The Role of Vorticity Dynamics in Vortex Breakdown

1 Abstract The role of vorticity dynamics in vortex breakdown is examined in a theoretical and computational study. Under the assumptions of steady, incompressible, axisymmetric, invis-cid ow, a theory is developed concerning the interaction of vortex tilting and stretching in the breakdown process. This analytic theory is then connrmed using an unsteady, incompressible, axisymmetric viscous ow solver. The theoretical and computational results are in excellent agreement. Both results point towards the importance of vortex tilting in initiating vortex breakdown. The agreement between the inviscid theory and viscous computations indicates that breakdown is primarily an inviscid process. A measure of the susceptibility to breakdown is developed from the invis-cid theory which corresponds well with known experimental and numerical trends concerning the occurrence of vortex breakdown. 2 Introduction Since the recognition of vortex breakdown in the ow over delta wings at high angles of attack by Peckham and Atkinson in 1957, many theoretical, experimental, and computational studies have been performed in an attempt to better understand the breakdown process. Several good reviews are available which summarize a large amount of this workk1]]2]]3]. This paper relies mainly on the recent theoretical results of Brown and Lopezz4]]5]. Their work identiied the need for negative azimuthal vorticity in order to stagnate the core of a vortex. In this paper, we focus on the mechanisms which produce negative vorticity. Speciically, the role of vorticity dynamics in the production of negative azimuthal vorticity is studied. The ows considered are assumed to be incompressible and axisymmetric. Although vortex breakdown ows are only occasionally axisymmet-ric upstream of breakdown and rarely axisymmetric downstream of breakdown, a great deal of insight into the role of vorticity dynamics may be gained from assuming only axisymmetric ows. Two diierent sets of axisymmetric, incompressible equations are used in this study of vortex breakdown. The computational study models the ow using an axisymmetric, unsteady, viscous, incompressible ow solver. For the analytic work, the further assumptions of steady and inviscid