Eliminating Turbulence in Spatially Intermittent Flows

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Science  19 Mar 2010:
Vol. 327, Issue 5972, pp. 1491-1494
DOI: 10.1126/science.1186091

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  1. Fig. 1

    Instability mechanism. (A and B) Turbulent puff in the experiment at Re = 2000. The flow direction is from right to left. (A) Centerline velocity during the passage of the puff. (Inset) Azimuthally averaged velocity profiles at three positions. Although the profile at L/D > 0 has the typical shape of an averaged turbulent velocity field, close to L/D = –1 a strong inflection point is observed, and further upstream (L/D < 0) the laminar parabolic flow is quickly recovered. (B) The vorticity transport shows that for L/D positive, vorticity moves downstream, whereas for L/D negative vorticity moves upstream. At L/D = 0 vorticity is created. (C) Time-averaged quantities for a numerically simulated puff (Re = 1900). Positions are given in the co-moving frame of reference so that the location of the vorticity source (dashed line) is fixed. The magnitude of the inflection point (26) is shown in red, the vorticity transport in black, and the turbulent kinetic energy in green. The latter is plotted on a log-linear scale.

  2. Fig. 2

    Control in the numerical simulations. An axially localized forcing is applied to the rear interface of a turbulent puff so as to distort the laminar profile. (Top) Snapshots of streamwise vorticity isocontours of the puff at time instants separated by 30 time units. (Bottom) Time-series of the turbulent energy of the puff. The red line corresponds to the puff when no control strategy is applied, whereas the black line shows the effect of applying the forcing (the circles correspond to the time instants when the snapshots of the top panel have been taken). The forcing is introduced at t = 50, and its intensity is exponentially increased until it saturates at about t = 100 (blue dashed line).

  3. Fig. 3

    Interaction of two turbulent puffs in the experiment. (A) The solid line indicates the centerline velocity of a pipe flow at Re = 2000. The two puffs are separated by L/D = 6. The centerline velocity in between the puffs does not recover the value of the laminar Hagen-Poiseuille flow. The dotted lines indicate the centerline velocity at corresponding times in the numerical simulations for a puff before (blue) and after (red) the localized forcing has been applied. (B) (Left) The (azimuthally averaged) velocity profile at the rear of the upstream (second) puff (L/D = 12) shows a strong inflection point, whereas the inflection point at the rear of the downstream (first) puff (L/D = 6) is much weaker and strongly influenced by the presence of the upstream puff following it. Eventually, the front puff disappears, whereas the rear one remains unchanged. (Right) Qualitatively, the same reduction of the inflection point is observed in the numerical simulation when the forcing has been applied, again resulting in the decay of turbulence.

  4. Fig. 4

    Control in the experiment. (A) Flow visualization image of an axial cross section of a segment of the pipe in the intermittent regime at Re = 2000. The flow (from right to left) is laminar on the left and turbulent on the right. For the visualization, the water was seeded with 50-μm particles (Mearlmaid AA, Ludwigshafen, Germany). The particles are un-isotropic flat platelets that tend to align with the shear, resulting in a uniform light reflection when the flow is laminar and a patchy nonuniform one in the presence of turbulence. Images were recorded (at a frame rate of 25 Hz) at two locations: one 100 D upstream and the other 100 D downstream of the control point. (B and C) The laminar-turbulent intermittency in pipe flow is shown in space-time plots (B and C), whereas the gray values of the flow visualization images (A) are averaged along the pipe radius. The averaged gray values obtained for each flow-visualization image are then plotted as vertical lines, hence displaying the axial variation of the flow in the vertical direction and the time variation horizontally. The space-time plot resulting from the data sampled 100 D upstream of the control point is shown in (B) and that from data sampled 100 D downstream is shown in (C). Each occurrence of a turbulent puff in the observation section results in a dark, almost vertical band in the figures. Upstream (B) of the control point, turbulent puffs appear at regular intervals (every ~5 s). Downstream (C) of the control point, the vertical bands and hence the turbulence completely disappear shortly after the control has been actuated at t = 40 s. The broad darker and lighter horizontal stripes in (B) and (C) are due to intensity variations. (D) Pressure drop measured over ~250 D in pipe flow (Re = 2030) and ~250 H in plane channel flow (Re = 1400), and in a square duct (Re = 1740) relative to the pressure drop in laminar flow.

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