Stability and temporal evolution of a swirling jet with centrifugally unstable azimuthal velocity

Abstract

A temporal linear instability analysis by the normal mode method and a direct numerical simulation (DNS) are performed to investigate the stability and temporal evolution of a swirling jet with centrifugally unstable Taylor vortex-like azimuthal velocity. A marked instability character is that the Kelvin–Helmholtz modes are dominant at lower axial wave numbers and the modes of centrifugal instability are dominant at higher axial wave numbers. The results of DNS show that the early linear stage of evolution of swirling jet agrees well with that predicted by linear stability theory. In the nonlinear stage, the centrifugally unstable velocity profile has important influences on the evolution dynamics. For the basic flow with small vortex core (ρ=1), the negative axial vorticity suppresses the eruption of vorticity from the core and the formation of secondary vortex ring pairs with opposite vorticity. For the basic flow with larger vortex core (ρ=4.5), the negative axial vorticity is away from the core region. Centrifugally unstable swirl is favorable for the formation of secondary ring pairs and their outward radial movement at computing parameters, and is thus beneficial for mixing enhancement.