Effect of an exit-geometry on pinch-off and mass entrainment of vortex rings in air

Abstract

The effects of the exit geometry of a vortex ring generator and initial conditions on evolution, formation, circulation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied experimentally and numerically. Two types of exit planes were chosen: an orifice with a wall and a cylindrical nozzle without a wall. Experiments and numerical simulations were performed over a wide range of exit-wedge angles (10° ≤ $\alpha$ ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4580) and length-to-diameter ratios (0.7 ≤ L/D ≤ 11) of the air jet. An experimental rig, provided with a novel type of vortex ring generator, was developed. Vortex rings were generated by pushing a solenoid-valve-controlled, pressurized-air jet through the circular opening of the orifice or nozzle. Particle image velocimetry technique was extensively used to explore the velocity and vorticity fields of the vortex rings. Hotwire anemometry was used to assist the measurement of exit-jet velocities. The exit geometry was found to significantly influence the entire course of propagation of the vortex ring. The orifice-generated vortex ring had superior characteristics to that produced by the nozzle under the same conditions. The vorticity generated along the wall in the orifice exit plane had a negligible effect on the circulation of the vortex ring within the specified range of Reynolds number. Compared to the nozzle-generated vortex ring, the orifice-generated ring showed reduced initial vorticity losses and less diffusive entrainment of ambient fluid. The vortex rings produced by the orifice attained more circulation, less entrainment of ambient fluid and hence rapidly propagated through longer distances in comparison to the nozzle-generated rings. For sharp edges ($\alpha$ ≤ 10°) of nozzle geometry, a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges ($\alpha$ ≥45°), b...