High weissenberg number simulation of an annular extrudate swell using the differential type constitutive equation

Annular extrudate swell simulations at high Weissenberg numbers were made using a differential type constitutive equation. The streamline-upwinding method with a sub-element for extra stress components, which is called SU4×4, is one of the best mixed finite element methods for computation of viscoelastic flows. Planar and capillary extrudate swell calculations at high Weissenberg numbers (We>1000) were accomplished by SU4×4. However, annular extrudate swell simulations at high We by SU4×4 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 under-relaxation method." The calculated We of annular extrudate swell simulation by the new under-relaxation method with SU4×4 was about 6∼250 times larger than those by SU4×4. Reasonable calculation results were obtained in an annular flow and a capillary extrudate swell by this method, and the reliability and the utility of the new under-relaxation method are shown. It is now possible to consider the swell shapes of annular extrudate under industrially useful conditions. The calculated swelling ratios were also compared with experimental ones.