Barriers to progress in the simulation of viscoelastic flows of molten plastics

Polymer melts exhibit some degree of viscoelasticity in most industrial forming operations, and elasticity is particularly important in flows involving an abrupt contraction or expansion in the flow direction. However, the incorporation of a viscoelastic constitutive equation into computer models for polymer processing poses many problems, and for this reason inelastic models have been used almost exclusively to represent rheological behavior for flow simulation in the plastics industry.;In order to explore the limits of viscoelastic flow simulations, we used two nonlinear viscoelastic models (Leonov and Phan-Thien/Tanner) to simulate axisymmetric and planar contraction flows and extrudate swell. Their predictions were compared with those obtained using a strictly viscous model (Carreau-Yasuda) and with experimental results. The models are implemented in a modified Elastic Viscous Split Stress (EVSS) mixed finite element formulation. The viscoelastic constitutive equations are calculated using the Lesaint-Raviart method, and the divergence-free Stokes problem is solved applying Uzawa's algorithm. The decoupled iterative scheme is used as a preconditioner for the Generalized Minimal Residual (GMRES) method. Numerical instability was observed starting at quite low elasticity levels. For the converging flows, the predicted flow patterns were in fair agreement with experimental results, but there was a large discrepancy in the entrance pressure drop. In the case of extrudate swell, the agreement with observation was poor, and convergence was impossible except at the lowest flow rate.;After exploring the limits of simulations using viscoelastic models, we conclude that there are serious barriers to progress in the simulation of viscoelastic flows of industrial importance. The ultimate source of the problem is the melt elasticity, and traditional numerical methods and rheological models do not provide a suitable basis for simulating practical flows. A new approach is required, and we propose that a rule-based expert system be used.