In recent years, the development of CAE (Computer Aided Engineering) in polymer processing has been remarkable, and it is expected to be more realistic in viscoelastic numerical simulation, particularly in three-dimensional complex geometry. Because of the problems of computational memory capacity, CPU time, and the numerical convergence of viscoelastic flow simulation, three-dimensional viscoelastic simulation applicable to industrial flow behaviors has not yet been attempted. In this paper, we developed the numerical simulation of three-dimensional viscoelastic flow within dies using a decoupled method, streamwise integration, and penalty function methods to decrease memory, and the TME ("Transformation of Equation of Motion to the Elliptic Equation," S . Tanoue, T. Kajiwara, and K. F'unatsu, The Eleventh Annual Meeting, the Polymer Processing Society Seoul, Korea, Extended Abstracts p.439) method, which raises the stability of convergence. We confinned the reliability of this simulation technique to compare simulation results with experimental data of the stress field at a downstream wall shear rate of 5.41s' within a 60" angle tapered contraction die. We compared the predictions of a viscoelastic model (Phan-Thien and Tanner model) with a pure viscosity model (Carreau model) at a downstream wall shear rate of 120s' and discovered a remarkable effect of viscoelasticity in the shear stress and first normal stress difference in particular in the tapered region.

A two‐dimensional simulation was developed for multi‐layer confluent viscoelastic flow in dies, using a finite element method. The simulated interface shape was compared with the experimental results of previous researchers, and the simulated results were confirmed. Two‐layer and three‐layer flows of two or three kinds of viscoelastic fluids were simulated. Fluids with different non‐Newtonian viscosities and the first normal stress differences were used. The layer thicknesses in dies are mainly determined by the shear viscosity and less by the elasticity of the fluid. The normal stress difference between the fluids forming an interface may be related to interfacial instability, and normal stresses near the interface were examined. The normal stress difference between both fluids was affected by the first normal stress difference and elongational viscosity.

Two kinds of practical approximate simulation methods for three-dimensional viscoelastic flow in a die have been developed by which solutions at high shear rate can be obtained with low memory capacity and CPU time. The velocity and stress fields were calculated separately. The velocity field was obtained using the pure-viscous non-Newtonian model and the stress field using the viscoelastic model by substituting this velocity field. In one case the White-Metzner model was applied as a viscoelastic model without a square term in stress. In the second case the stress field was calculated by the streamwise integration which could apply even to the viscoelastic model including the square of stress. In addition a modified pure-viscous non-Newtonian model has been developed respresenting the strain-thickening elongational viscosity in order to extend these approximate methods to similar materials. The velocity field which was calculated using a modified pure-viscous non-Newtonian model was considerably closer to that for the viscoelastic model with the same flow characteristics as shown for the original pure-viscous non-Newtonian model.

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