Transverse and lateral confinement effects on the oscillations of a free cylinder in a viscous flow

The different types of instabilities of free cylinders (diameter $D$, length $L$) have been studied in a viscous flow (velocity $U$) between parallel vertical walls of horizontal width $W$ at a distance $H$: the influence of the confinement parameters $D/H$ and $L/W$ has been investigated. As $D/H$ increases, there is a transition from stable flow to oscillations transverse to the walls and then to a fluttering motion with oscillations of the angle of the axis with respect to the horizontal. The two types of oscillations may be superimposed in the transition domain. The frequency $f$ of the transverse oscillations is independent of the lateral confinement $L/W$ in the range: 0.055 \le L/W \le 0.94$for a given cylinder velocity$V_{cx}$and increases only weakly with$V_{cx}$. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of$L/W$for a given$V_{cx}$value. The experimental values of$f$are also independent of the transverse confinement$D/H$. The frequency$f_f$of the fluttering motion is significantly lower than$f$:$f_f$is also nearly independent of the cylinder diameter and of the flow velocity but decreases significantly as$L/W$ increases. The fluttering instability is then rather a 3D phenomenon involving the full length of the cylinder and the clearance between its ends and the side walls.

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