Flow force measurements and the wake transition in purely inline vortex-induced vibration of a circular cylinder

We present a series of experiments on a one-degree-of-freedom circular cylinder allowed to exhibit pure translational motion in the streamwise direction. Our displacement measurements confirm the existence of two nonzero amplitude regions in the amplitude response: one at lower reduced velocities, which is accompanied by a symmetric shedding, and one at higher reduced velocities, which is accompanied by asymmetric shedding. Besides the typical displacement measurements that have been conducted in previous studies on this system, the current experiments include force measurement results for such systems. A combination of (i) synchronized displacement measurements, force measurements, and flow visualizations, (ii) a very fine reduced velocity step, and (iii) a highly controlled setup, which allows a pure inline displacement, has enabled us to (i) observe an intermediate wake mode, which occurs for reduced velocities between the range of symmetric and asymmetric reduced velocities, and (ii) relate the wake transition to the fine changes in the ratio of fluctuating lift to fluctuating drag. We call the wake mode that we have identified the alternating-symmetric mode, since in this mode two vortices of opposite signs are shed per cycle of oscillations, but their sizes relative to one another alternate for every cycle.

Figure 1

Schematic of the inline VIV setup when (a) looking in the direction of flow, with flow normal to the page, and (b) looking perpendicular to flow, with flow from left to right.

Figure 2

(a) Dimensionless displacement amplitude, $A^{*}$, vs reduced velocity, $U^{*}$, for the current paper as well as previous studies, together with (b) the displacement frequency ratio, $f^{*}$, vs $U^{*}$ for the current paper.

Figure 3

(a) Magnitude of the fluctuating drag coefficient and (b) its frequency ratio, plotted vs $U^{*}$ and Re.

Figure 4

(a) Fluctuating $C_D$, (b) dimensionless displacement amplitude, $A^{*}$, (b) fluctuating $C_D$, and (c) phase difference between the two signals, plotted against $U^{*}$ and Re. The phase difference of approximately 0 deg corresponds to a positive transfer of energy from the fluid to the structure.

Figure 5

(a) The ratio of fluctuating lift to fluctuating drag, $R_f$, and (b) the dimensionless amplitude of displacement plotted as a function of $U^{*}$ and Re. Different symbols are used to indicate different wake modes depending on the values of $R_f$ within the region. (c) The fluctuating force ratio, $R_f$, plotted against reduced velocity for the region of symmetric shedding. The increase in the value of $R_f$ toward the end of the region indicates a change in the nature of the symmetric wake mode.

Figure 6

(a) Time history and (b) frequency contents of the dimensionless displacement, together with the (c) time histories and (d) frequency contents of coefficients of fluctuating lift and drag, all for $U^{*}=2.1$.

Figure 7

Symmetric S-I shedding shown for $U^{*}=2.1$. Flow is from top to bottom.

Figure 8

(a) Time history and (b) frequency contents of the dimensionless displacement, together with the (c) time histories and (d) frequency contents of coefficients of fluctuating lift and drag, all for $U^{*}=2.27$.

Figure 9

Alternating-symmetric shedding shown for $U^{*}=2.27$. Flow is from top to bottom.

Figure 10

(a) Time history and (b) frequency contents of the dimensionless displacement, together with the (c) time histories and (d) frequency contents of coefficients of fluctuating lift and drag, all for $U^{*}=2.77$.

Figure 11

Weak and competitive shedding shown for $U^{*}=2.77$. Flow is from top to bottom.

Figure 12

(a) Time history and (b) frequency contents of the dimensionless displacement, together with the (c) time histories and (d) frequency contents of coefficients of fluctuating lift and drag, all for $U^{*}=3.45$.

Figure 13

Asymmetric shedding mode shown for $U^{*}=3.45$. Flow is from top to bottom.