Generating fully developed flow profiles for simulations of viscoelastic fluids described by differential models

In this paper, an iterative method is developed to compute the flow profiles of a viscoelastic fluid without solvent part described by various differential models in case of a two-dimensional fully developed channel flow. Therefore, the tensorial formulation of the models for the conformation tensor is written as a nonlinear one dimensional system of equations for the unknown components of the conformation tensor, the pressure and the velocity field. On the basis of an initial guess for the pressure drop, the unknown quantities can be determined iteratively. For sufficiently high relaxation times, the resulting flow profiles show typical viscoelastic behaviour. Furthermore, corresponding two-dimensional Finite Element simulations of a Poiseuille flow through a plane channel are used to perform a validation of the determined flow profiles for the Giesekus model.