On the structure of vortex rings from inclined nozzles

We carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston-cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. Fluids, vol. 10, 1998, pp. 400-416) and Troolin & Longmire (Exp. Fluids, vol. 48, 2010, pp. 409-420). We show that the flow is dominated by the interaction of two main vortical structures: The primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666-1671). We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core.