The effect of vortices structures on the flow-induced vibration of three flexible tandem cylinders
Graphic abstract
Introduction
Flow-induced vibration (FIV) is a phenomenon oftentimes occurring in practical situations, such as chemical towers, chimney stacks, wind turbines, offshore structures, tubes in steam generators and so on, which has been investigated both in academia and industry, given their theoretical and practical significance. Vortex-induced vibration (VIV) of a single cylinder caused by Von-Karman street is the most typical category, which had been extensively studied by previous researchers [1], [2], [3], [4], [5]. The tandem cylinders subjected to a uniform or nonuniform flow with strong interference effect have long been a highlight for the suppression or utilization of FIV. The complicated vibration responses and mechanisms of tandem cylinders especially under different scales of vortices structures are still undergoing investigation.
Generally, the system of tandem plain cylinders immersed in a uniform flow is the excellent research object to understand FIV. The flow patterns around the tandem plain cylinders had been systematically summarized by Sumner [6] and Zhou [7]. In a previous investigation, we identified the vibration characteristics with four regimes based on the spans l (the nondimensional center-to-center distance) of tandem cylinders (m*ζs=0.882, hereafter, m*is mass ratio, ζs is damping ratio) in a ABL wind tunnel experiment, where cylinder 1 vibrated divergently similar to galloping in Regime Ⅰ (l<1.6) but was suppressed in Regime Ⅱ (1.6≤l<3), cylinder 2 always vibrated significantly in all four regimes, and cylinder 3 had a distinct vibration only in Regimes Ⅱ, Ⅲ (3≤l≤5,) and Ⅳ (l >5) [8]. Correspondingly, four velocity interference criteria were proposed to explain the coupling effect of vortex induced vibration and wake induced galloping for tandem cylinders (m*ζs=0.075) [9]. Bokaian and Geoola [10] investigated FIV of an elastic cylinder placed in the wake of a fixed cylinder, where the downstream cylinder (m*ζs=0.109) was free to vibrate transversely in a uniform flow. In their research, four distinct dynamic responses were identified, depending on the l: galloping only (l=1.09), vortex excitation only (l>3), separated vortex excitation and galloping (2<l<3), and combined vortex excitation and galloping (l=1.5). Kim et al. [11] carried out the wind tunnel experiments of tandem cylinders (m*ζs=6.36) with 1.1≤l≤4.2, in which five vibration characteristics were also classified. Qin et al. [12] conducted an experimental investigation on FIV of two tandem cylinders (m*ζs=0.58) for 1.2≤l≤6.0, with remarkable findings of that the initial state of the cylinders, vibrating or stationary, could extremely affect the vibration behavior of others. Assi et al. [13], [14] focued on the downstream cylinder vibration (m*ζs=0.018) for l=4~6. It was found that the vortices generated from the upstream cylinder played an important role, and the remarkable vortex interaction excitation mechanism was conceived. The two works mentioned above inspired us that the vortex structures in different scales generated by the cylinders may drastically interact on the FIV of tandem cylinders. Some researchers have noticed the importance of vortices and focused on the vortex evolutions around tandem plain cylinders. Huera-Huarte and Bearman [15] obtained the vorticity fields of two flexible tandem cylinders through DPIV, in which upstream cylinder underwent larger transverse vibrations at the small span caused by the alternating vortex shedding between the cylinders or a reattachment of the shear layers to the rear body. As the spans between the cylinders increased, the coupling through the wake reattachment became weaker and they started to respond more like what might be expected of a single cylinder. Similar dynamic vortex structures for various spans of tandem cylinders in low Reynolds number [16] and subcritical Reynolds number [17], [18] were obtained and analyzed. Nevertheless, to the best of our knowledge, the impact of vortices in different structures and scales on FIV of tandem cylinder has not been thoroughly reported.
In order to change vortices structures, the passive vibration control method of installing strakes on the surface of cylinder is effective. The size of the strakes depends on its width (also called as height) and pitch. The two parameters had been widely investigated by the researchers from the perspective of suppressing VIV of a single cylinder, in which the vortex shedding was disturbed and regular vortex structures was destroyed to be irregular by the strakes [19]. For example, Brankovic and Bearman [20] conducted an experiment that the straked cylinder responded over a narrow range of reduced velocities, and its maximum amplitude decreased over 60% compared with that of a plain cylinder, due to that the vortex shedding disappeared. Quen et al. [21], [22] conducted a research to find the optimal parameters of strakes on suppressing VIV of flexible cylinders in the cross flow and inline directions simultaneously. The most effective configuration of strakes in terms of the dynamic responses was pitch =10D and height =0.15D model, that could efficiently destroy the shear layer and vortex shedding, and the pitch was not as sensitive as the width for the flow-induced vibration of cylinders. Korkischko and Meneghini [23] estimated the effect of varying the geometric parameters of helical strakes on suppressing VIV of a single cylinder. When the heights of strakes were 0.2D and 0.25D, the VIV amplitude of the single cylinder was almost completely suppressed by strakes preventing the vortex shedding from becoming correlated along the span. Trim et al. [24] reviewd the suppression efficiency of the coverage of three-strand helical strakes with pitch/height 17.5D/0.25D and 5.0D/0.14D for VIV of a single cylinder in a uniform flow by towing a cylinder model. Ranjith et al. [25] concluded that the helical strakes with pitch =10D and height =0.15D were very effective in suppressing the vortex shedding from circular cylinders and could reduce the strength of vortex shedding by approximately 99%. Similar results by numerical simulations were reported by Holland et al. [26] and Zhu et al. [27]. Liu et al. [28] proved that cylinders with triangle and circular sections had better suppression effect than that with rectangular section inside the lock-in region, but cylinders with triangle section helical strakes had the best vortex suppression effect outside the lock-in region. Senga and Larsen [29] examined the suppression efficiency of three-strand helical strakes with pitch/height 17.5D/0.25D and 5D/0.14D, and the variation of amplitudes, frequencies and phase angles were discussed. Thus, the effective size of strakes has been obtained, and the disturbed irregular vortices generated by the strakes can monotonously decrease VIV of a single cylinder.
However, this clear connection between disturbed vortices structures and responses of FIV disappears when the strakes are installed in tandem cylinders, due to the existence of unsteady inflow, strong shear layers interaction and wake interference between the tandem cylinders. Gao et al. [30], [31] evaluated the suppression of VIV response by strakes with different coverage rates in uniform and linearly sheared flow, showing that the best performance of strakes in a uniform current was 75% coverage, but it was 50% in a linearly sheared flow. Ren et al. [32] carried on an experiment to study VIV for a flexible cylinder fitted with helical strakes in an oscillatory flow. The results showd that the suppression efficiency of strakes was not as ideal in oscillatory flow as those in steady flow. Assi et al. [33] compared suppression efficiency between helical strakes and control plates setting in downstream cylinders at l=4, in which it was demonstrated that helical strakes lose their suppression efficiency when unsteady excitation was present in the upstream wake. Korkischko et al. [34] reported that strakes lose their effectiveness when a downstream straked cylinder elastically mounted was immersed in the wake of an upstream plain fixed cylinder at l=3.4. Li et al. [35] conducted an experiment to study the coupling effect of smoothed upstream cylinder and straked downstream cylinder, in which the highest suppression efficiency (70.57% at l=8) was obtained for tandem cylinders, and the dynamic feedback of smoothed upstream cylinder smaller than the downstream cylinder was concluded. Similar results were also reported in [36], [37].
Therefore, FIV response of tandem cylinders is believed to become complex and unclear in the ABL with respect to the strong shear layers interaction and wake interference. Undoubtedly, FIV responses of upstream cylinders and downstream cylinders cannot keep the same pace. Taking artificial measurement to disturb the flow field of any cylinder will lead to the impact on the others. The FIV characteristics of tandem cylinders under different vortex structures have not been reported and need to be studied systematically. Thus, we conducted the investigation of FIV of tandem cylinders which can vibrate freely in two directions under different oncoming, gap and wake vortices structures at two specific spans. These spans can represent the typical shear layer interaction and wake interference regime. The various of vortices structures are generated by the flexible plain cylinder, flexible straked cylinder and rigid cylinder. The vibration response and mechanism of all the cases were obtained to comprehensively understand FIV characteristics under different vortices, and then contribute to the integral FIV control and utilization of tandem cylinders.
Section snippets
Experiment setup
The FIV of three flexible straked cylinders compared with plain cylinders and rigid cylinders in tandem arrangement were conducted experimentally to investigate the effect of different vortex structures. As shown in Fig. 1, all the tests were performed in a low turbulence (0.07%) and closed-loop wind tunnel with a 2.3 m long, 1 m high and 1 m wide test-section. The uniform wind velocity varied gradually from 0.9 m/s to 18 m/s. The geometric scale was selected as 1:200. To reproduce the flow
Velocity profiles in the gap of cylinders
The velocity profiles in the wake of upstream cylinders will be changed by the strakes causing fluctuated inlet conditions for downstream cylinders, that affect the FIV of downstream cylinders. Based on the experiment of Assi [13], the vibration characteristics of a single cylinder in a shear flow and uniform flow are different, where the lock-in region in shear flow is expanded. Thus, the unclear velocity profiles of tandem cylinders caused by the strakes were analyzed at first. As Figs. 6 and
Conclusions
The impact of different vortex structures on flow-induced vibration of three tandem flexible cylinders with large mass ratio (m*=126 and 130) and wide velocity range (Ur∈ [2], [35]) in the ABL are experimentally and numerically investigated. Three cylinders, including the plain cylinder, the straked cylinder and the rigid cylinder, are responsible for the various vortices. The vibration responses and vortices evolutions of tandem cylinders at two specific spans representing different mechanisms
CRediT authorship contribution statement
Xiantao Fan: Conceptualization, Methodology, Investigation, Formal analysis, Writing - original draft. Zhongchen Wang: Software, Validation. Yang Wang: Writing - review & editing. Wei Tan: Supervision, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research work presented in this paper is financially supported by the National Natural Science Foundation of China (21978202).
References (52)
A critical review of the intrinsic nature of vortex-induced vibrations
J Fluid Struct
(2004)- et al.
An overview of modeling and experiments of vortex-induced vibration of circular cylinders
J Sound Vib
(2005) Circular cylinder wakes and vortex-induced vibrations
J Fluid Struct
(2011)Two circular cylinders in cross-flow: A review
J Fluid Struct
(2010)- et al.
Experimental investigation on flow-induced vibration of flexible multi cylinders in atmospheric boundary layer
Int J Mech Sci
(2020) - et al.
Vibration mode and velocity interference mechanism of tandem cylinders at subcritical Reynolds number
J Wind Eng Ind Aerod
(2020) - et al.
Flow-induced vibrations of two circular cylinders in tandem arrangement. Part 1: Characteristics of vibration
J Wind Eng Ind Aerod
(2009) - et al.
Numerical investigation on interactive FIO of two-tandem cylinders for hydrokinetic energy harnessing
Ocean Eng
(2019) - et al.
Measurements of transverse forces on circular cylinders undergoing vortex-induced vibration
J Fluid Struct
(2006) - et al.
Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser
Appl Ocean Res
(2014)