Quenching of unsteady vortex breakdown via harmonic modulation

Juan M. Lopez, Y.D. Cui, F. Marques and T.T. Lim

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Movie 1. Movie 2. Movie 3.

Movie 1 shows 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 = &Omega 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 in the video). The video 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 and Perry (1992a) for this natural limit cycle flow, LCN.

Movies 2 and 3 display the flow behavior 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 behavior as 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.


Movie 4 is 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.


Movie 5. Movie 6.

Movie 5 shows 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.

Movie 6 shows 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.