Flow-induced vibrations of a D-section prism at a low Reynolds number

Abstract

This paper presents the response and the wake modes of a freely vibrating D-section prism with varying angles of attack ( $\alpha = 0^\circ \text {--}180^\circ$ ) and reduced velocity ( $U^* = 2\text {--}20$ ) by a numerical investigation. The Reynolds number, based on the effective diameter, is fixed at 100. The vibration of the prism is allowed only in the transverse direction. We found six types of response with increasing angle of attack: typical vortex-induced vibration (VIV) at $\alpha = 0^\circ \text {--}35^\circ$ ; extended VIV at $\alpha = 40^\circ \text {--}65^\circ$ ; combined VIV and galloping at $\alpha = 70^\circ \text {--}80^\circ$ ; narrowed VIV at $\alpha = 85^\circ \text {--}150^\circ$ ; transition response, from narrowed VIV to pure galloping, at $\alpha = 155^\circ \text {--}160^\circ$ ; and pure galloping at $\alpha = 165^\circ \text {--}180^\circ$ . The typical and narrowed VIVs are characterized by linearly increasing normalized vibration frequency with increasing $U^*$ , which is attributed to the stationary separation points of the boundary layer. On the other hand, in the extended VIV, the vortex shedding frequency matches the natural frequency in a large $U^*$ range with increasing $\alpha$ generally. The galloping is characterized by monotonically increasing amplitude with enlarging $U^*$ , with the largest amplitude being $A^* = 3.2$ . For the combined VIV and galloping, the vibration amplitude is marginal in the VIV branch while it significantly increases with $U^*$ in the galloping branch. In the transition from narrowed VIV to pure galloping, the vibration frequency shows a galloping-like feature, but the amplitude does not monotonically increase with increasing $U^*$ . Moreover, a partition of the wake modes in the $U^*$ – $\alpha$ parametric plane is presented, and the flow physics is elucidated through time variations of the displacement, drag and lift coefficients and vortex dynamics. The angle-of-attack range of galloping is largely predicted by performing a quasi-steady analysis of the galloping instability. Finally, the effects of $m^*$ and ${\textit {Re}}$ , the roles of afterbody and the roles of separation point in determining vibration responses and vortex shedding frequency are further discussed.

Critical effect of fore-aft tapering on galloping triggering for a trapezoidal body

“…For instance, unlike the FIV response of a circular cylinder that will transfer into desynchronization after the lock-in range with increasing inflow velocity, the FIV response of a square cylinder will involve galloping instability (Zhao 2015;Zhao et al 2019). Past experimental and numerical results also indicated that the attack angle (or, direction of the incoming flow) of the elastically mounted bluff body will significantly affect the accompanied structural stability situation (Zhao et al 2014;Seyed-Aghazadeh, Carlson & Modarres-Sadeghi 2017;Chen et al 2022). In terms of the FIV response of an asymmetrical bluff body, Zhao, Hourigan & Thompson (2018) experimentally investigated the dynamic response (including lock-in and galloping) of the flow past an elastically mounted forward-or backward-facing D section.…”

“…This study (Zhao et al 2018) also applied Den Hartog's stability criterion (Den Hartog 1956) (discussed later herein) in order to explain the differences in response caused by the different facing orientations of the obstacle in the flow. Chen et al (2022) conducted the numerical investigation of a FIV system consisting of a D-section prism with varied attack angles at a low Reynolds number. The presented results were generally similar to those of Zhao et al (2018) and displayed a more detailed response differentiation with reference to the variations of maximum amplitude envelope at different angles of attack.…”

“…The pattern is spatially displaced as a whole in the transverse direction as the body moves. This kind of wake behaviour is regarded as the mS + nS mode, and m + n 5 for the galloping regime (Seyed-Aghazadeh et al 2017;Zhu et al 2021;Chen et al 2022). Although the structural amplitude of the trapezoid concerned in figure 14 is not as significant as that of the D section and triangular bodies for the same U r (or, vibration frequency), a perusal could help to determine the wake at U r = 25 as the 5S + 5S pattern (cf.…”

“…2014; Seyed-Aghazadeh, Carlson & Modarres-Sadeghi 2017; Chen et al. 2022). In terms of the FIV response of an asymmetrical bluff body, Zhao, Hourigan & Thompson (2018) experimentally investigated the dynamic response (including lock-in and galloping) of the flow past an elastically mounted forward- or backward-facing section.…”

“…Chen et al. (2022) conducted the numerical investigation of a FIV system consisting of a -section prism with varied attack angles at a low Reynolds number. The presented results were generally similar to those of Zhao et al.…”