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On the lock-on of vortex shedding to oscillatory actuation around a circular cylinder
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10.1063/1.4772977
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Affiliations:
1 Department of Mechanical Engineering, Florida A&M/Florida State University, Tallahassee, Florida 32310, USA and Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, Florida 32310, USA
a) Electronic mail: pmm06d@my.fsu.edu.
b) Electronic mail: ktaira@fsu.edu.
Phys. Fluids 25, 013601 (2013)
/content/aip/journal/pof2/25/1/10.1063/1.4772977
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/1/10.1063/1.4772977

## Figures

FIG. 1.

Computational setup for the present study. (a) Control setup for separated flow around a circular cylinder. (b) Computational domain setup with 5 different multi domains. The inner most domain (domain 1) is of size (, ) ∈ [−1, 3] × [−2, 2], and the largest one (domain 5) is [−31, 33] × [−32, 32]. Each domain has 200 × 200 cells.

FIG. 2.

Steady and oscillatory momentum coefficients ( and ) for tangential non-zero-mean sinusoidal actuation (Eq. ) with varied forcing amplitude .

FIG. 3.

Representative cases with (left, / = 1.05) and without (right, / = 0.3) lock-on, for = 0.05. Shown on top are phase diagrams with ( , ) and on the bottom are the frequency contents of the drag coefficient time series.

FIG. 4.

Time-average coefficient of drag ( ) shown for different forcing amplitudes over a range of actuation frequency ( / ). The dashed line (−− −) corresponds to the average baseline drag. Actuation is applied normal (left) and tangential (right) to the surface at the separation point (θ = 58°).

FIG. 5.

Contour plots for the change in time-average drag ( ) resulting from normal and tangential forcing for varied actuation amplitude () and frequency ( / ). Actuators located at θ = 58°. Solid lines represent the boundaries between cases with (○) and without (•) lock-on.

FIG. 6.

Contour plots of the flow without actuation and with normal sinusoidal actuation with Eq. and = 0.50.

FIG. 7.

Comparison of the time-average drag coefficient for different actuator positions on the cylinder. All cases are for tangential forcing and = 0.06, using Eq. . Results for zero-average forcing with Eq. is also shown.

FIG. 8.

Different lock-on profiles observed for = 0.05 with non-zero-mean forcing, Eq. . Cases (i)-(v) are described in text.

FIG. 9.

Contour plots of flows with non-zero-mean tangential sinusoidal actuation and = 0.05 (Eq. ). All cases are related to Fig. .

FIG. 10.

The left figure shows the reduction in for increasing actuator strength with steady blowing, Eq. . The dashed line (−− −) corresponds to the average drag from the case without actuation. The right plot shows the corresponding maximum amplitude in the frequency spectrum for each amplitude.

FIG. 11.

Contour plots of flows with steady tangential actuation for = 0.05 and 0.09 with Eq. .

FIG. 12.

The change in and lock-on characteristics for zero-mean tangential actuation. The left figure shows for different forcing amplitudes over a range of actuation frequency ( / ). The dashed line (−−−) corresponds to the average baseline drag. The right plot represents the corresponding lock-on characteristics with the change in shown by the counters for varied actuation amplitude () and frequency ( / ). Solid lines represent the boundaries between cases with (○) and without (•) lock-on.

FIG. 13.

Time history of the drag coefficient for Cases (I)-(III) (see text) using non-zero-mean sinusoidal forcing with Eq. and = 0.03. Shown by the dashed line (−−−) is the baseline average drag . Inserted contour plots represent the vorticity fields for Case (III).

## Tables

Table I.

Lift and drag coefficients and Strouhal number for flow over a circular cylinder at = 100.

/content/aip/journal/pof2/25/1/10.1063/1.4772977
2013-01-02
2014-04-17

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