Using a 12-bit CMOS camera (Phantom Miro EX4, Vision Research, Ametek, New Jersey, USA) fitted with an 18-70 mm focal length lens (Nikon, Tokyo, Japan), we recorded the flow images for both these methods at 1200 fps and 50 μs exposure time. Because of the low exposure time, we additionally illuminated the background using two 1000W halogen lamps. The camera was placed to record a lateral view of vortex ring propagation in a plane perpendicular and vertical to the nozzle exit plane. The external diameter of the nozzle served as a calibration scale for the images.
Based on exit diameter of the nozzle (D o ) and the ring average velocity (U avg ), we define non-dimensional time T n = U avg t/D 0 where t is the measured time. Similarly, the axial distance X n from the nozzle exit is nondimensionalized with the exit diameter D 0 and given by X n = X/D 0 . The dimensionless diameter of the ring is given by D n = D vb /D 0 , where D vb is the instantaneous diameter of vortex bubble (i.e., diameter of the ring with entrained air; Fig 1), and dimensionless velocity of the ring is given by U n = U vb /U avg where U vb is instantaneous velocity of the vortex bubble.