Numerical simulation of vortex rings in non-Newtonian fluids

The impulsive viscous flow through an orifice produces vortex rings that self-propagate until total dissipation of the vorticity. This work aims to study numerically such vortex rings for different types of non-Newtonian fluids, including the power-law, Carreau and simplified Phan-Thien-Tanner (PTT) rheological models, with particular focus on the post-formation phase. The simulations were carried out with the finite-volume method, considering small stroke ratios (L/D ≤ 4) and laminar flow conditions (Re_G ≤ 10³), while parametrically varying shear-thinning, inertia and elasticity. The vortex rings generated in power-law fluids revealed some peculiar features compared to Newtonian fluids, such as a faster decay of the total circulation, a reduction of the axial reach and a faster radial expansion. The behavior in Carreau fluids was found to be bounded between that of power-law and Newtonian fluids, with the dimensionless Carreau number controlling the distance to each of these two limits. The vortex rings in PTT fluids showed the most disruptive behavior compared to Newtonian fluids, which resulted from a combined effect between inertia, elasticity and viscous dissipation. Depending on the Reynolds and Deborah numbers, the dye patterns of the vortex rings can either move continuously forward or unwind and invert their trajectory at some point. Elasticity resists the self-induced motion of the vortex rings, lowering the axial reach and creating disperse patterns of vorticity. Overall, this work shows that the particular non-Newtonian rheology of a fluid can modify the vortex ring behavior typically observed in Newtonian fluids, confirming qualitatively some experimental observations.