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Quenching of vortex breakdown oscillations via harmonic modulation

Published online by Cambridge University Press:  06 March 2008

J. M. LOPEZ ,
Y. D. CUI ,
F. MARQUES  and
T. T. LIM
J. M. LOPEZ
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe AZ 85287, USA
Y. D. CUI
Affiliation:
Temasek Laboratories, National University of Singapore, 119260Singapore
F. MARQUES
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
T. T. LIM
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 119260Singapore
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Abstract

Vortex breakdown is a phenomenon inherent to many practical problems, such as leading-edge vortices on aircraft, atmospheric tornadoes, and flame-holders in combustion devices. The breakdown of these vortices is associated with the stagnation of the axial velocity on the vortex axis and the development of a near-axis recirculation zone. For large enough Reynolds number, the breakdown can be time-dependent. The unsteadiness can have serious consequences in some applications, such as tail-buffeting in aircraft flying at high angles of attack. There has been much interest in controlling the vortex breakdown phenomenon, but most efforts have focused on either shifting the threshold for the onset of steady breakdown or altering the spatial location of the recirculation zone. There has been much less attention paid to the problem of controlling unsteady vortex breakdown. Here we present results from a combined experimental and numerical investigation of vortex breakdown in an enclosed cylinder in which low-amplitude modulations of the rotating endwall that sets up the vortex are used as an open-loop control. As expected, for very low amplitudes of the modulation, variation of the modulation frequency reveals typical resonance tongues and frequency locking, so that the open-loop control allows us to drive the unsteady vortex breakdown to a prescribed periodicity within the resonance regions. For modulation amplitudes above a critical level that depends on the modulation frequency (but still very low), the result is a periodic state synchronous with the forcing frequency over an extensive range of forcing frequencies. Of particular interest is the spatial form of this forced periodic state: for modulation frequencies less than about twice the natural frequency of the unsteady breakdown, the oscillations of the near-axis recirculation zone are amplified, whereas for modulation frequencies larger than about twice the natural frequency the oscillations of the recirculation zone are quenched, and the near-axis flow is driven to the steady axisymmetric state. Movies are available with the online version of the paper.

JFM classification

Vortex Flows: Vortex breakdown Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 441 - 464
Copyright
Copyright © Cambridge University Press 2008

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References

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Lopez et al. supplementary material

Movie 1. Dye flow visualization of vortex breakdown in a confined cylindrical container with the top lid stationary and the bottom lid rotating at a constant angular speed Ω. For the condition shown here, H/R = 2.5 and Re = Ω R2/ν = 2800, where R is the radius of the cylinder and H is the height of the fluid domain (only the central core flow near the axis is shown). The movie shows strong pulsing of the central recirculation zone on the axis and the formation and folding of lobes every period, which follows the detailed description of the chaotic advection given in Lopez & Perry (1992a) for this natural limit cycle flow, LCN.

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Video 466.3 KB

Lopez et al. supplementary material

Movies 2 and 3. The flow behaviour when the rotating lid is modulated at Ω(1+A sin(Ωft)), where A is the relative forcing amplitude and Ωf is the forcing frequency. At A = 0.04 and a relatively low forcing frequency of ωf = Ωf/Ω = 0.2, movie 2 shows qualitatively similar behaviour to that in movie 1 without the forcing. On the other hand, at the same forcing amplitude A, but higher forcing frequency of ωf = 0.5, the flow displays a quenching of the oscillations associated with the vortex breakdown bubble, as can be seen in movie 3.

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Video 455 KB

Lopez et al. supplementary material

Movies 2 and 3. The flow behaviour when the rotating lid is modulated at Ω(1+A sin(Ωft)), where A is the relative forcing amplitude and Ωf is the forcing frequency. At A = 0.04 and a relatively low forcing frequency of ωf = Ωf/Ω = 0.2, movie 2 shows qualitatively similar behaviour to that in movie 1 without the forcing. On the other hand, at the same forcing amplitude A, but higher forcing frequency of ωf = 0.5, the flow displays a quenching of the oscillations associated with the vortex breakdown bubble, as can be seen in movie 3.

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Video 371.2 KB

Lopez et al. supplementary material

Movie 4. The laser cross-section of the flow under the same conditions as in movie 3, obtained using fluorescent dye illuminated with a thin laser sheet along the meridional plane. While the vortex breakdown bubble is quenched to a quasi-steady state, there clear evidence of unsteadiness in the bottom left corner region and the sidewall region. An upward propagating wave near the upper sidewall boundary layer region can be also observed.

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Video 2.1 MB

Lopez et al. supplementary material

Movie 5. The computed streamlines ψ (left panel) and azimuthal component of vorticity η (right panel) of the forced limit cycle state LCF under the same conditions as the experimental case in movie 2, i.e. at Re = 2800, H/R = 2.5, A = 0.04 and ωf = 0.2.

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Video 3.3 MB

Lopez et al. supplementary material

Movie 6. The computed streamlines ψ (left panel) and azimuthal component of vorticity η (right panel) of the forced limit cycle state LCF under the same conditions as the experimental cases in movies 3 and 4, i.e. at Re = 2800, H/R = 2.5, A = 0.04 and ωf = 0.5.

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Video 1.9 MB