Estudo de um novo modelo constitutivo de fluidos viscoplásticos : análise numérica do escoamento em uma contração abrupta 4:1

Abstract

Flow of viscoplastic material is extremely common in many industrial processes. A practical application includes the drilling of petroleum wells where the drilling mud must carry the drill chips with a minimum pumping power. It is obtained using a drilling mud as a highly viscoplastic material. The material used on cementation of drilling wells also exhibit a highly viscoplastic behavior. Other interesting phenomenon involving viscoplastic materials is the mucus displacement in pulmonary airways. The good understanding of the physical mechanism involved in all processes mentioned before is dependent of a good rheological characterization of the viscoplastic material involved. The viscoplastic behavior of the liquid is generally modelled by the generalized Newtonian liquid model with a typical viscosity function equation. One of the most common equation employed is the Herschel-Bulkley viscosity function. This equation predict an infinite viscosity in the limit of zero-shear-rate and this behavior is not compatible with continuity equation for many complex flows. In the present work a viscosity function recently proposed by Souza Mendes and Dutra (2004) is used to perform numerical simulations via finite element method of the flow of yield-stress materials. This viscosity function encompasses most of the viscoplastic and pseudoplastic models such as Herschel-Bulkley, Papanastasiou, Bingham and Carreau as special cases. In order to compare with the results available in the literature, the geometry chosen is the classic 4:1 abrupt contraction. One important dimensionless number analyzed is the jump number J that gives a relative measure of the shear rate jump that occurs when the extra-stress-tensor reaches the yield-stress plateau on the flow field