A study of the geometry and parameter dependence of vortex breakdown

Abstract

The types of vortex breakdown observed in the torsionally driven cylinder (TDC) flow and in the flow through an open-ended pipe are compared. The connection between the various breakdown types is specifically addressed, and the differences in manifestation of breakdown are attributed to the different Reynolds number regimes involved. Here, in both cases, the Reynolds number is based on quantities associated with the vortex core immediately upstream of breakdown, rather than the more geometry-specific Reynolds number defined in the previous work. Thus, the relationship between the TDC flow and the flows observed in other, more open geometries, is clarified. The predominantly asymmetric breakdown observed in open high Reynolds number flows is replaced by a closed bubble form with decreasing Reynolds number in the TDC. Three-dimensional numerical simulations support this interpretation, showing that the 3D spiral type of breakdown is replaced by a TDC-type axisymmetric breakdown in an open pipe as the Reynolds number is reduced. The stability of the three-dimensional solutions indicates that spiral breakdown modes stabilise at lower Reynolds number, leading to an axisymmetric breakdown state as a stable evolved flow solution.