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

TL;DR

This study investigates how transverse and lateral confinement affect the oscillation behaviors of a free cylinder in viscous flow, revealing transitions from stable to oscillatory states and characterizing their frequency dependencies.

Contribution

It provides a detailed analysis of confinement effects on cylinder oscillations, highlighting the independence of transverse oscillation frequency from lateral confinement and the 3D nature of fluttering instability.

Findings

Transverse oscillation frequency is independent of lateral confinement.

Fluttering frequency decreases with increasing L/W ratio.

Oscillation types can be superimposed in the transition domain.

Abstract

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.