Flow-induced vibrations of a rotating cylinder in an arbitrary direction

Abstract

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in an arbitrary direction and forced to rotate about its axis, are examined via two- and three-dimensional simulations, at a Reynolds number equal to 100, based on the body diameter and inflow velocity. The behaviour of the flow–structure system is investigated over the entire range of vibration directions, defined by the angle $\unicode[STIX]{x1D703}$ between the direction of the current and the direction of motion, a wide range of values of the reduced velocity $U^{\star }$ (inverse of the oscillator natural frequency) and three values of the rotation rate (ratio between the cylinder surface and inflow velocities), $\unicode[STIX]{x1D6FC}\in \{0,1,3\}$, in order to cover the reference non-rotating cylinder case, as well as typical slow and fast rotation cases. The oscillations of the non-rotating cylinder ($\unicode[STIX]{x1D6FC}=0$) develop under wake-body synchronization or lock-in, and their amplitude exhibits a bell-shaped evolution, typical of vortex-induced vibrations (VIV), as a function of $U^{\star }$. When $\unicode[STIX]{x1D703}$ is increased from $0^{\circ }$ to $90^{\circ }$ (or decreased from $180^{\circ }$ to $90^{\circ }$), the bell-shaped curve tends to monotonically increase in width and magnitude. For all angles, the flow past the non-rotating body is two-dimensional with formation of two counter-rotating spanwise vortices per cycle. The behaviour of the system remains globally the same for $\unicode[STIX]{x1D6FC}=1$. The principal effects of the slow rotation are a slight amplification of the VIV-like responses and widening of the vibration windows, as well as a limited asymmetry of the responses and forces about the symmetrical configuration $\unicode[STIX]{x1D703}=90^{\circ }$. The impact of the fast rotation ($\unicode[STIX]{x1D6FC}=3$) is more pronounced: VIV-like responses persist over a range of $\unicode[STIX]{x1D703}$ but, outside this range, the system is found to undergo a transition towards galloping-like oscillations characterised by amplitudes growing unboundedly with $U^{\star }$. A quasi-steady modelling of fluid forcing predicts the emergence of galloping-like responses as $\unicode[STIX]{x1D703}$ is varied, which suggests that they could be mainly driven by the mean flow. It, however, appears that flow unsteadiness and body motion remain synchronised in this vibration regime where a variety of multi-vortex wake patterns are uncovered. The interaction with flow dynamics results in deviations from the quasi-steady prediction. The successive steps in the evolution of the vibration amplitude versus $U^{\star }$, linked to wake pattern switch, are not captured by the quasi-steady approach. The flow past the rapidly-rotating, vibrating cylinder becomes three-dimensional over an interval of $\unicode[STIX]{x1D703}$ including the in-line oscillation configuration, with only a minor effect on the system behaviour.

Flow-induced vibrations of a cylinder along a circular arc

“…elastically mounted cylinders in a cross-current at (e.g. Bourguet & Lo Jacono 2014; Bourguet 2019). Descriptions of the simulation approach, boundary conditions and discretizations, as well as detailed validations were reported in these prior works.…”

“…It can be noted that comparable symmetry breaking phenomena may exist for rectilinear vibrations in an arbitrary direction (e.g. Bourguet 2019).…”

“…with a single degree of freedom, under the effect of a uniform oncoming flow normal to its axis, represents a canonical problem to study a particular form of FIV, called vortex-induced vibrations (VIV). This system has been extensively examined in prior works, where the direction of motion was either normal to the current (Feng 1968;Mittal & Tezduyar 1992;Hover, Techet & Triantafyllou 1998;Khalak & Williamson 1999;Shiels, Leonard & Roshko 2001;Klamo, Leonard & Roshko 2006;Leontini et al 2006;Riches & Morton 2018), aligned with the current (Naudascher 1987;Okajima, Kosugi & Nakamura 2002;Cagney & Balabani 2013;Konstantinidis 2014;Gurian, Currier & Modarres-Sadeghi 2019;Konstantinidis, Dorogi & Baranyi 2021) or at an arbitrary angle (Brika & Laneville 1995;Bourguet 2019;Benner & Modarres-Sadeghi 2021). In the following, the directions normal and parallel to the current are referred to as the cross-flow and in-line directions, respectively.…”

Experimental Study on Vibration of a Rotating Pipe in Still Water and in Flow

“…The study of rotating cylinders in flow is mainly supported by elasticity, both in numerical simulations and experimental studies [21,[25][26][27][28]. Indeed, the drilling pipe is flexible and freely supported rotating pipe experiments are deficient, which is significant when illustrating the vibration behaviour of the drilling pipe in flow.…”