On the generation of a spiral-type vortex breakdown in an enclosed cylindrical container

Abstract

Earlier experimental studies [see H. U. Vogel, “Experimentelle Ergebnisse über die Laminare Strömung in einem zylindrischen Gehäuse mit darin rotierender Scheibe,” Max-Planck-Inst. Bericht 6 (1968) and M. P. Escudier, “Observations of the flow produced in cylindrical container by a rotating endwall,” Exp. Fluids 2, 189 (1984)] showed that vortex breakdown in an enclosed cylindrical container with one rotating endwall could exhibit either one, two, or three recirculating bubbles depending on the combination of Reynolds number Re and aspect ratio H∕R, at least for H∕R⩽3.5. However, a recent numerical study by Serre and Bontoux [“Vortex breakdown in a three-dimensional swirling flow,” J. Fluid Mech. 459, 347 (2002)] at H∕R=4.0 showed that under some conditions, an S-shape vortex structure follows by a spiral-type vortex breakdown could also be produced. This finding is most interesting because, to the best of our knowledge, a spiral-type vortex breakdown in an enclosed cylindrical container has not been produced previously in experiments. The aim of the present investigation is to verify if these vortex structures can be produced under laboratory conditions. Experiments conducted using dye visualization techniques confirm their existence, even for H∕R as low as 3.65. However, attempts to produce similar vortex structures in low aspect ratio cases (H∕R⩽2.5) by “artificially” introducing three dimensionality into the flow was less successful. Here, the confined environment makes a bubble-type vortex breakdown extremely robust, and the imposed asymmetry merely distorts the bubble geometry. The present study also reveals that the formation of a bubble-type vortex breakdown is associated with helical instability of decreasing wavelength, and the S-shape structure is linked with a similar instability of increasing wavelength.