Dynamics of vortex rings in cross-flow

Vortex rings formed in a cross-flow by continuous and/or single pulsations of a jet were studied. The pulsations were provided by the periodic closing and opening of a jet flow and/or by the sudden movement of a circular piston inside a cylinder, respectively. Single pulsations were selected to investigate the effects of different jet exit geometries on the generation, dynamics and penetration of vortex rings: one geometry was a straight walled tube, and the other was a sharp-edged orifice with the same exit diameter. Continuous pulsation was used to study its effects on the development of vortex rings and their penetration in a cross-flow. Pulsation frequency and the ratio of piston velocity to cross-flow velocity were selected as key parameters for each experiment. Detailed measurements were made using flow visualization techniques, including laser induced fluorescence, and hot-film anemometry. Characteristic parameters investigated consisted of the translational velocity, circulation, diameter and core of the ring. To theoretically simulate the dynamics of vortex rings in cross-flow, a numerical simulation for three-dimensional vortex rings was performed based on a Lagrangian, grid-free, three-dimensional vortex method. For continuous pulsations, it was found that, at low frequencies, the fluid in the vortex rings penetrated into the cross-flow to a height much greater than that for high frequency pulsation or for a steady jet injection (up to five times). Dynamically, the downstream segment of the vortex rings moved upward (tilted) by about 3° to 4° under the effect of interaction between the vortex ring and the cross-flow. This type of motion was also qualitatively predicted by the numerical simulation of three-dimensional vortex rings incross-flows. The detailed velocity field within a vortex ring generated by pulses at 1 Hz was measured using a hot-film probe. From the study of the velocity field along the exit centerlines it was observed that the vortex rings were fully-formed at Z = 3.0 d_j. This is in agreement with other experiments in air as well as computational results. Single pulsations showed that the vortex ring penetration height was much greater for a sharp-edged orifice than for a straight walled tube, for the same piston and cross-flow velocities. Hence, it was seen that the jet exit boundary condition is a key parameter which determines the formation process of a vortex ring, its penetration and characteristic parameters mentioned above.