The generation of axial vorticity in solid-propellant rocket-motor flows

We examine small deviations from axial symmetry in a solid-propellant rocke t motor, and describe a 'bath-tub-vortex' effect, in which substantial axia l vorticity is generated in a neighbourhood of the chamber centreline. The unperturbed flow field is essentially inviscid at modest Reynolds numbers, even at the chamber walls, as has long been known, but the inviscid perturb ed flow is singular at the centreline, and viscous terms are required to re gularize it. We examine perturbations sufficiently small that a linear anal ysis is valid everywhere (epsilon Re small, where epsilon is a measure of t he perturbation amplitude and Re is a Reynolds number), and larger perturba tions in which a nonlinear patch is created near the centreline of radius O (root epsilon). Our results provide an explanation of swirl experimentally observed by others, and a cautionary note for those concerned with numerica l simulations of these flows, whether laminar or turbulent.