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Flow-induced oscillations of a flexibly mounted triangular prism allowed to oscillate in the cross-flow direction are studied experimentally, covering the entire range of possible angles of attack. For angles of attack smaller than $\\unicode[STIX]{x1D6FC}=25^{\\circ }$ (where $0^{\\circ }$ corresponds to the case where one of the vertices is facing the incoming flow), no oscillation is observed in the entire reduced velocity range tested. At larger angles of attack of $\\unicode[STIX]{x1D6FC}=30^{\\circ }$ and $\\unicode[STIX]{x1D6FC}=35^{\\circ }$ , there exists a limited range of reduced velocities where the prism experiences vortex-induced vibration (VIV). In this range, the frequency of oscillations locks into the natural frequency twice: once approaching from the Strouhal frequencies and once from half the Strouhal frequencies. Once the lock-in is lost, there is a range with almost-zero-amplitude oscillations, followed by another range of non-zero-amplitude response. The oscillations in this range are triggered when the Strouhal frequency reaches a value three times the natural frequency of the system. Large-amplitude low-frequency galloping-type oscillations are observed in this range. At angles of attack larger than $\\unicode[STIX]{x1D6FC}=35^{\\circ }$ , once the oscillations start, their amplitude increases continuously with increasing reduced velocity. At these angles of attack, the initial VIV-type response gives way to a galloping-type response at higher reduced velocities. High-frequency vortex shedding is observed in the wake of the prism for the ranges with a galloping-type response, suggesting that the structure’s oscillations are at a lower frequency compared with the shedding frequency and its amplitude is larger than the typical VIV-type amplitudes, when galloping-type response is observed.

This paper presents a comprehensive study of flow-induced vibrations of a D-section prism with various angles of attack $\\alpha$ ($= 0^{\\circ }\\unicode{x2013}180^{\\circ }$) and reduced velocity $U^*$ (= 2–20) via direct numerical simulations at a Reynolds number ${Re} = 100$. The prism is allowed to vibrate in both streamwise and transverse directions. Based on the characteristics of vibration amplitudes and frequencies, the responses are classified into nine different regimes: typical VIV regime ($\\alpha = 0^{\\circ }\\unicode{x2013}30^{\\circ }$), hysteretic VIV regime ($\\alpha = 35^{\\circ }\\unicode{x2013}45^{\\circ }$), extended VIV regime ($\\alpha = 50^{\\circ }\\unicode{x2013}55^{\\circ }$), first transition response regime ($\\alpha = 60^{\\circ }\\unicode{x2013}65^{\\circ }$), dual galloping regime ($\\alpha = 70^{\\circ }$), combined VIV and galloping regime ($\\alpha = 75^{\\circ }\\unicode{x2013}80^{\\circ }$), narrowed VIV regime ($\\alpha = 85^{\\circ }\\unicode{x2013}145^{\\circ }$), second transition response regime ($\\alpha = 150^{\\circ }\\unicode{x2013}160^{\\circ }$) and transverse-only galloping regime (${\\alpha = 165^{\\circ }\\unicode{x2013}180^{\\circ }}$). In the typical and narrowed VIV regimes, the vibration frequencies linearly increase with increasing $U^*$. In the hysteretic and extended VIV regimes, the vibration amplitudes are large in a wider range of $U^*$ as a result of the closeness of the vortex shedding frequency to the natural frequency of the prism because of the shear layer reattachment and separation point movement. In the two galloping regimes, the transverse amplitude keeps increasing with $U^*$ while the streamwise amplitude stays small or monotonically increases with increasing $U^*$. In the combined VIV and galloping regime, the vibration amplitude is relatively small in the VIV region while drastically increasing with increasing $U^*$ in the galloping region. In the transition response regimes, the vibration frequencies are galloping-like but the divergent amplitude cannot persist at high $U^*$. Furthermore, a wake mode map in the examined parametric space is offered. Particular attention is paid to physical mechanisms for hysteresis, dual galloping and flow intermittency. Finally, we probe the dependence of the responses on Reynolds numbers, mass ratios and degrees of freedom, and analyse the roles of the shear layer reattachment and separation point movement in the appearance of multiple responses.

Shedding of vortices can be observed in the wake of a fixed cylinder at Reynolds numbers larger than $Re=47$. This might give the impression that a vortex-induced vibration (VIV), which occurs when the frequency of vortex shedding in the wake of a flexibly mounted cylinder synchronizes with the natural frequency of the structure, could be observed only at Reynolds numbers larger than $Re=47$. Recent numerical simulations and theoretical work, however, have shown that it is possible to observe VIV at subcritical Reynolds numbers, i.e. Reynolds numbers smaller than $Re=47$. In these studies, a VIV has been observed numerically at Reynolds numbers as low as $Re=22$. In the present work, the first experimental evidence of VIV at subcritical Reynolds number is presented. We have designed and built an experimental set-up that makes it possible to conduct VIV experiments at subcritical Reynolds numbers, and at a constant Reynolds number over the entire lock-in range (i.e. the range for which oscillations are observed). Using this experimental set-up, we have confirmed experimentally that VIV can indeed be observed at subcritical Reynolds numbers, by observing VIV at Reynolds numbers as low as $Re=19$. We have observed subcritical VIV both when the Reynolds number stays constant over the entire lock-in range, and when the Reynolds number increases with increasing reduced velocity, while staying within the subcritical range.

While it has been known that an afterbody (i.e. the structural part of a bluff body downstream of the flow separation points) plays an important role affecting the wake characteristics and even may change the nature of the flow-induced vibration (FIV) of a structure, the question of whether an afterbody is essential for the occurrence of one particular common form of FIV, namely vortex-induced vibration (VIV), still remains. This has motivated the present study to experimentally investigate the FIV of an elastically mounted forward- or backward-facing D-section (closed semicircular) cylinder over the reduced velocity range $2.3\\leqslant U^{\\ast }\\leqslant 20$ , where $U^{\\ast }=U/(f_{nw}D)$ . Here, $U$ is the free-stream velocity, $D$ the cylinder diameter and $f_{nw}$ the natural frequency of the system in quiescent fluid (water). The normal orientation with the body’s flat surface facing upstream is known to be subject to another common form of FIV, galloping, while the reverse D-section with the body’s curved surface facing upstream, due to the lack of an afterbody, has previously been reported to be immune to VIV. The fluid–structure system was modelled on a low-friction air-bearing system in conjunction with a recirculating water channel facility to achieve a low mass ratio (defined as the ratio of the total oscillating mass to that of the displaced fluid mass). Interestingly, through a careful overall examination of the dynamic responses, including the vibration amplitude and frequency, fluid forces and phases, our new findings showed that the D-section exhibits a VIV-dominated response for $U^{\\ast }<10$ , galloping-dominated response for $U^{\\ast }>12.5$ , and a transition regime with a VIV–galloping interaction in between. Also observed for the first time were interesting wake modes associated with these response regimes. However, in contrast to previous studies at high Reynolds number (defined by $Re=UD/\\unicode[STIX]{x1D708}$ , with $\\unicode[STIX]{x1D708}$ the kinematic viscosity), which have showed that the D-section was subject to ‘hard’ galloping that required a substantial initial amplitude to trigger, it was observed in the present study that the D-section can gallop softly from rest. Surprisingly, on the other hand, it was found that the reverse D-section exhibits pure VIV features. Remarkable similarities were observed in a direct comparison with a circular cylinder of the same mass ratio, in terms of the onset $U^{\\ast }$ of significant vibration, the peak amplitude (only approximately 6 % less than that of the circular cylinder), and also the fluid forces and phases. Of most significance, this study shows that an afterbody is not essential for VIV at low mass and damping ratios.

Coherent waving interactions between vegetation and fluid flows are known to emerge under conditions associated with the mixing layer instability. A similar waving motion has also been observed in flow control applications, where passive slender structures are used to augment bluff body wakes. While their existence is well reported, the mechanisms which govern this behaviour, and their dependence on structural properties, are not yet fully understood. This work investigates the coupled interactions of a large array of slender structures in an open-channel flow, via numerical simulation. A direct modelling approach, whereby the individual structures are fully resolved, is realised via a lattice Boltzmann-immersed boundary-finite element model. For steady flow conditions at low–moderate Reynolds number, the response of the array is measured over a range of mass ratio and bending rigidity, spanning two orders of magnitude, and the ensuing response is characterised. The results show a range of behaviours which are classified into distinct states: static, regular waving, irregular waving and flapping. The regular waving regime is found to occur when the natural frequency of the array approaches the estimated frequency of the mixing layer instability. Furthermore, after normalising with respect to the natural frequency of the array, the frequency response across the examined parameter space collapses onto a single curve. These findings indicate that the coherent waving mode is in fact a coupled instability, as opposed to a purely fluid-driven response, and that this specific regime is triggered by a lock-in between the fluid and structural natural frequencies.