CALCULATION OF STEADY-STATE VISCOELASTIC FLOW THROUGH AXISYMMETRICAL CONTRACTIONS WITH THE EEME FORMULATION

The EEME/finite-element method is used to compute steady flows of fluids with constitutive behavior described by the Modified Upper Convected Maxwell Model of Apelian and a modified form of the dumbbell model of Chilcott and Rallison through abrupt, axisymmetric contractions. Both constitutive models predict constant viscosity and shear thinning first normal stress coefficient, but differ qualitatively in the behavior of the elongational viscosity. Asymptotic analysis for both models predicts that the solution has Newtonian-like spatial structure near the reentrant corner and integrable stresses and velocity gradients there. With the Newtonian-like asymptotics, the stress field can be approximated by conventional Lagrangian finite elements and computed by the streamline upwind Petrov Galerkin (SUPG) method. The finite element calculations are stable and convergent: higher values of Deborah number are reached with increasing mesh refinement. Moreover, the predicted asymptotic structure of the stress and velocity fields is recovered near the corner in the calculations. Calculations with both constitutive equations show the stretching of the Newtonian corner vortex toward the reentrant corner and its growth upstream with increasing Deborah number for 4:1 and 8:1 contraction ratios. The characteristics of the computed vortex are in semi-quantitative agreement with experiments for Boger fluids for which the flow is axisymmetric and steady.