LUSAS, Kingston upon Thames, United Kingdom

Full Bibliographic Reference for this chapter
R. Tenchev, O. Harlen, P.K. Jimack, M.A. Walkley, "Finite Element Modelling of Two- and Three-Dimensional Viscoelastic Polymer Flows", in M. Papadrakakis, B.H.V. Topping, (Editors), "Trends in Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 5, pp 81-101, 2008. doi:10.4203/csets.20.5
Keywords: polymer melts, viscoelastic flow, finite element methods, arbitrary Lagrangian-Eulerian meshes.

Understanding and controlling the flow of polymer melts is of great importance in polymer processing industries. Both the qualitative and the quantitative features of such flows are determined by the rheology of the melt, which in turn depends upon the underlying molecular structures. Consequently, there are a number of different length scales at which simulations may be undertaken in order to obtain macro-scale flow descriptions. In this research we work only at the continuum scale by making use of quantitative macroscopic constitutive laws which are based upon theory involving the physics of molecular alignment and entanglement.

This particular paper presents an overview of our recently-developed finite element software tool for the simulation of two- and three-dimensional fluid flows arising in viscoelastic polymer melts. A wide range of melt rheologies may be considered via macroscopic constitutive laws, and three specific examples are considered in this presentation. The flows considered all comprise of solutions of high molecular weight polymers at relatively low velocities. This leads to a model of a high viscosity fluid with relatively small transient and inertial effects. The three specific constitutive models that are considered in this work are described in detail within the paper.

Having introduced the governing equations the paper then goes on to provide an overview of the software. As well as the time-stepping routines that lie at the core of the software, a number of pre- and post-processing routines are also provided. The former include the ability to generate geometries, meshes and boundary conditions, as well as specifying fluid properties, whereas the latter include a wide range of visualisation capabilities. The software itself is embedded in a user-friendly run-time environment that allows real-time visualisation of results and parameters to be modified during a computation.

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