The dynamics of confined vortices

Abstract

Referring to flow-visualization and laser-Doppler anemometer measurements of swirl and axial velocity profiles, we discuss the physics of the flow in a cylindrical vortex tube as various independent parameters are varied. Three main classes of flow occur, depending upon the location of a vortex jump within the vortex tube. We present evidence to suggest a connection between vortex breakdown and the criticality and stability of the vortex core upon which it occurs and attempt to reconcile the various explanations that have been proposed for the breakdown phenomenon. Similarities and differences between the present experiments and those of previous investigators are also pointed out. Finally, as an Appendix, we present the results of a hydraulic analogue of our vortex experiment.

Control of axisymmetric vortex breakdown in a constricted pipe: Nonlinear steady states and weakly nonlinear asymptotic expansions

“…Secondary helical disturbances may then grow, the mode selection and internal structure of the breakdown pattern being then viewed as a consequence of the stability properties of the axisymmetric breakdown solution itself. 7 This has been confirmed by the recent numerical simulations of Ruith et al, 10 who have shown that the early stage of breakdown is axisymmetric. For large swirl numbers, a finite time is needed before this flow pattern is altered by the subsequent development of large-scale spiral waves of various azimuthal wavenumbers, wrapped around and behind the axisymmetric bubble.…”

“…3 In return, the understanding of the sequence of events leading to vortex breakdown remains limited despite extensive theoretical, numerical, and experimental researches over the last decades. 2,[4][5][6][7][8] This results in a poor effectiveness of the techniques applied to flow control, 9 hence motivating the undertaking of further fundamental investigations.…”

Simulations of confined turbulent vortex flow

“…At the outlet, a zero-gradient boundary condition was imposed. Only in one case (with the largest D e /D ratio, and at Re = 4600) unrealistic behavior of the flow starting at the exit boundary, and propagating upstream was observed which was probably due to subcriticality [13] at the exit plane. Application of a convective exit boundary strongly reduced (but not fully solved) the problem.…”

“…In measuring the radial velocity profiles, Escudier and co-workers took care to traverse their LDA measuring volume through the vortex core center (defined as the position with zero transverse velocity), which in general does not coincide with the geometrical center of the flow facility [11]. Furthermore, in [11] (and also in [13]) flow visualization photographs were presented at various Reynolds numbers, and various D e /D ratios.…”

“…Furthermore, vortex breakdown was observed inside, or slightly upstream of the exit pipe. A third important observation when visualizing the flow was the clear distinction between the vortex core region where radial mixing is strongly suppressed, and the outer region that shows turbulent vortical structures (Taylor-Gö rtler vortices [2,13]). The large-eddy simulation of the vortex tube flow with a full representation of the geometry and operating conditions as used in the experiments is the subject of the study described in the present article.…”