Vortex-flow regimes

Abstract

Analysis of a considerable body of new data, based upon flow-visualization experiments, reveals a simple criterion for the occurrence of vortex breakdown at a fixed location in a tube: Re B ∼ Ω -3 R −1 , where Ω is the circulation number, R the ratio of the radial to tangential velocities in the inflow region, and Re B the pipe Reynolds number at which vortex breakdown occurs. The constant of proportionality is found to be practically independent both of the pipe flare angle α and the type of breakdown observed (bubble, spiral, etc.) although the latter is shown to depend on Re B . Theoretical support for the experimental results is derived from the analysis of Benjamin (1962) combined with similarity arguments.