Flow of yield-stress liquids through an axisymmetric abrupt expansion-contraction

We analyze the effect of inertia on the flow of viscoplastic liquids through an axisymmetric expansion followed by a contraction. The fluid is assumed to behave according to the Generalized Newtonian Liquid (GNL) model whose viscosity function is given by the SMD equation [1]. The conservation equations of mass and momentum, together with the constitutive equation, are approximated by a mixed Galerkin least-squares (GLS) formulation in terms of pressure and velocity. A parametric study is performed to investigate the influence of inertia and viscoplasticity on this flow. It was found that the topology of the yield surface is strongly affected by the flow intensity, but only mildly influenced by the shear-thinning fluid behavior. Inertia dramatically changes the topology of the yield surfaces, such that the fore-aft symmetry observed for low-inertia flows in the middle tube is lost.