An extension to the universal time scale for vortex ring formation

The formation of vortex rings emanating from orifices with different orifice-to-tube diameter ratios D-0/D-p is studied using time-resolved particle image velocimetry. The invariants of the motion in their non-dimensional form are computed and presented in the non-dimensional time space t* = U(0)t/D-0, where the subscript 0 refers to the exhaust quantities. The classic slug-flow model is revisited and extended to account for the contraction of the flow when fluid is being pushed out through the orifice. Accordingly, a new time scale in terms of the contracted quantities (subscript star) is defined as T * = U(star)t/D-star. Results show that the modified slug-flow model unifies the formation number of orifices and straight nozzles with a value of approximately 4.

Automated summary

This study examines vortex rings formed from orifices with different orifice-to-tube diameter ratios, calculating non-dimensional invariants and introducing a new time scale to unify the formation numbers of orifices and straight nozzles.