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Growth and separation of a start-up vortex from a two-dimensional shear layer
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10.1063/1.4758793
/content/aip/journal/pof2/24/10/10.1063/1.4758793
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/10/10.1063/1.4758793

Figures

Image of FIG. 1.
FIG. 1.

Layout of plasma actuator for the impulsive generation of an isolated two-dimensional line vortex. Note wall-jet and free-jet profiles shown for sake of clarification.

Image of FIG. 2.
FIG. 2.

(a) Experimental setup showing the laser light plane, two high-speed cameras, and the plasma actuator mounted on a manual traverse unit placed inside acrylic glass container. The flow is from left to right. (b) Schematic of the two fields of view. The larger field of view (80 mm × 50 mm) was used to characterize the vortex growth while the smaller field of view (20 mm × 12 mm) was used to resolve the high velocity gradients inside the shear layer.

Image of FIG. 3.
FIG. 3.

Sample smoke visualization of vortex evolution for Case D. As the vortex evolves, it convects downstream in the horizontal direction as well as away from the shear layer in the vertical direction. Flow is from left to right. The masked region marks the base plate.

Image of FIG. 4.
FIG. 4.

(a) An example of velocity distribution inside the vortex with feeding shear layer (along line A-A as shown in the lower left figure) for case C at t = 22 ms. The measured velocities from both fields of view (black triangles for FOV = 80 mm × 50 mm and open circles (red online) for FOV = 20 mm × 12 mm) are compared. The velocity distribution exhibits four regions (i.e., zones 1-4) on the upper side of the shear layer. (b) Sample vorticity field of the jet flow exhibiting upper (counter-clockwise) and lower (clockwise) shear layers. The numbers on this plot depict vorticity levels.

Image of FIG. 5.
FIG. 5.

The x-position of the vortex core as a function of time. The slope of the solid lines represents the mean convective speed of the vortex (u c ) obtained using the Biot-Savart relation.

Image of FIG. 6.
FIG. 6.

Model of vortex growth based on Kaden, 19 with growth due to the inflow of circulation-containing mass from the shear layer with thickness D and a maximum velocity u max . The vortex with radius r, and circulation Γ, travels with a velocity u c .

Image of FIG. 7.
FIG. 7.

Vortex radius for different test cases together with predictions by the proposed growth model (solid black lines). The growth rate due to viscous diffusion, (Lamb-Oseen model), is included for comparison. The dashed line marks the approximate onset of the vortex-growth plateau.

Image of FIG. 8.
FIG. 8.

Vortex strength for different test cases together with predictions by the proposed growth model (solid lines). The dashed line marks the approximate onset of the vortex-growth plateau and is the same as in Fig. 7 .

Image of FIG. 9.
FIG. 9.

(a) Schematic representing the separation mechanism of the vortex from the feeding shear layer, where κ is the radius of curvature of the shear layer and + represents the center of shear-layer curvature. The separation is linked to a competition between the shear layer's tendency to remain in the streamwise direction and the induced velocity from the vortex on the shear layer. (b) Sample planar streamlines in the stationary frame of reference before (left) and after (right) the separation of vortex from the shear layer. (c) Vorticity contours corresponding to velocity fields in (b).

Image of FIG. 10.
FIG. 10.

Γ* is a measure of the competition between the induced velocity from the vortex and the tendency of fluid particles in the shear layer to move in the streamwise direction. Γ* decreases in time due to the reduced contribution of vortex-induced velocity leading to a flattening of the shear-layer. The dashed line marks the approximate separation time of the vortex from the shear layer, as seen in Figs. 7 and 8 .

Image of FIG. 11.
FIG. 11.

The drop in the vortex radius-to-spacing ratio suggests that S depends on the overall flow field rather than the growth of the vortex itself. The dashed line marks the approximate separation time of the vortex from the shear layer, as seen in Figs. 7 and 8 .

Image of FIG. 12.
FIG. 12.

Parameter S/H provides a measure of the shear-layer curvature. The drop in the shear-layer curvature corresponding to the separation of the shear layer from the vortex is marked by the dashed line (the same line as in Figs. 7 and 8 ). The drop occurs at the same approximate time of the plateau in vortex growth. For clarity, cases B-D have been plotted with a vertical offset of S/H = 1, 2, and 3, respectively.

Tables

Generic image for table
Table I.

Plasma actuator voltage and shear-layer characteristics for different test cases.

Generic image for table
Table II.

Statistics of u o /u max  for different test cases.

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/content/aip/journal/pof2/24/10/10.1063/1.4758793
2012-10-19
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Growth and separation of a start-up vortex from a two-dimensional shear layer
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/10/10.1063/1.4758793
10.1063/1.4758793
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