Global Stability Analysis of Vortex Breakdown in Misaligned Compressible Swirling Jet*

A vortex breakdown is an important phenomenon for many engineering applications and contains a complicated mechanism of transition from a bubble vortex breakdown to several types such as spiral, double helix, and turbulent vortex breakdowns.  Many of global stability analyses on the transition have been conducted and revealed instability mechanisms and wavemaker regions.  In the previous studies, an incompressible flow was considered and a base flow was an axisymmetric bubble obtained from an axisymmetric profile of a longitudinal vortex.  However, for more practical cases, the base flow is not limited to be axisymmetric. Also, the compressibility should be taken into consideration.  At this work, an asymmetic bubble for a compressible flow was obtained as the base flow by introducing an offset between the axis of a swirling flow and the axis of a jet flow.  Based on this base flow, we conducted the global stability analysis on the transition from the bubble vortex breakdown to the spiral vortex breakdown.  From this analysis, we examine differences in a growth rate, a frequency, and the three-dimensional structure of an unstable mode.