A revisitation of generalized Newtonian fluids

Abstract

Creating an entry vortex growth simulation to show viscous and elastic fluid behaviors has always been a major challenge for the computational rheology of well-characterized polymer melts with extension thickening. For one thing, it is difficult to ensure stable convergence and reliable solutions via the viscoelastic constitutive equations at a relatively high Deborah number. From a revisitation of the generalized Newtonian fluids (GNFs), deriving the weighted viscosity is natural with the coexistence of shear and extensional flow; it is called the eXtended GNF (GNF-X) model. Herein, 3D contraction flow simulations incorporating the GNF-X weighted viscosity were significantly carried out over a wide range of Deborah numbers. Numerical results regarding changes in vortex sizes exhibit the same trend of experimental observations, while the predictive accuracy is enhanced for a quantitative comparison. More importantly, the vortex formation, in terms of the weighted viscosity and the extensional flow, is demonstrated with supporting evidence.