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On multiple manifestations of the second response branch in streamwise vortex-induced vibrations
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10.1063/1.4816293
/content/aip/journal/pof2/25/7/10.1063/1.4816293
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4816293

Figures

Image of FIG. 1.
FIG. 1.

Sketch representing the S-I, A-II, SA, and A-IV modes.

Image of FIG. 2.
FIG. 2.

Plan and elevation view of the test section used, including fishing wire supports. The red arrows indicate the reference frame employed.

Image of FIG. 3.
FIG. 3.

Amplitude response (a) and dominant frequency of transverse velocity fluctuations measured at (/, /) = (3, 0) (b), for the three sets of PIV measurements detailed in Table I ; Case 1, blue circles; Case 2, green squares; and Case 3, red triangles. Cases 1 and 2 correspond to experiments in which the reduced velocity was incrementally increased, while in Case 3 it was decreased.

Image of FIG. 4.
FIG. 4.

Raw displacement signals measured in each of the three cases at ; Case 1, (a); Case 2, (b); and Case 3, (c).

Image of FIG. 5.
FIG. 5.

Histograms of the displacement signals measured in each of the three cases at ; Case 1, ; Case 2, ; and Case 3, . The displacement signals were band-pass filtered, with cut-off frequencies of 10 Hz and 40 Hz.

Image of FIG. 6.
FIG. 6.

Sample instantaneous vorticity fields depicting the wake modes observed at ; the A-II mode (Case 3, ) (a); the SA mode (Case 2, ) (b); and the A-IV mode (Case 1, ) (c). (b) and (c) correspond to the cylinder in its most downstream position, while the cylinder motion in (a) is negligible. Contour levels are ω / = ±1.5, ±3….

Image of FIG. 7.
FIG. 7.

Amplitude response for the three sets of PIV measurements detailed in Table I ; Case 1, circles; Case 2, squares; and Case 3, triangles. The symbol colour denotes the dominant wake mode observed at each point; A-II, yellow; SA, red; and A-IV, green. The stars indicate the reduced velocities examined in the flow visualisation study of Nishihara , while red-green diamonds indicate the points at which Konstantinidis observed mode competition between the SA and A-IV modes.

Image of FIG. 8.
FIG. 8.

(a)–(h) Phase-averaged vorticity fields over one shedding cycle for , while the A-II mode is present and the cylinder amplitude response is negligible. Contour levels are ω / = ±1, ±2….

Image of FIG. 9.
FIG. 9.

(a)–(h) Phase-averaged vorticity fields over one shedding cycle for , while the SA mode is present and the cylinder amplitude response is at a local maximum (/ = 0.0621). Contour levels are ω / = ±1, ±2…. The corresponding cylinder displacements are shown in (i).

Image of FIG. 10.
FIG. 10.

(a)–(h) Phase-averaged vorticity fields over one shedding cycle for , at the peak of the second response branch. The amplitude response is large (/ = 0.0621), but lower than that which occurs when the SA mode dominates at the same reduced velocity. Contour levels are ω / = ±0.5, ±1…. The corresponding cylinder displacements are shown in (i).

Image of FIG. 11.
FIG. 11.

Phase-averaged vorticity field calculated for the SA mode at (a), and the A-IV mode at (b). Contour levels are ω / = ±0.75, ±1.5…. The λ-criterion has been employed to detect coherent vortices, and vorticity at any point which was not found to be part of a coherent vortex was set to zero. The corresponding phase-averaged cylinder displacement is indicated by the closed symbol in (c) for the SA mode (red squares) and A-IV mode (blue circles).

Tables

Generic image for table
Table I.

Details of the three sets of PIV measurements, including the reduced velocity range and the number of measurement points examined within each set.

Generic image for table
Table II.

Mean (/) and standard deviation (σ( )) of the peak heights of displacement signals measured at for Cases 1–3.

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/content/aip/journal/pof2/25/7/10.1063/1.4816293
2013-07-31
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On multiple manifestations of the second response branch in streamwise vortex-induced vibrations
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4816293
10.1063/1.4816293
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