Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow
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2.P. S. Krueger and M. Gharib, “The significance of vortex ring formation to the impulse and thrust of a starting jet,” Phys. Fluids 15, 1271 (2003).
3.Flow visualization of ring formation and measurements of ring velocity with and without the shroud in place confirmed that the shroud had negligible effect on vortex ring formation.
4.Due to limitations of the pump supplying the co-flow, could not be achieved for
5.N. Didden, “On the formation of vortex rings: Rolling-up and production of circulation,” Z. Angew. Math. Phys. 30, 101 (1979).
6.M. Rosenfeld, E. Rambod, and M. Gharib, “Circulation and formation number of laminar vortex rings,” J. Fluid Mech. 376, 297 (1998).
7.At additional uncertainty is present because the pinchoff process is completed near the end of the shroud where the co-flow obtains a slight radial component. This may affect the pinchoff process, but the authors estimate the uncertainty in the reported formation numbers at to be within
8.For the case where the finite thickness of the vortex ring generator and the relatively large for and for leads to the formation of an annular wake behind the vortex ring generator after the jet and co-flow reach steady-state values. The vorticity in this wake decreases to zero as the co-flow and jet mix downstream of the nozzle exit.
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