UNSTEADY FINITE-VOLUME SIMULATION OF OLDROYD-B FLUID THROUGH A 3-DIMENSIONAL PLANAR CONTRACTION

The equations for viscoelastic flows of an Oldroyd-B fluid are integra ted using the finite volume technique. The numerical algorithm was dev eloped to treat three-dimensional (3D) unsteady flows using Cartesian coordinates on a non-uniform staggered grid. The primitive variables, velocities, pressure and extra-stresses are used in the formulation. A ll inertia terms in the momentum and constitutive equations are taken into account and are discretized in space using a quadratic upwind sch eme. Case studies have been conducted for the start-up Couette flow, t wo-dimensional (2D) 4:1 and 3D 4:1:4 planar contractions. The numerica l solutions agree very well with analytical solutions for the start-up Couette flow. The size of the corner vortex for the 4:1 planar contra ction, in the 2D case, is in good agreement with previous computations . Comparison between 2D calculation for a qualitative analysis, using the Oldroyd-B fluid, and measurements [1] of a 5.0 wt.% solution of po lyisobutylene in tetradecane, is presented for the velocity and normal stress difference at several cross sections in the planar contraction . New results showing the vector field, streamlines and extra-stress c omponents are presented for a 3D 4:1:4 planar contraction at high Debo rah numbers (27.3). (C) 1997 Elsevier Science B.V.