粘弾性流体の高ワイセンベルグ数問題および二重管ダイスウェルシミュレーション

Abstract

It is difficult to analyze numerically the annular extrudate swell of a viscoelastic fluid at high Weissenberg numbers (We>100) though the streamline-upwinding (SU) finite element method is used. We first reviewed the past mathematical studies of the high Weissenberg number problem of the Maxwell model and the Oldroyd-B model. The Newtonian stress term in the Oldroyd-B model allows a solution to the steady-state flow problem in practical geometries at high Weissenberg numbers. This term suppresses the change of type to hyperbolic in the governing equations for steady state viscoelastic flow. We proposed a new calculation technique, THE (Transformation of Momentum equation to the Elliptic equation), which involves an underrelaxation of the deformation rate tensor in the viscoelastic flow governing equations for high We annular extrudate swell simulation. And we used THE to annular extrudate swell simulation problem for the Giesekus model. The limitations of calculated We by TME with SU were about 6 times (at α=0.1) and over 250 times (at α=0.5) higher than those by SU only. However it may be necessary to refine the mesh, including the use of TME, for high We annular extrudate swell simulation at α=0.1.