A group-velocity criterion for breakdown of vortex flow: An application to measured inlet profiles

Vortex flows exhibiting breakdown in a slightly divergent duct were measured. The slowly varying vortex flow field downstream of the entrance and upstream of the breakdown region is obtained numerically by using the inviscid quasi-cylindrical approximation. In these calculations, the Faler and Lebovich's experimental data were used as the starting conditions at the entrance of the duct. The group velocity of wave propagation for the axisymmetric mode (n = 0) and the asymmetric modes (n = + or - 1 and n = + or - 2) are calculated for the entrance conditions. For the theoretically predicted slowly varying flow field downstream of the entrance, the wave characteristics of the n = 0 and n = + or - 1 modes are presented. It was concluded that the flows which subsequently undergo vortex breakdown are all predicted to be supercritical and stable to infinitesimal inviscid disturbances, including the axially symmetric as well as the nonsymmetric perturbations.