Numerical Simulation of a Non-Newtonian Fluid during the Filling Process of a Die

In this paper, a numerical model is developed which can predict behavior of non-Newtonian fluids. These kinds of fluids have complex rheology and simulation of their behavior has always been a challenge. The present study concentrates on a special type of non-Newtonian fluids called viscoplastic. To investigate their behavior a numerical model is developed in which the free surface is determined by volume-of-fluid method. To validate the model, flow properties of Herschel-Bulkley are modeled and compared with the experimental results reported in the literature. Afterwards, filling of a ۲D cavity with Bingham fluid is simulated. Models which are used for Herschel-Bulkley and Bingham fluids are Herschel-Bulkley and Papanastasiou models, respectively. Five flow patterns are observed by changing the Reynolds and Bingham numbers of the flow. It is shown that formation of voids which undesirably occurs during the filling process can be eliminated by controlling the flow velocity. The obtained results well agree with those reported in the literature.