Streamwise vortex breakdown in supersonic flows

Abstract

Transition processes in supersonic streamwise vortices with wake flows are numerically simulated for Mach numbers from 1.5 to 5.0. This paper discusses the effect of an axial velocity deficit on the breakdown for a fixed small swirl number. For the evolution of the linear unstable mode at Mach 2.5, although the linear-growth range is short, the eigenfunction profiles of the mode resolved from a numerical simulation are generally consistent with those obtained from the linear stability analysis. For the discovery of the supersonic vortex breakdown, when the deficits are large within Mach number 2.5, spiral breakdowns occur with the azimuthal wavenumber |m| = 1. This suggests that there might be a correlation between the breakdown and absolute instability not only in subsonic but also in supersonic flows. As a means of determining when this breakdown will occur, this study proves under the condition of compressible flows that such a spiral breakdown occurs where the integrated enstrophy in a plane perpendicular to the axial flow is close to a maximum in the streamwise variation. Ultimately, this study found that the axial velocity on the vortex axis increases in shock-free supersonic vortex breakdowns; thus, there is no stagnation point and the breakdown configuration is only of a spiral type. The features for this breakdown are quite different from those of subsonic breakdowns, as they only depend on the swirl intensity.