In-line flow-induced vibrations of a rotating cylinder

Abstract

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the direction parallel to the current and subjected to a forced rotation about its axis, are investigated by means of two-and three-dimensional numerical simulations, at a Reynolds number equal to 100 based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 2 (first vibration region), then the body and the flow are steady until a rotation rate close to 2.7 where a second vibration region begins. Each vibration region is characterized by a specific regime of response. In the first region, the vibration amplitude follows a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency). The maximum vibration amplitudes, even though considerably augmented by the rotation relative to the non-rotating body case, remain lower than 0.1 cylinder diameters. Due to their trends as functions of the reduced velocity and to the fact that they develop under a condition of wake-body synchronization or lock-in, the responses of the rotating cylinder in this region are comparable to the vortex-induced vibrations previously described in the absence of rotation. The symmetry breaking due to the rotation is shown to directly impact the structure displacement and fluid force frequency contents. In the second region, the vibration amplitude tends to increase unboundedly with the reduced velocity. It may become very large, higher than 2.5 diameters in the parameter space under study. Such structural oscillations resemble the galloping responses reported for non-axisymmetric bodies. They are accompanied by a dramatic amplification of the fluid forces compared to the non-vibrating cylinder case. It is shown that body oscillation and flow unsteadiness remain synchronized and that a variety of wake topologies may be encountered in this vibration region. The low-frequency, large-amplitude responses are associated with novel asymmetric multi-vortex patterns, combining a pair and a triplet or a quartet of vortices per cycle. The flow is found to undergo three-dimensional transition in the second vibration region, with a limited influence on the system behaviour. It appears that the transition occurs for a substantially lower rotation rate than for a rigidly mounted cylinder.

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

“…In the absence of rotation (figure 3a), the evolution of the vibration amplitude as a function of U exhibits, for each θ > 0 • , a bell shape centred about U ≈ 6. The vibrations occurring for θ = 0 • at Re = 100 remain very small and are not visible in the plot; they also present a bell-shaped evolution but centred about U ≈ 3, as shown in a prior work (Bourguet & Lo Jacono 2015). From θ = 0 • , the peak amplitude and the width of the bell increase monotonically with θ , up to θ = 90 • , as also observed by Brika & Laneville (1995)…”

“…For α = 1, clear differences can be noted between the responses observed for θ = 45 • and θ = 135 • whereas for α = 0, these two configurations are equivalent. twice larger than those reported in a previous study for θ = 0 • (Bourguet & Lo Jacono 2015). In addition, the shape of the response curve varies from one case to the other: a quasi-linear evolution is noted for θ = 110 • while pronounced undulations occur for θ = 150 • .…”

“…The lock-in condition is always established and the oscillation period generally coincides with the fundamental period of the flow unsteadiness (inverse of the fundamental frequency of v), except in some three-dimensional flow cases where subharmonics of the displacement appear in the flow velocity spectrum. Due to the large number of vortices involved in some wake patterns and their distorted shapes, this nomenclature, also employed in a prior work (Bourguet & Lo Jacono 2015), may appear more systematic than the approach based on the identification of single vortices (S) and pairs (P) of vortices (Williamson 1988).…”

“…The present study focuses on the FIV of a flexibly mounted, rigid circular cylinder, free to oscillate in an arbitrary direction and forced to rotate about its axis; it follows two prior works concerning comparable configurations where the cylinder was allowed to move in the direction either normal to the current (Bourguet & Lo Jacono 2014) or aligned with the current (Bourguet & Lo Jacono 2015) and it aims at bridging the gap between the contrasted results reported in these previous papers, as explained in the following. These physical configurations may be regarded as paradigms of symmetry breaking in fluid-structure interaction.…”

“…The flow was also found to remain two-dimensional under transverse oscillation, in a range of α where the rotation causes three-dimensional transition when the body does not oscillate. The case where the elastically mounted, rotating cylinder is free to move in the in-line direction was addressed in a previous study (Bourguet & Lo Jacono 2015), with the same physical parameters as those selected in the above-mentioned paper and in the present work. Contrary to what was observed with the cross-flow degree of freedom, two distinct regions emerge in the rotation rate-reduced velocity domain: a region of VIV-like responses for α < 2 and a region where the vibrations resemble galloping responses, with amplitudes continuously increasing with U , for α > 2.7.…”