A UNIVERSAL TIME-SCALE FOR VORTEX RING FORMATION

The formation of vortex rings generated through impulsively started je ts is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide r ange of piston stroke to diameter (L/D) ratios. The results indicate t hat the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading v ortex ring formed is disconnected from that of the trailing jet. On th e other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in t his paper, is referred to as the 'formation number'. In all cases, the maximum circulation that a vortex ring can attain during its formatio n is reached at this non-dimensional time or formation number. The uni versality of this number was tested by generating vortex rings with di fferent jet exit diameters and boundaries, as well as with various non -impulsive piston velocities. It is shown that the 'formation number' lies in the range of 3.6-4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number base d on the Kelvin-Benjamin variational principle for steady axis-touchin g vortex rings. It is shown that based on the measured impulse, circul ation and energy of the observed vortex rings, the Kelvin-Benjamin pri nciple correctly predicts the range of observed formation numbers.