Dynamics and mixing of vortex rings in crossflow

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Abstract
Direct numerical simulation is used to study the effect of crossflow on the dynamics, entrainment and mixing characteristics of vortex rings issuing from a circular nozzle. Three distinct regimes exist, depending on the velocity ratio (ratio of the average nozzle exit velocity to free-stream crossflow velocity) and stroke ratio (ratio of stroke length to nozzle exit diameter). Coherent vortex rings are not obtained at velocity ratios below approximately 2. At these low velocity ratios, the vorticity in the crossflow boundary layer inhibits roll-up of the nozzle boundary layer at the leading edge. As a result, a hairpin vortex forms instead of a vortex ring. For large stroke ratios and velocity ratio below 2, a series of hairpin vortices is shed downstream. The shedding is quite periodic for very low Reynolds numbers. For velocity ratios above 2, two regimes are obtained depending upon the stroke ratio. Lower stroke ratios yield a coherent asymmetric vortex ring, while higher stroke ratios yield an asymmetric vortex ring accompanied by a trailing column of vorticity. These two regimes are separated by a transition stroke ratio whose value decreases with decreasing velocity ratio. For very high values of the velocity ratio, the transition stroke ratio approaches the ‘formation number’. In the absence of trailing vorticity, the vortex ring tilts towards the upstream direction, while the presence of a trailing column causes it to tilt downstream. This behaviour is explained. In the absence of crossflow, the trailing column is not very effective at entrainment, and is best avoided for optimal mixing and entrainment. However, in the presence of crossflow, the trailing column is found to contribute significantly to the overall mixing and entrainment. The trailing column interacts with the crossflow to generate a region of high pressure downstream of the nozzle that drives crossflow fluid towards the vortex ring. There is an optimal length of the trailing column for maximum downstream entrainment. A classification map which categorizes the different regimes is developed.

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