Date
Thu, 18 Jan 2001
Time
14:00 - 15:00
Location
Comlab
Speaker
Prof Francisco Marques
Organisation
University Politecnica de Catalunya

The flow in a cylinder with a rotating endwall has continued to

attract much attention since Vogel (1968) first observed the vortex

breakdown of the central core vortex that forms. Recent experiments

have observed a multiplicity of unsteady states that coexist over a

range of the governing parameters. In spite of numerous numerical and

experimental studies, there continues to be considerable controversy

with fundamental aspects of this flow, particularly with regards to

symmetry breaking. Also, it is not well understood where these

oscillatory states originate from, how they are interrelated, nor how

they are related to the steady, axisymmetric basic state.

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In the aspect ratio (height/radius) range 1.6 2.8. An efficient and

accurate numerical scheme is presented for the three-dimensional

Navier-Stokes equations in primitive variables in a cylinder. Using

these code, primary and secondary bifurcations breaking the SO(2)

symmetry are analyzed.

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We have located a double Hopf bifurcation, where an axisymmetric limit

cycle and a rotating wave bifurcate simultaneously. This codimension-2

bifurcation is very rich, allowing for several different scenarios. By

a comprehensive two-parameter exploration about this point we have

identified precisely to which scenario this case corresponds. The mode

interaction generates an unstable two-torus modulate rotating wave

solution and gives a wedge-shaped region in parameter space where the

two periodic solutions are both stable.

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For aspect ratios around three, experimental observations suggest that

the first mode of instability is a precession of the central vortex

core, whereas recent linear stability analysis suggest a Hopf

bifurcation to a rotating wave at lower rotation rates. This apparent

discrepancy is resolved with the aid of the 3D Navier-Stokes

solver. The primary bifurcation to an m=4 traveling wave, detected by

the linear stability analysis, is located away from the axis, and a

secondary bifurcation to a modulated rotating wave with dominant modes

m=1 and 4, is seen mainly on the axis as a precessing vortex breakdown

bubble. Experiments and the linear stability analysis detected

different aspects of the same flow, that take place in different

spatial locations.

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