A three-dimensional flow simulation using a viscoelastic constitutive equation and a segregated finite element scheme

Numerical simulations of viscoelastic polymeric fluids have practical relevance to develop and optimise polymer processing techniques, such as injection moulding. Commercial injection moulding simulations software have been dominated by assuming Newtonian, Power law and other Generalised Newtonian constitutive equations for fluid flow. However injection moulding involves injection of molten polymer into complex cavities to form fabricated parts. This process is non-isothermal and strongly affected by viscoelastic fluid flow phenomena, involving complex rheological properties. Commercial injection moulding software do not always predict the realistic flow behaviour borne of these properties. It is essential to use a suitable viscoelastic constitutive equation for realistic flow behaviour inside the mould. Since there are no commercial injection moulding software available with viscoelasticity simulation capability yet, this paper attempts to develop a general three-dimensional simulation strategy for viscoelastic flow. Hitherto, virtually all viscoelastic simulations have been in academic circles. The application of viscoelastic constitutive equation in industrial polymer processing has not gained industrial acceptance. This is because determining a suitable constitutive equation has been elusive, the adequate determination of the constitutive equation’s parameters, and the numerical problems that are associated with using such constitutive equations, which requires sophisticated numerical techniques and extended computer facilities. This research discusses the role of various viscoelastic constitutive equations in the manifestation of flow effects. The rheological parameters and constitutive equation parameters for commercial grade polymer melt were obtained from steady state and dynamic state experimental data. Because of the mathematical formulation and nature of viscoelastic constitutive equations, a simulation in three-dimension is necessary for best possible results. A three dimensional simulation of the process has been developed to understand the viscoelastic effects, in particular the viscoelastic nature of polymer melts and the nature of viscoelastic constitutive equations. A segregated finite element scheme is utilised, where velocities and the corresponding pressure field are computed alternatively in an iterative scheme, taking viscoelastic contributions into account. This research also discusses various issues/difficulties encountered when using a typical viscoelastic constitutive equation. In particular this research presents simulation results of a differential type viscoelastic constitutive equation. It is anticipated that flows in complex geometries can be assembled from flows in simple geometries. A successful flow simulation in a simple geometry, such as contraction geometry, will ultimately lead to improvement of simulations of polymer flow in such processes as extrusion and injection moulding, where the complex flows can involve much simple-geometry, such as contractions and expansions. This research work presents simulation of Oldroyd-B model in shear flow, planar and axisymmetric contraction flow for time dependent and steady state. Experiment in axisymmetric contraction was carried out to verify some results.