On the formation and sustenance of the compressible vortex rings in starting axisymmetric jets: A phenomenological approach

Abstract

The present work numerically investigates the formation and sustenance of a primary vortex ring (PVR) and counter-rotating vortex rings (CRVRs) in laminar, axisymmetric, continuously blowing compressible jets. The effect of jet Reynolds number (Rej), jet Mach number (Mj), and pressure-ratio (pjpa) on these compressible vortex rings and their flow dynamics is explored. The core bow shock is formed in the inviscid core of the transonic/supersonic jets for sustaining the supersonic flow field in the PVR. The embedded shock (ES) and vortex-induced shock (VIS) are also found to sustain the evolving PVR in the supersonic jets. The effect of Mj and pjpa on the circulation and pinch-off of the PVR is also investigated. For over-expanded and perfectly expanded supersonic jets, Kelvin–Helmholtz vortices (KHVs) entrained into the PVR interact with the ES to cause a shock–vortex interaction, which results in the appearance of multiple VISs. It is established that the different events of interaction of KHV with the ES inside the PVR after the pinch-off are a manifestation of two factors: (i) the constraint imposed on the PVR by quasi-time-invariance of circulation around a material curve enclosing the PVR and (ii) the requirement of spatially cyclic property distribution inside the PVR. The shock-shear layer–vortex interaction in under-expanded jets is also investigated using vorticity analysis and oblique shock theory. For under-expanded jets, apart from the Mach-reflection timescale, the CRVR pattern formation is also governed by the initial strength of the slip-stream, which, in turn, is regulated by all three parameters, i.e., Rej, Mj, and pjpa.