Further Simulations of Viscoelastic Entry Flows Using a Heuristic Approach

The entry flow of viscoelastic fluids is simulated numerically for various tubular and planar abrupt geometries using the finite element method. Test fluids include polymer solutions (Boger fluids) and polymer melts (LDPE, PS) for which shear viscosity and normal stress data are available. Instead of using any established viscoelastic consti tutive equation, the Viscometric Approximation Theory (VAT) is used which simplifies the equations to their steady simple-shear flow counterpart thus overcoming problems of convergence. This heuristic approach, although not rigorous and consistent with consti tutive principles, is shown to capture intricate details of the flow field found experimen tally. These include the growth of the reservoir vortex with flowrate from a concave to a straight and then a convex shape in a 4:1 tubular contraction; the appearance of a second lip vortex in a 16:1 tubular contraction for low flow rates; the difference in vortex size and streamline patterns of LDPE and PS melts in a 6:1 planar contraction This heuristic ap proach is thus recommended for studying the effect of normal stresses in viscoelastic flows with a main direction for engineering calculations much as the lubrication approximation has been used in the past for purely viscous fluids.