Instability-driven frequency decoupling between structure dynamics and wake fluctuations

Flow-induced dynamics of flexible structures is, in general, significantly modulated by periodic vortex shedding. Experiments and numerical simulations suggest that the frequencies associated with the dominant motions of structures are highly coupled with those of the wake under low-turbulence uniform flow. Here we present experimental evidence that demonstrates a significant decoupling between the dynamics of simple structures and wake fluctuations for various geometries, Reynolds numbers, and mass ratios. High-resolution particle tracking velocimetry and hot-wire anemometry are used to quantitatively characterize the dynamics of the structures and wake fluctuations; a complementary planar particle image velocimetry measurement is conducted to illustrate distinctive flow patterns. Results show that for structures with directional stiffness, von Kármán vortex shedding might dominate the wake of bodies governed by natural-frequency motion. This phenomenon can be a consequence of Kelvin-Helmholtz instability, where the structural characteristics of the body dominate the oscillations.

Figure 1

(a) Geometry of the four acrylic plates. (b) Schematic of the experimental setup in the wind tunnel. (c) Schematic of the experimental setup in the RIM flume.

Figure 2

(a) Spectra of the streamwise velocity motion of the wide plate $(\circ )$ and wake fluctuations (−) under $U_r=26$. The vertical dashed lines mark $f_{n1}$ based on free oscillation tests (same for all configurations). (b) Same as (a) but under $U_r=53$. (c) The 2D spectrum of the structure motion highlighting the dominant oscillation frequency of the plate across various flow velocities. The blue dashed line indicates the vortex shedding frequency following $\text{St}=0.145$.

Figure 3

Streamwise velocity spectra under $U=5.2$ m ${\mathrm{s}}^{-1}(\circ )$ and $U=10.2$ m ${\mathrm{s}}^{-1}\left(▵\right)$ for the (a) slender rectangular plate $(U_r=104$ and 204), (b) trapezoidal plate $(U_r=18$ and 35), and (c) triangular plate $(U_r=12$ and 23). Also shown are the 2D premultiplied wake spectra for $U=10.2$ m ${\mathrm{s}}^{-1}$ along the height of the (d) slender rectangular $\left(U_r=204\right)$, (e) trapezoidal $\left(U_r=35\right)$, and (f) triangular plates $\left(U_r=23\right)$. The vertical dashed lines in (a)–(c) indicate the dominant oscillation frequency of the plate.

Figure 4

(a) Streamwise velocity spectra of the small rectangular plate with low-mass ratio at $U_r=6.8(\circ )$, 9.$5(\square )$, and 12.$1\left(▵\right)$. (b) The 2D spectrum of the structure oscillations highlighting the dominant frequency component for a range of velocities.

Figure 5

(a) Snapshot of the normalized swirling strength ${\mathrm{\Lambda }}_{ci}b/U_0$ past the plate at $\text{Re}=4\times {10}^3$. (b) Streamwise velocity fluctuation of the slender plate at the very near wake $(x/b=1$ and $y/b=0.5)$ under $U_r=114$.

Figure 6

Spectra of the oscillations of a circular cylinder under $U=6.2$ m ${\mathrm{s}}^{-1}(U_r=16.6,\circ )$ and 9.5 m ${\mathrm{s}}^{-1}(U_r=24.4,▵)$ with a low-stiffness support in the (a) streamwise direction and (b) spanwise direction.