Snap-through dynamics of a buckled flexible filament in a uniform flow

Abstract

The flow-induced snap-through dynamics of a buckled flexible filament was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity and Reynolds number on the mode transition were systematically examined. Three different modes were observed when the aforementioned parameters were varied: an equilibrium mode, a streamwise oscillation mode and a snap-through oscillation mode. Two mode transitions occurred when the bending rigidity was lowered and the length and Reynolds number were increased: a direct transition from the equilibrium mode to the snap-through oscillation mode and the successive appearance of the three modes. An increase in transverse fluid force induced the snap-through oscillation mode. A vortex-induced vibration and a self-excited vibration occurred in the streamwise oscillation mode and the snap-through oscillation mode, respectively. A wake pattern of 2S appeared in the streamwise oscillation mode, and a pattern of 2S + 2P appeared in the snap-through oscillation mode. A hysteresis was observed near the critical Reynolds number. The hysteresis loop increased in magnitude with increasing bending rigidity. The greater energy harvesting was achieved by the larger deflection and the higher strain energy. We found that most of the strain energy was concentrated in the last half of the filament.

Buckled elastic sheet as a vortex generator in dual channels

“…An increase in K * b leads to a growth in Re c , suggesting that a higher flow strength is needed to initiate the SSTM of a stiffer sheet, particularly at larger K * b values. This finding aligns with the results of Mao et al (2023), where a uniform flow is considered. As L* increases, an initial decrease in the required Re c value is observed, reaching a minimum at L* = 0.7, after which it starts to increase, forming a 'V'-shaped curve (figure 13a).…”

“…In the SSTM, there is a mild increase in the oscillation amplitude of Y * m (A*) with rising K * b values (figure 4b). The snapping frequency, however, initially increases and then decreases as K * b increases (figure 4c), a pattern consistent with the numerical results of Mao et al (2023) under uniform flow conditions. The turning point in this process occurs at K * b = 1.25 × 10 −3 , beyond which the sheet exhibits regular snap-through oscillation (figure 4a).…”

“…The SSTM is characterized by the sheet repeatedly snapping from one channel to the other at a relatively low frequency, as illustrated in supplementary movie 1 available at https://doi.org/10.1017/jfm.2024.244. This mode is self-excited, induced by a synergistic interaction between the sheet's motion and aero/hydrodynamic forces (Mao, Liu & Sung 2023). DM involves the sheet exhibiting rapid yet minor vibrations within one channel without crossing the mid-wall of the dual channels, as shown in supplementary movie 2.…”

“…The length ratio (L*) is reported to play a pivotal role in influencing the snap-through oscillations of elastic sheets in a uniform flow (Kim et al 2021a;Mao et al 2023) and in the context of a single laminar channel flow (Wang et al 2023). In this study, we examined the impact of L* on the snap-through oscillations of elastic sheets in a dual-channel flow system, with a special focus on the sheet's vortex generation performance.…”