Resonant Vibrations of Bluff Bodies Cause Multivortex Shedding and High Frequency Forces

A flexibly mounted circular cylinder in cross-flow, with natural frequencies in the inline and transverse directions having a ratio close to $2:1$, exhibits drastic changes in the vortex structures in its wake, the frequency content of the fluid forces, and the orbital shape of its resulting motions. Stable multivortex patterns form in the cylinder wake, associated with large high-frequency force components.

Figure 1

Cylinder trajectories overlaid on the third harmonic magnitude of the lift force. Blue—trajectory moves downstream at the top of the figure-eight (C: Clockwise); black—trajectory moves upstream at the top of figure-eight (CC: Counterclockwise); flow is left to right. Contours indicate the third harmonic lift coefficient magnitude over the total lift coefficient magnitude. Darkest green denotes a third harmonic magnitude less than 25% of the total lift; lightest yellow denotes a third harmonic magnitude greater than 75% of the total lift.

Figure 2

Visualization of the modes of vortex shedding in the wake of a vibrating circular cylinder at $\mathrm{Re}=10000$. PIV planar images show (a) vortex triplets, and (b) quintuplets—red denote counterclockwise and blue clockwise vorticity. Labeled vortices represent structures that remained coherent in the time-resolved wake near the cylinder over one half cycle. Figure (c) depicts three-dimensional DNS results in the form of instantaneous pressure isocontours, demonstrating the spatial persistence of vortex triplets; $f_x/f_y=2$, $V_{\mathrm{rn}}=5.45$. Numbers 1,2, and 3 indicate the vortices in one vortex triplet.

Figure 3

Lift force characteristics when vortex triplets prevail. Figure (a) shows a composite of normalized lift coefficient spectra as functions of reduced velocity, demonstrating the dominance of the third harmonic in a region around $V_{\mathrm{rn}}\approx 7$. Figure (b) shows the time trace of the cylinder response ($Y/D$) and the corresponding lift coefficient ($C_L$) for $f_x/f_y=1.9$, $V_{\mathrm{rn}}=6.5$. Figure (c) shows the comparison between experiment and 3-D DNS of the normalized lift coefficient spectrum.