Surface tension effect to die-swell extrusion of viscoelastic fluid

The die-swell problem for Viscoelastic fluid by using the finite element methods (FEM) under the semi-implicit Taylor-Galerkin pressure correction principle with consistent streamline upwinding is presented. The assumptions of incompressible fluid, creeping flow, no gravitational effect, temperature independence and no slip effect are used. The two-dimensional governing equations, in which the equations are nonlinear partial differential equations,are consists of the conservation of mass and momentum, and Oldroy-B model with We < 1. The deformation of fluid at free surface will be affect by surface tension force, thus both dynamic and kinematic boundary conditions are considered. These conditions make the simulation result looked reasonable. Evolution of die-swell flow: the variations of velocities, pressure, stresses, shear rate and extension rate. The simulation program has been created to generate grid and compute the solutions, which utilize remeshing and interpolating techniques as well as the gradient recovery for increased accuracy and stability of solutions. The results exhibit the same trend as the experimental solutions.