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High weissenberg number simulation of an annular extrudate swell using the differential type constitutive equation
Author(s) -
Tanoue Shuichi,
Kajiwara Toshihisa,
Iemoto Yoshiyuki,
Funatsu Kazumori
Publication year - 1998
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10202
Subject(s) - die swell , weissenberg number , swell , materials science , mechanics , finite element method , relaxation (psychology) , discretization , constitutive equation , flow (mathematics) , mathematics , mathematical analysis , physics , composite material , extrusion , thermodynamics , psychology , social psychology
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.