Circulation of Vortex Rings Formed From Tube and Orifice Openings

Two common configurations for generating vortex rings via jet pulses are the tube and orifice geometries. The orifice geometry forces the flow to contract as it approaches the jet exit plane, which can strongly affect vorticity flux and the circulation of the resulting ring. The author’s recent extension of the traditional slug model for vortex ring circulation (called the “pressure corrected” or PC model) accounts for the geometric differences between the tube and orifice cases, but model validation for the orifice geometry has been limited due to the lack of data for this configuration. The present study compares process of circulation generation by tube and orifice geometries using numerical simulations of finite duration jets from tube and orifice openings. Total jet slug length-to-diameter ratios (L/D) in the range of 0.5 to 3.5 and a jet Reynolds number of 2000 are considered. The numerical results confirm the underlying assumptions of the PC model. The model results for the tube geometry are within 14% of the numerical results. Incorporating the scaling of ring velocity with ejected jet length (X/D) obtained from the present numerical results improves the predictions for the orifice case, giving accuracy to within 20%. The overall geometry effect appears as a two-fold increase in circulation for the orifice case over the tube case at the same L/D.