Growing Process and Structure of Axisymmetric Vortex Breakdown : 1st Report, An Inviscid Linear Model of the Growing Process of a Bubble

Abstract

This paper examines the axisymmetric type vortex breakdown in a swirling pipe flow, in order to clarify the growing process of a bubble. The unsteady flow field is investigated based on the inviscid linear theory of the internal wave (inertia wave). An expression of the time-dependent flow field with the internal wave propagation, which satisfies the condition of arbitrary velocity change at the upstream boundary of the circular pipe, is derived. Using this expression, the transition of the flow field, the streamlines and the streaklines calculated by computer are examined. The unsteady flow field, as the result of a sudden azimuthal velocity change at the upstream boundary, clearly shows the birth of a bubble and its growing process into a stationary state. The theoretical results are compared with the experimental growing process of the bubble in an actual swirling pipe flow obtained by the visualization technique. both results agree with each other fairly well concerning the bubble structure during the growing period. The behaviour of the fluid elements which are entrained into the bubble is also examined from the results of calculated pathlines.