Direct numerical simulation of spatially developing, three-dimensional swirling jets

Abstract

Vortex breakdown of nominally axisymmetric, swirling incompressible jets and wakes issuing into a semi-infinite domain is studied by means of direct numerical simulations, as well as local and global linear stability analyses. A two-parametric low entrainment velocity profile for which the steady, axisymmetric breakdown is well studied (Grabowski W J and Berger S A 1976 J. Fluid Mech. 75 525–44) is selected to discuss the role of the applied swirl in the existence and mode selection of vortex breakdown. As the swirl parameter is increased, bubble, helical and double-helical breakdown modes are observed for the moderate Reynolds number applied. It is shown that a local transition from super- to subcritical flow, as defined by Benjamin (Benjamin T B 1962 J. Fluid Mech. 14 593–629), accurately predicts the swirl parameter yielding breakdown. Thus the basic form of breakdown is axisymmetric. A transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability in the wake of the bubble, giving rise to a self-excited global mode. Preliminary axisymmetric results of a global linear instability analysis agree favourably with the direct numerical simulation and thus encourage extension of the global analysis to helical modes. This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.