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Modelling of optimal vortex ring formation
平成18年11月10日（金）１６：３０〜１８時
電気通信大学 東4号館 8階 AV会議室
Previous studies show that vortex rings generated in the laboratorycan be optimized for efficiency, based on the jet length-to-diameterratio L/D, with peak performance occurring 3.5 < L/D < 4.5 (Gharibet. al, J. Fluid Mech., 360, 1998).
The objective of the present research is to develop predictive modelof the optimal vortex ring formation. For this purpose we consideredan analytical solution describing the evolution of a vortex ring fromthin to thick-cored form in the Stokes approximation. The presentcontribution extends analysis reported in (Kaplanski and Rudi,Phys. Fluids, 17, 2005) and is used to give prediction for thelimiting value of L/D on the basis of thekinematic approach. Thecalculated value 3.5 is identical to the result by Shusser and Gharib(Phys. Fluids, 12, 2000), who suggested this approach and used theNorbury's invariants. A particular attention is given to the dynamicapproach in order to understand the effect of the vortex ringpinch-off process (dynamical separation of the leading vortex ringfrom the trailing flow). It is shown that the model is applicable notonly for prediction of the critical L/D and appropriate thenormalized energy and circulation, but also vortex ring properties atthe pinch-off.