The generation of axial vorticity in solid-propellant rocket-motor flows (Q2711542)

The authors examine small deviations from axial symmetry in a solid-propellant rocket motor, and propose a description of `bath-tub-vortex' effect in which substantial axial vorticity is generated in a neighbourhood of the chamber centreline. The unperturbed flow field is essentially inviscid at moderate Reynolds numbers, even at the chamber walls, as has long been known, but the inviscid perturbed flow is singular at the centreline, and viscous terms are required to regularize it. The authors consider sufficiently small perturbations, so that a linear analysis is valid everywhere provided that \(\varepsilon \text{Re}\) is small, where \(\varepsilon\) is a measure of perturbation amplitude, and Re is Reynolds number. Additionally, the authors study larger perturbations in which a nonlinear patch is created near the centreline of radius \(O(\sqrt\varepsilon)\). The obtained results give an explanation of experimentally observed swirls, and a cautionary note for those concerned with numerical simulations of these flows, whether laminar or turbulent.