NUMERICAL SOLUTION OF 4:1 CONTRACTION PROBLEM FOR VISCOELASTRIC FLOW WITH SLIP EFFECT

Abstract

This dissertation presents the slip effect of 4:1 contraction and free surface problems under feedback pressure-driven velocity flow technique. The Navier-Stokes equations are modeled for Newtonian and viscoelastic fluids but constitutive equation is only applied for Oldroyd-B flow. The studies of both cases are attributed to flow behaviors especially for pressure, velocity, stresses and streamline paths. The numerical solutions are obtained by a semi-implicit Taylor-Galerkin pressure-correction finite element method (STGFEM). In addition, the velocity gradient recovery and the streamline-upwind Petrov/Galerkin (SUPG) schemes are chosen to stabilize the converged solutions under the two dimentional isothermal incompressible flow. For Newtonian and Oldroyd-B fluids with and without the slip effect, the solutions of 4:1 contraction flow is executed in planar system for sharp and rounded corner shapes while axisymmetric flow is opted for extrudate swell. The benchmarks are displayed with results from STGFEM versus analytical and numerical solutions. The comparisons show that these two simulation problems are evaluated with efficiency of feedback treatment. At the same direction, the accuracy results under slip velocity drive the outcomes approaching to real problems.