HIGH WEISSENBERG NUMBER SIMULATION OF AN ANNULAR EXTRUDATE SWELL USING THE DIFFERENTIAL TYPE CONSTITUTIVE EQUATION

Annular extrudate swell simulations at high Weissenberg numbers were m ade using a differential type constitutive equation. The streamline-up winding method with a sub-element for extra stress components, which i s called SU4x4, is one of the best mixed finite element methods for co mputation of viscoelastic flows. Planar and capillary extrudate swell calculations at high Weissenberg numbers (We>1000) were accomplished b y SU4X4. However, annular extrudate swell simulations at high Fire by SU4X4 were not successful. The calculated We was less than about 4. A new calculation technique using a Newton-Raphson discretization of the equation of motion was developed. This technique is called a ''new un der-relaxation method.'' The calculated We of annular extrudate swell simulation by the new under-relaxation method with SU4X4 was about 6 s imilar to 250 times larger than those by SU4X4. Reasonable calculation results were obtained in an annular flow and a capillary extrudate sw ell by this method, and the reliability and the utility of the new und er-relaxation method are shown. It is now possible to consider the swe ll shapes of annular extrudate under industrially useful conditions. T he calculated swelling ratios were also compared with experimental one s.