Some New Aspects of the Invariants of the Rate of Deformation Tensor and their Application in Viscoelastic Polymer Melts

Abstract

Non-Newtonian fluids, such as polymer melts, are modeled with viscoelastic models. In this work the use of the anisotropic mobility tensor of Giesekus and Phan Thien and Tanner in order to generalize the Maxwell model is discussed. Similarities in one-dimensional flows are needes to reproduce real fluid behavior under shear and elongation deformations. But the fact of different anisotropic mobility tensors in the models show that there are also differences in two and three-dimensional viscoelastic flows. Therefore, we introduce a flow type parameter, using the invariants of the rate of deformation tensor. Here, the flow type is fully independent of the material model and therefore universally deployable. The numerical framework is done with Open FOAM a Finite Volume based library. The stabilization of the simulations is carried out applying the Viscous Formulation and the Discrete Elastic Viscous Stress Splitting methods. A 4:1 contraction benchmark is done over a wide range of the Deborah number in order to show the stability of the methods used. Furthermore, the flow type parameter is applied on a Cross-Slot geometry. Here, the influence of the elasticity in the Euler velocity field and the rate of deformation tensor are shown to be dependent on the model used.