Stability of a viscous subsonic swirl flow

Abstract

The results of calculating the stability of a three-dimensional swirl flow of a viscous heat-conducting gas are presented. The stability characteristics are determined using the linear time-dependent theory of plane-parallel flow stability. The main undisturbed axisymmetric vortex flow was determined numerically using a quasi-cylindrical approximation for the complete set of Navier-Stokes equations. The circulation of the peripheral velocity in the cocurrent flow surrounding the viscous vortex core was assumed to be constant. In analyzing the stability, nonaxisymmetric perturbations in the shape of waves traveling along the vortex axis with both positive and negative wavenumbers were considered; in these two cases the perturbation rotation is either the same or opposite in sense to the rotation in the vortex core. Neutral stability curves are determined for various values of the swirling parameter and the cocurrent flow Mach number.