On the axisymmetric stability of heated supersonic round jets

Abstract

We perform an inviscid, spatial stability analysis of supersonic, heated round jets with the mean properties assumed uniform on either side of the jet shear layer, modelled here via a cylindrical vortex sheet. Apart from the hydrodynamic Kelvin–Helmholtz (K–H) wave, the spatial growth rates of the acoustically coupled supersonic and subsonic instability waves are computed for axisymmetric conditions ( m =0) to analyse their role on the jet stability, under increased heating and compressibility. With the ambient stationary, supersonic instability waves may exist for any jet Mach number M j ≥2, whereas the subsonic instability waves, in addition, require the core-to-ambient flow temperature ratio T j / T o >1. We show, for moderately heated jets at T j / T o >2, the acoustically coupled instability modes, once cut on, to govern the overall jet stability with the K–H wave having disappeared into the cluster of acoustic modes. Sufficiently high heating makes the subsonic modes dominate the jet near-field dynamics, whereas the supersonic instability modes form the primary Mach radiation at far field.