Critical formation parameters of orifice generated turbulent vortex rings

Vortex rings are generated experimentally by a brief discharge of fluid through a sharp-edge nozzle or orifice. Based on initial parameters, the ring can be either laminar or turbulent and if the amount of fluid released exceeds a threshold value, energy is shed in a trailing wake in the form of hairpin vortices. In this study we reproduce the transition map of Glezer (1988) for an orifice outlet and assess the universality of the formation number (Gharib et al. (1998)). An actuator pushes fluid through a tube following a specific velocity program. In the case of nozzle geometries, the rolling-up of the vortex sheet occurs in the extension of the tube. Because an orifice apparatus consists of a flat plate covering the end of the tube, the ratio of the tube diameter D_p to the orifice diameter D₀ is expected to modify the formation process and the transition to turbulence. More precisely, the transition line is found to be shifted toward lower values of circulation-based Reynolds numbers Re_Γ = U₀L₀/2ν while the formation number is observed to be closer to unity. As the ratio D_p/D₀ tends to 1, the formation number tends towards those of Gharib.