Modulated rotating waves in an enclosed swirling flow

H. M. Blackburn, Juan Lopez

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

The loss of axisymmetry in a swirling flow that is generated inside an enclosed cylindrical container by the steady rotation of one endwall is examined numerically. The two dimensionless parameters that govern these flows are the cylinder aspect ratio and a Reynolds number associated with the rotation of the endwall. This study deals with a fixed aspect ratio, height/radius = 2.5. At low Reynolds numbers the basic flow is steady and axisymmetric; as the Reynolds number increases the basic state develops a double recirculation zone on the axis, so-called vortex breakdown bubbles. On further increase in the Reynolds number the flow becomes unsteady through a supercritical Hopf bifurcation but remains axisymmetric. After the onset of unsteadiness, another two unsteady axisymmetric solution branches appear with further increase in Reynolds number, each with its own temporal characteristic: one is periodic and the other is quasi-periodic with a very low frequency modulation. Solutions on these additional branches are unstable to three-dimensional perturbations, leading to nonlinear modulated rotating wave states, but with the flow still dominated by the corresponding underlying axisymmetric mode. A study of the flow behaviour on and bifurcations between these solution branches is presented, both for axisymmetric and for fully three-dimensional flows. The presence of modulated rotating waves alters the structure of the bifurcation diagram and gives rise to its own dynamics, such as a truncated cascade of period doublings of very-low-frequency modulated states.

Original languageEnglish (US)
Pages (from-to)33-58
Number of pages26
JournalJournal of Fluid Mechanics
Volume465
DOIs
StatePublished - Aug 25 2002

Fingerprint

Swirling flow
swirling
Reynolds number
very low frequencies
aspect ratio
vortex breakdown
Aspect ratio
axisymmetric flow
three dimensional flow
period doubling
unsteady flow
steady flow
low Reynolds number
containers
Hopf bifurcation
frequency modulation
Frequency modulation
Steady flow
Unsteady flow
cascades

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Modulated rotating waves in an enclosed swirling flow. / Blackburn, H. M.; Lopez, Juan.

In: Journal of Fluid Mechanics, Vol. 465, 25.08.2002, p. 33-58.

Research output: Contribution to journalArticle

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