Fluid-structure interactions (FSI) behaviour of two unequal-diameter flexible cylinders in tandem configuration

Highlights

• An experimental investigation was carried out to study the FIV of two tandem flexible cylinders with different diameters.

• When the large cylinder is located upstream, the small cylinder has a slight effect on the CF and IL FIV responses.

• The downstream cylinder exhibits more complicated behaviour due to the significant wake effect from the upstream cylinder.

Abstract

Fluid-structure interactions (FSI) of multiple cylindrical structures frequently occur in crossflows. Due to the different wake interference regions of flexible cylinders with different diameters, the interaction between multiple cylinders is complicated and sensitive to the centre-to-centre spacing ratio and diameter ratio. Limited information has been presented on the flow-induced vibration (FIV) of two unequal-diameter flexible cylinders in a tandem arrangement. In this paper, an experimental investigation was carried out in a towing tank to study the FIV of two tandem flexible cylinders with different diameters that can vibrate in both the cross-flow (CF) and in-line (IL) directions. There were two IL spacing ratios (T/d = 12.0 and 6.0, where T is the centre-to-centre distance between two cylinders, and d is the diameter of the small cylinder), and the diameter ratio (d/D, where D is the diameter of the large cylinder) was nearly 0.5. The aspect ratios/mass ratios of the small cylinder and the large cylinder were 350/1.90 and 181/1.47, respectively. The towing velocity varied from 0.05 to 1.00 m/s with an interval of 0.05 m/s. The Reynolds numbers for the small and large cylinder were 800–16000 and 1600–32000, respectively. The CF vibration of the upstream large cylinder with T/d = 6.0 was suppressed at Vrs = 16.28–18.79, whereas the CF vibration of the large cylinder with T/d = 12.0 was not influenced. The downstream cylinder exhibited more complicated behaviour due to the significant wake effect from the upstream cylinder, which is consistent with the two equal-diameter cylinders. The FIV response of the downstream small cylinder was more sensitive to the IL spacing ratio. Because of the wake shielding effect of the large cylinder, the downstream small cylinder vibrated at low IL dominant frequencies, and the IL to CF frequency ratio (f_IL/f_CF) was approximately 1.0. Moreover,wake-induced flutter was observed on the downstream small cylinder.

Introduction

Multiple cylindrical structures are often arranged in tandem in various engineering applications, such as tubes in heat exchangers, overhead transmission line bundles, and offshore risers. When the incoming flow passes through a group of multiple cylinders, the flow-induced vibration (FIV) phenomenon may occur. Among the previous studies on the FIV of multiple cylinders, the configuration with two cylinders in tandem has received more attention (Papaioannou et al., 2008; Kim et al., 2009; Assi et al., 2010; Carmo et al., 2011; Huang and Herfjord, 2013; Xu et al., 2018b,2018c,2019).

For the flow patterns of two identical stationary cylinders in a tandem arrangement, there are three basic regimes: the extended-body regime, the reattachment regime and the co-shedding regime (Zdravkovich, 1987; Zhou and Yiu, 2006; Sumner, 2010). The wake is classified into three regimes depending on spacing ratio T/d (where T is the centre-to-centre spacing of the two cylinders, and d is the diameter of two identical cylinders). (i) The extended-body regime takes place when 1.0 < T/d < 2.0, and the free shear layers roll up to form a single vortex street. (ii) In the reattachment regime (2.0 < T/d < 5.0), the free shear layers separated from the upstream cylinder are more likely to reattach onto the surface of the downstream cylinder. (iii) In the co-shedding regime (T/d > 5.0), a vortex is generated by the upstream cylinder and subsequently interacts with those separated from the downstream cylinder.

For two elastically supported rigid cylinders arranged in tandem, vortex shedding is the main mechanism that causes the initial vibration of the cylinder (Borazjani and Sotiropoulos, 2009). The cross-flow (CF) and in-line (IL) FIV responses of multiple cylinders are more complicated than those of an isolated cylinder. Borazjani and Sotiropoulos (2009) numerically investigated the FIV of two elastically mounted cylinders in a tandem arrangement at Re = 200. The two vibrating cylinders approach each other at sufficiently high reduced velocities, which significantly reduces the size of the gap region, thereby eliminating gap flow. In such cases, the two cylinders vibrate as a single body with vibration amplitudes lower than those where the gap flow is active. Huang and Herfjord (2013) experimentally studied two elastically mounted rigid cylinders in a tandem arrangement subjected to steady flow with T/d = 2.0–5.0. Both cylinders were free to vibrate in both the CF and IL directions. The FIV response of the downstream cylinder was dependent upon the reduced velocity, which was influenced by the wake of the upstream cylinder. The upstream cylinder was nearly unaffected by the downstream cylinder when the initial T/d was greater than 3.0. However, the FIV response of the downstream cylinder was largely influenced by the upstream cylinder in the T/d range tested.

The increasing demand for offshore risers and transmission lines has prompted studies into the FIV of multiple flexible cylinders. Research has shown that the wake flow of two tandem flexible cylinders undergoing FIV is completely three dimensional (Wang et al., 2017). According to the reduced velocity, Griffith et al. (2017) divided the flow pattern of two tandem cylinders with a small pitch ratio (centre-to-centre spacing of the two cylinders to the cylinder diameter) into three modes. The combination of vortices with the same sign corresponds to the first mode. In the second mode, the amplitude of the downstream cylinder is relatively larger and moves completely out of the wake of the upstream cylinder. The vortex pair propagates backward, and the subsequent vortex pair catches up with the previously formed vortex pair. They merge and form an irregular vortex street. In the third mode, the small amplitude of the upstream cylinder and the large amplitude of the downstream cylinder cause a vortex to appear in the gap. In the reattachment regime, the vortex shedding is synchronized to form a more regular periodic vortex. In the co-shedding regime, the superposition of the wakes makes them more complex and non-periodic (Papaioannou et al., 2008; Bao et al., 2012). Huera-Huarte and Bearman (2011) and Huera-Huarte and Gharib (2011) experimentally studied the dynamic response of two flexible cylinders with near and far wake interference for spacing ratio T/d ranging from 2.0 to 8.0. When the spacing ratio was sufficiently large, the response of the upstream cylinder exhibited typical vortex-induced vibration (VIV) and was almost the same as that of an isolated flexible cylinder. Because the vortex in the gap, the downstream cylinder had a large response amplitudes caused by wake-induced vibration. Later, Huera-Huarte et al. (2016) performed experimental investigation of the FIV of a flexible cylinder located behind a stationary cylinder at various spacing ratios (T/d = 2.0–6.0). The FIV was found to be a multi-mode response comprising large-amplitude contributions from several adjacent modes. Wang et al. (2017) investigated the effect of T/d on the hydrodynamic interactions and the FIV responses of two tandem flexible cylinders. The FIV response of the two flexible cylinders was found to be similar to the typical response at a small T/d. Once T/d was sufficiently large for the vortex to be detached from the upstream cylinder, the downstream cylinder was vibrated by the wake of the upstream cylinder. Xu et al. (2018b) experimentally observed that the FIV response of the downstream cylinder was determined by lower frequencies and dominant modes due to the wake shielding effect. When the cylinders were in a tandem arrangement, the influence of the IL spacing ratio on the IL response was more remarkable than that on the CF response. Ma et al., 2019 studied the hydrodynamic characteristics of two flexible cylinders connected in tandem. Both wake shielding effect and the vortex shedding effect influenced the hydrodynamic features of the downstream cylinder. In addition, when T/d = 6.0, due to the wake shielding effect, the fatigue damage of the downstream cylinder is reduced. The downstream cylinder suffered more serious IL fatigue damage under T/d = 10.0 and 16.0 at some reduced velocities owing to the dominant modal lag (Xu et al., 2020).

Cylindrical structures with equal diameters are special, whereas unequal-diameter cylinders are more common in offshore engineering. For example, considering the needs of technology and economy, it is necessary to arrange smaller-diameter auxiliary pipes as ties near the main pipe. These “piggyback” pipes can effectively reduce the cost of installing the pipeline, but the presence of small-diameter cylinders has a certain hydrodynamic impact on the area near the main pipe. Moreover, cylinders that serve different operational functions can form the same cluster, such as drilling and production risers. From the perspective of space-saving and economic benefits, the diameters of these risers are different, and the diameter ratio generally varies between 1.0 and 4.0.

When subjected to the ocean flow, the falling vortex shedding generated by these cylindrical structures can affect the stability and safety of the slender cylinders. Although some FIV characteristics of two cylinders with different diameters can be studied by considering equal-diameter cylinders, other unequal-diameter characteristics remain unrevealed. There are fewer studies on the staggered arrangement (Dalton et al., 2001; Pearcey et al., 2017; Zhao et al., 2007; Xu et al., 2020). Gao et al. (2010) and Lee et al. (2012) studied the flows around two cylinders with unequal diameters in a side-by-side arrangement, whereas few studies have been performed on unequal-diameter cylinders in a tandem arrangement. Qin et al. (2017) studied the CF FIV on an elastically mounted large cylinder in the wake of a smaller stationary cylinder. The diameter ratios (d/D) and IL spacing ratios T/d varied from 0.2 to 1.0 and from 2.0 to 6.5, respectively. The severe vibration of the cylinder depended on both d/D and T/d. It was found that as T/d increased, vibrations of the large cylinder occurred at a smaller d/D. The wake from the small cylinder was narrow, and the shear layer tended to switch its direction from one side to the other. Huang and Sworn (2011) studied the hydrodynamic interaction of elastically supported rigid cylinders that oscillated freely in the CF and IL directions in a water tank. The diameter of the upstream cylinder was twice that of the downstream cylinder, and the T/D varied from 1.0 to 10.0. Moreover, the Reynolds number was in the subcritical range. The test results showed that the vibration response of the downstream cylinder was dependent on its actual reduced velocity. The frequency components of the CF FIV of the downstream cylinder included the vortex shedding of the upstream cylinder and its vortex shedding. The relative importance of the two sources of excitation was influenced by T/D. Later, Huang and Sworn (2013) conducted FIV experiments of two tandem and staggered cylinders with unequal diameters. The T/D varied from 1.0 to 15.0. For the upstream cylinder, the VIV was similar to the classical lock-in response unless the T/D was less than 2.0.

As previously mentioned, the studies of FIV response have mainly focused on equal-diameter cylindrical structures in tandem, side-by-side and staggered arrangements. In our previous experimental studies on two identical cylinders undergoing FIV (Xu et al., 2018a, 2018b, 2020), it was found that the multi-mode and high-amplitude features can better reflect the dynamic response of the long flexible cylinders. Few studies have investigated the FIV response of two unequal-diameter flexible cylinders (Xu et al., 2020); instead, previous studies mainly focused on the flow patterns of multiple cylinders with different diameters. This study performed experiments on unequal-diameter cylinders to investigate their interesting FIV phenomena. Multiple long flexible cylindrical structures in a tandem arrangement are prone to experiencing FIV. Such vibrations are the main source of fatigue failures, and these vibrations can result in structural damage when combined with wake interactions.

The outline of the rest of this paper is as follows. Section 2 presents a detailed description of the experimental setup and experimental details and introduces the methods for processing the measured strain signals and the reconstruction of the displacement responses. Section 3 presents and discusses the experimental results. Finally, some conclusions are drawn in Section 4.