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Flows between rotating disks


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Members: F. Moisy, O. Doare, T. Pasutto, G. Gauthier, P. Gondret, M. Rabaud.

Collaborations: O. Daube (CEMIF / LME), C. Nore (LIMSI), P. Le Quéré (LIMSI).


The instability patterns in the flow between rotating disks enclosed in a stationary cylinder are experimentaly investigated. In our experimental setup (figure 1), the lower disk (in black) rotates in the transparent cylindrical cylinder, which may rotate as well. The instability patterns are characterized by means of simple visualizations and by Particle Image Velocimetry (PIV).

Figure 1: Sketch of the experimental setup.

The experimentaly observed flow patterns are summarized in the regime diagram in figure 2. The horizontal and vertical axis represent the angular velocity of each disk. The aspect ratio of the cell has been fixed to R/h = 21. The yellow and pink areas correspond to the boundary layer instabilities, observed in corotation and weak counter-rotation. The blue area correspond to the shear layer instability, only observed in the counter-rotating flow.

Figure 2: Regime diagram of the various flow patterns oberved in the flow between rotating disks.

Boundary layer instabilities

The flow, initialy homogeneous for low rotation rates, bifurcates towards a propagating circular wave state (figure 3). As the rotation rate is further increased, another instability pattern appears, in the form of a set of spiral arms. This pattern is called "positive spirals", because the arms make a positive angle with respect to the azimuthal velocity of the fluid. Circular waves and positive spirals are confined in the inward boundary layer close to the stationary disk (Gauthier et al. 1999).

Figure 3 : Visualizations using Kalliroscope flakes of the boundary layer instability patterns : positive spirals and circular waves.

Shear layer instability

The flow between counter-rotating disks give rise to a new instability pattern (figure 3), which consists in a polygonal set of vorticies surrounded by spiral arms. (Moisy et al 2003, 2004). The spiral arms now make a negative angle with the azimuthal velocity (Gauthier et al 2002). For low aspect ratios, R/h between 2 and 6, only the central polygonal pattern can be seen, while for larger aspect ratios (R/h > 14) only the spiral arms can be seen.

Figure 4: Visualizations using Kalliroscope flakes of the shear layer instability for various interdisk gaps. The flow pattern consists in a polygonal set of vortices (here 3, 4 and 5 vortices) surrounded by "negative" spiral arms. In the first picture (a), only the polygonal pattern can be seen. In the last picture (d), only the spiral arms are present.

Particle Image Velocimetry measurements allowed us to identify the mechanism responsible for these flow patterns observed in the counter-rotating regime. This velocity measurement technique allows to reconstruct the instantaneous 2D velocity field from image correlations of particles lighted by a horizontal laser sheet between the two disks.

In figure 5, an intense annular shear layer (in red) may be seen, that separates two fluid regions rotating in opposite directions. This shear layer is prone to a Kelvin-Helmholtz - like instability, that breaks the axisymmetry of the base flow. The spiral arms result from the interaction of the shear layer instability with the outward boundary layer over the faster rotating disk.


Figure 5: Velocity and vorticity fields, measured at mid-height by PIV. In figure (a) an intense shear layer, in red, becomes unstable and gives rise to a polygon, with a decreasing number of sides as the rotation rate is increased.

The new class of instability revealed in our experiment has motivated a numerical study of the flow between counter-rotating disks, by O. Daube (CEMIF / LME). Figure 6, obtained for large aspect ratio, shows a spiral pattern in excellent agreement with the ones observed experimentally.

Figure 6: Numerical simulation of the 3D flow between counter rotating disks. The annular shear layer may be seen (in blue), together with the "negative" spiral rams.

Publications

  • C. Nore, F. Moisy and L. Quartier, Experimental observation of near-heteroclinic cycles in the von Karman swirling flow, Phys. Fluids 17 (6), 064103 (2005) [Abstract].
  • F. Moisy, O. Doaré, T. Pasutto, O. Daube and M. Rabaud, Experimental and numerical study of the shear layer instability between two counter-rotating disks, J. Fluid Mech. 507, 175-202 (2004). [Abstract].
  • F. Moisy, T. Pasutto and M. Rabaud, Instability patterns in the flow  between counter-rotating disks, Nonlinear Processes in Geophysics 10 (3), 281-288 (2003). [Abstract].
  • G. Gauthier, Ph. Gondret, F. Moisy et M. Rabaud, Instabilities in the flow between co and counter-rotating disks, J. Fluid Mech 473, 1-21 (2002) [Abstract].
  • G. Gauthier, P. Gondret, F. Moisy and M. Rabaud, Patterns between two rotating disks, Phys. Fluids 14 (9), S7 (2002) [Gallery 2002 | PDF (224Kb)].
  • G. Gauthier, Ph. Gondret et M. Rabaud, Axisymmetric propagating vortices in the flow between a stationary and a rotating disk, J. Fluid Mech. 386, 105-126 (1999 ). [Abstract].
  • G. Gauthier, Ph. Gondret et M. Rabaud, Motions of anisotropic particles: application to visualization of three directional flows, Phys. Fluids 10 , 2147-2154 (1998 ). [Abstract].

Last modification: September 25 2007, 15:59:55.