{'fraction_non_alphanumeric': 0.02574257425742574, 'fraction_numerical': 0.0, 'mean_word_length': 5.2407407407407405, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The generation of axial vorticity in solid-propellant rocket-motor flows

We examine small deviations from axial symmetry in a solid-propellant rocket motor, and describe a ‘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 modest 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. We examine perturbations sufficiently small that a linear analysis is valid everywhere (εRe small, where ε is a measure of the perturbation amplitude and Re is a Reynolds number), and larger perturbations in which a nonlinear patch is created near the centreline of radius O(√ε). Our results provide an explanation of swirl experimentally observed by others, and a cautionary note for those concerned with numerical simulations of these flows, whether laminar or turbulent.