Formation of an orifice-generated vortex ring

The formation of orifice-generated vortex rings, at a Reynolds number of 5300 and for a tube-to-orifice diameter ratio of 2.0, is experimentally investigated for stroke-to-diameter ratios of 0.5(0.5)5.0. A significant increase is observed in the production of the total invariants of the motion, namely the circulation Gamma, the hydrodynamic impulse I and the kinetic energy E, compared with the equivalent nozzle-generated vortex rings. The formation number, as defined by Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121-140), is found to be approximately 2.0. By measuring the kinematics and the invariants of the ring for increasing stroke ratios, a limiting process in the ring formation is observed, which allows us to define the critical parameters and time scales in the vortex formation process. In particular, it was shown that the ring circulation, impulse, and energy do not reach their asymptotic state at the same non-dimensional time and stroke ratio, hence these two terms cannot be used interchangeably. The stroke ratio required to produce a ring with maximum energy is defined as the 'optimal stroke ratio', which is found to be around 4. The non-dimensional time at which the ring reaches this state, termed the `optimal formation time', is found to be approximately 6-7. The non-dimensional vortex ring numbers alpha = E/rho(1/2) Gamma(3/2) I-1/2, beta = Gamma/rho(-1/3IU2/3)-U-1/3 and gamma = (V) under bar/rho(-3/2) Gamma(-3/2) I-3/2, are measured to be 0.33, 1.8 and 1.9, respectively, consistent with previous experimental, numerical and analytical work, suggesting these numbers to be universal for all isolated vortex rings.