abstract
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A general purpose finite element program has been developed for numerical modelling of flow of polymer melts through processing equipment. Several problems have been solved for two-dimensional creeping flow. These include flow in the gap between calender rolls, driven cavity flows and planar entry and exit flows with free surfaces (extrudate swell) in slit dies. Newtonian, power-law and viscoelastic models have been used under isothermal and nonisothermal conditions. Slip at the boundary walls has also been incorporated. An "upwind" scheme for triangular elements has been used to stabilize the solution when convection is considered in the nonisothermal analysis. The free surfaces are determined through an iterative technique that allows no flow normal to the surface.
The finite element analysis of calendering shows that the power-law model describes adequately the behaviour of the polymer melt and the results are in good agreement with experimental data. The shape and location of the free surface of the melt bank is also determined an compares well with photographs available in the literature. Entry and exit flow calculations in slit dies and the determination of extrudate swell are in good agreement with theoretical and experimental studies for inelastic fluids. Visco-elastic calculations performed using the Criminale-Ericksen-Filbey (CEF) constitutive equation diverged for high elasticity levels (Deborah number above 1.0). A simple constitutive equation based on empirical relations for polymer melts was found to enjoy a wider convergence range for elasticity levels encountered in practical situations (De < 5). It predicts several phenomena of polymer melts such as vortex size and intensity, entrance and exit pressure losses and extrudate swell in agreement with experimental findings. It is proposed that such empirical relations can be used along with the finite element method to predict successfully the flow of polymer melts in various polymer processes.