Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s. Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.


Introduction
In offshore oil and gas engineering, long delivery systems (pipelines and risers) are necessary for transporting multiphase hydrocarbons from subsea wellheads to central production platforms (Malekzadeh et al., 2012a). Slugging frequently encountered in gas-liquid two-phase flow is one of the challenging flow-assurance problems for such long pipeline-riser systems. Particularly, severe slugging occurs at low gas and liquid flow rates when the two-phase flow streams from a downward or even horizontal segment into a riser (Fabre et al., 1990;Malekzadeh et al., 2012b). Severe slugging is a cyclic process consisting of four stages (Schmidt et al., 1985;Taitel, 1986): slug formation, slug production, gas-penetration/liquid-blowout and liquid-blowdown/liquid-fallback. The cyclical production of extremely long liquid slugs and fast gas blowdown (Baliño et al., 2010;Baliño, 2014) result in various problems such as large-amplitude pressure and flow rate fluctuations, reservoir flow oscillations and overflow or interruption of the terminal separator (Malekzadeh et al., 2012b). Con-sequently, a great threat is posed to the steady operation of hydrocarbon production, the efficient management of reservoir and the mechanical integrity of structure (Xing et al., 2013).
Extensive efforts have been dedicated to investigating severe slugging both experimentally and numerically. Schmidt et al. (1980Schmidt et al. ( , 1985 compared the severe slugging with the hydrodynamic slugging in a simulated offshore pipeline-riser system. Severe slugging is characterized by the generation of liquid slugs at the riser base with the upstream pipeline in stratified flow, while hydrodynamic slugging is characterized by many liquid slugs being lifted along the riser. Malekzadeh et al. (2012a) conducted experiments at a 35 m pipeline inclined at -2.54° from the horizontal followed by a 15.5 m high vertical riser. Five types of flow regime were observed: hydrodynamic slug flow, unstable oscillations, severe slugging type 1 (SS1), severe slugging type 2 (SS2) and severe slugging type 3 (SS3). The pure liquid slug length is larger than the riser length for SS1 (typical type), while the slug length is smaller than the riser length in type 2. The pure liquid slug becomes aerated liquid slug in type 3. A series of experiments were carried out by Fabre et al. (1990) with a mixture of air and water in a laboratory-scale flow loop with a 25 m horizontal or inclined pipeline followed by a 13.5 m high vertical riser. The severe slugging was not only observed in a downward inclined pipeline but also in a horizontal pipeline followed by a vertical riser. It was found that the mean void fraction in the riser underwent large-scale variations and the pressure at the riser bottom was sensitive. In the horizontal-pipe and vertical-riser system, the gas penetration appears before the liquid level reaching the riser outlet so that the slug length is shorter than the riser length. Several one-dimensional mathematical models were proposed to investigate the behavior of severe slugging in such pipeline-riser system (Schmidt et al., 1980;Fabre et al., 1990;Taitel et al., 1990;Sarica andShoham, 1991, Baliño et al., 2010). Although the predicted results are consistent with the experimental data, there are many limitations when trying to extrapolate the result to practical production systems (Nemoto and Baliño, 2012).
Apart from the vertical configuration, risers are usually deployed as free-hanging catenary or S-shaped (lazy S and steep S) patterns, especially for water depth exceeding 1000 m (Mokhatab, 2007;Mokhatab and Towler, 2007). Tin (1991) reported experimental study of severe slugging in a flexible riser. The effects of riser geometry on severe slugging behavior were identified. In the experiments conducted by Das et al. (1999), it was observed that the cycle time and slug length were sensitive to the gas velocity. Large slugs are broken into smaller slugs (Nydal et al., 2001;Yeung and Tchambak, 2003) in an S-shaped riser, where the pressure cycling behavior shows significant difference with that in a vertical riser (Tin, 1991;Montgomery, 2002).
Since the dramatic fluctuations of pressure and flow rate are caused by severe slugging, flexible risers in curved configurations are easily excited to vibrate, which may in turn affect the slug flow in risers. It is a complicated unstable fluid-structure interaction. In the past decades, studies of flow-induced vibration (FIV) mainly focused on the vortexinduced vibration (VIV) as external currents flow past risers (Huarte et al., 2006;Huang et al., 2011;Zhu et al., 2016). However, the internal multiphase flow may induce vibration as well as the external current. How large is the vibration amplitude induced by internal slug flow? Whether the flow regime in a curved flexible riser is affected by the vibration? These questions are worth investigating before designing proper measures to suppress the vibration and flow instability.
This work aims to investigate the dynamic response of a free-hanging flexible riser induced by internal flow and the characteristics of gas-liquid two-phase flow in the riser. The external current is not considered in this study. To accomplish the objective, experimental tests were carried out in a flexible riser with the aspect ratio of 134. Different gas and liquid flow rates are considered and discussed.

Experimental setup
The experiments were conducted in a pipeline-riser system consisting of a horizontal pipeline and a free-hanging flexible riser, as shown in Fig. 1. Both the pipeline and riser are made of transparent silica gel tube (flexible material) with elastic modulus E of 6.2 MPa and density ρ r of 1028 kg/m 3 . The external diameter (D) and internal diameter (D i ) are 10 mm and 8 mm, respectively. The riser hanging in air is deployed as a catenary form in a vertical plane (xoz plane) with the vertical height of 1 m and the horizontal span of 0.76 m. The length (L) of the riser is 1.34 m so that the aspect ratio (L/D) is 134. The two ends of the riser were fixed at the support frame, and no pretension was exerted on the riser. The origin of the coordinate system is located at the inlet of the riser. Thus the configuration of the catenary riser is expressed as: (1) A horizontal tube with the length of 1 m was arranged upstream of the riser. Gas and liquid were mixed in the tube and a stable two-phase flow was achieved before entry into the riser. As many previous studies, air and water were adopted as the experimental fluids. They were supplied by the respective systems but gathered through a Y-junction (mixer). Water was supplied from a storage tank by means of a centrifugal pump with a maximum flow rate of 4 L/min, while air was supplied by a rotary compressor with a maximum flow rate of 10 L/min at standard conditions (101325 Pa, 293.15 K). Before the air being introduced into the Ymixer, it was firstly stored in a buffer vessel in order to reduce the pressure fluctuations from the compressor. The riser discharged the gas-liquid flow into a two-phase separator, where air and water were separated by gravity at atmospheric pressure. After separation, the air was exhausted into atmosphere while the water returned to the storage tank.

Measurement techniques and data processing methods
Both the water and air flow rates were controlled by manual valves. Before the fluids entered the Y-mixer, their flow rates were monitored separately. The water flow rate was measured by an electromagnetic flowmeter with a maximum measurement capacity of 3.3 L/min and an accuracy of 0.5%. The air flow rate was measured by a float flowmeter with a maximum measurement capacity of 3 L/min and an accuracy of 1%. Experiments were performed over a certain range of gas and liquid flow rates according to the Froude number criterion: where v practice and v model are the flow velocities in practice 634 ZHU Hong-jun et al. China Ocean Eng., 2018, Vol. 32, No. 6, P. 633-645 v and model test, respectively, h practice and h model are the riser heights in practice and model test, respectively, and g is the gravity acceleration. According to the parameters of one real flexible riser installed on the west coast of Hainan Island, China, in experiments, the gas superficial velocity ( ) at standard conditions was set as 0.1-0.6 m/s, and the liquid superficial velocity ( ) ranged from 0.06 m/s to 0.3 m/s, where q G and q L are the gas and liquid flow rates, respectively, and A is the cross-section area of the riser. Thus the gas-liquid ratio (R GL ) ranged from 0.333 to 10, and the mixture velocity ( ) was in the range of 0.16-0.90 m/s.
Since the pressure fluctuation at the riser base may provide dynamic information on the development of the two-phase flow (Li et al., 2013), one pressure transducer (Model: YPT1000-T02, accuracy: 0.1%) was mounted at the riser inlet. Additionally, the outlet pressure was monitored by another pressure transducer with the sampling frequency of 100 Hz.
As shown in Fig. 1, apart from the basic fluid parameters, the flow regime was recorded by a high speed camera (Model: Baumer HXG20). The water in the upstream storage tank was dyed black by ink in order to identify the liquid slugs clearly. The vibration displacements of the riser were monitored by two high speed cameras from different views (side view and bottom view). Such high speed imaging method was successfully applied in recording the VIV of a curved flexible riser in our previous study (Zhu et al., 2016). The high speed camera placed on one side of the riser was used to record the vibration displacement of the riser in the xoz plane and the flow pattern in the riser simultaneously. The high speed camera placed under the riser was employed to record the vibration displacement along the y direction. In order to capture the displacement clearly, twenty-one black markings with the height of 1 cm and center-to-center spacing of 6 cm were marked along the riser by oily marker pen, and the first marking was located at the distance of 8 cm from the riser inlet. Thus, different markings represent different locations. The sampling frequency of high speed cameras was set as 100 frames per second, and each frame was 2048×1088 pixels with image resolution of 9.12 pixels per mm 2 .
The measurement devices were calibrated prior to the tests, and the fluids were allowed to flow for 10 min prior to data acquisition. The image was recorded for 2 min in each test so that 12000 pictures arrayed in time series were collected by each camera. As shown in Fig. 2, the displacements of markings along the riser are obtained by comparing the adjacent images. Firstly, the coordinate system in the images was defined according to the actual coordinate system shown in Fig. 1, and the correlation of image pixel unit with actual size was established with the height of each marking in the image corresponding to 1 cm (Zhu et al., 2016). Secondly, the markings in each image were recognized based on the moment invariants (Hu, 1962). Thirdly, the number of translational pixels for each marking was picked up from adjacent images, and the vibration displacements were easily obtained by converting the pixels to actual sizes. The image post-processing started from the first frame and ended in the last frame for each test. Finally, the displacement of each marking in the xoz plane was extrac-  ZHU Hong-jun et al. China Ocean Eng., 2018, Vol. 32, No. 6, P. 633-645 ted from the images recorded by the side camera, while the displacement along the y direction was extracted from the images recorded by the lower camera.

Decay tests
In order to determine the natural frequency of the flexible riser hanging in air and the system damping ratio, decay tests were carried out prior to the experiments. In the decay tests, the riser is filled with water. An initial displacement is exerted on the riser, and then the free attenuation response is recorded. The concerned parameters were obtained by Fast Fourier Transform (FFT). The first-order and second-order natural frequencies are 1.95 Hz (f 1n ) and 3.98 Hz (f 2n ), respectively and the system damping ratio (ζ) is 0.1018.

Results and discussions
3.1 Flow characteristics Fig. 3 shows the three flow patterns observed in the flexible riser. At v SL ≤0.18 m/s, transient cyclic severe slugging occurs with four stages in each cycle, similar to the severe slugging found in a vertical riser by Schmidt et al. (1980Schmidt et al. ( , 1985 and that in a catenary riser by Mokhatab (2007). The process of severe slugging is depicted in Fig.  3a. At the beginning, liquid accumulates at the bottom of the riser with the upstream horizontal pipeline in stratified flow. The accumulation of liquid creates a blockage for the gas. This stage is called slug formation. As gas and liquid continue to flow into the pipeline while the gas passage is blocked, liquid slug is generated and the slug front in the riser rises gradually. Meanwhile the gas is compressed at the bottom of the riser and the pressure is buildup. This stage is known as slug production. It should be noted that the liquid level does not reach the outlet of the riser in this stage, i.e. the slug length is smaller than the length of the riser, which coincides well with the observation in a horizontal-pipe and vertical-riser system by Fabre et al. (1990). When the gas pressure at the riser base is high enough to overcome the hydrostatic head in the riser, the gas penetrates into the riser, and the liquid slug is pushed toward the riser top. This stage is called liquid blowout. Finally, the gas flushes the liquid column out of the riser and the hydrostatic pressure de-creases. This is the liquid blowdown stage. Once the gas is expelled, the liquid level falls (liquid-fallback) and a new cycle starts (Malekzadeh et al., 2012a). However, the riser is never full of liquid during the whole process, which is similar to the severe slugging type 3 (Baliño et al., 2010;Nemoto and Baliño, 2012;Li et al., 2013;Baliño, 2014). As reported by Fabre et al. (1990), the horizontal pipeline cannot provide a favorable terrain for liquid accumulation as an inclined pipeline with negative slope. Thus the gas penetration occurs before the liquid level reaches the riser outlet.
As the liquid superficial velocity increases from 0.18 m/s to 0.30 m/s, the flow regime evolves into unstable oscillation flow or stable slug. As shown in Fig. 3b, when the air superficial velocity is larger than 0.2 m/s, the gas void fraction in the riser varies over time, though the gas and liquid continuously flow through the riser base into the riser. We call this flow regime as unstable oscillation flow (USO), which is a transitional flow between severe slugging and stable slug (Li et al., 2013). It is clearly seen that the liquid slug is aerated and the slug length has intermittent unstable oscillations. Therefore, the processes of liquid slug production and spontaneous vigorous blowdown disappeared. This observation is consistent with that reported by Malekzadeh et al. (2012a). When the liquid superficial velocity is larger than 0.24 m/s at v SG =0.1 m/s, relatively stable hydrodynamic slugs (STB) are generated and the gas and liquid flow out of the riser alternately, as shown in Fig. 3c. Fig. 4 provides the flow regime map based on the considered cases. It is seen that the severe slugging (SS3) occurs at low liquid flow rates. As the liquid superficial velocity increases, the flow pattern evolves to unstable oscillation flow. However, when the gas flow rate is small, the flow regime changes from unstable oscillation flow to stable slug flow. It should be mentioned that the flow pattern map is not a complete one due to the limited flow rates.
When the liquid superficial velocity is 0.06 m/s, SS3 occurs at the six considered gas velocities. The liquid slug length and the rising velocity of the slug are compared in Fig. 5. It is observed that the larger the gas superficial velocity is, the shorter the liquid slug will be. The maximum slug length is reduced by 68.4% as the gas superficial velo- city increases from 0.1 m/s to 0.6 m/s. High-speed gas accumulates quickly at the riser base so that the liquid does not have enough time to form a longer slug. As a result, the hydrostatic head in the riser becomes smaller as the gas superficial velocity increases, and it is easier to lift the liquid slugs. The slug rising velocity at v SG =0.6 m/s is about three times as large as that at v SG =0.1 m/s. Consequently, the cycle of severe slugging becomes shorter, which is in agreement with that in Das et al. (1999). The liquid slug in a fixed riser is also compared in Fig. 5. The slug length is reduced significantly after the riser is fixed. It indicates that the vibration of riser affects the accumulation of liquid in the riser bottom and thereby the slug length. As the lifting energy mainly comes from the gas kinetic energy. The smaller the gas superficial velocity is, the more obvious the difference between the fixed riser and the free-vibrating one will be.
3.2 Pressure fluctuation at the riser base Fig. 6 depicts the time histories of pressure at the riser base. The average pressure grows as the liquid superficial velocity increases. The flow pattern changing from severe slugging to unstable oscillation flow is the main cause. For unstable oscillation flow, the gas and liquid flow out of the riser continuously and the total liquid length in the riser becomes larger as the flow accelerates. However, the unstable oscillation flow presents lower period and smaller amplitude as compared with SS3. The reason is that SS3 needs sufficient time to complete the cyclic process. Especially, the stages of slug formation and slug production are time consuming. Additionally, the pressure at the riser base in SS3 is mainly controlled by the hydrostatic head, which reaches the maximum value at the end of the slug-production stage and decreases to the minimum value after the liquid is flushed out. This observation is consistent with previous studies (Schmidt et al., 1985;Fabre et al., 1990;Malekzadeh et al., 2012a;Li et al., 2013). As shown in Fig.  6, the average pressure decreases as the gas superficial velocity increases. It is mainly attributed to more gas penetrating into the liquid slug at high gas flow rates. Additionally, the gas compression process is shortened and the liquid slug is pushed up more quickly, resulting in the shorter period of pressure fluctuation. Fig. 7 displays the instantaneous pressure at the riser base at v SG =0.10 m/s, and the corresponding transient flow regime at typical moments. As stated above, the flow pattern changes from severe slugging (SS) to unstable oscillation flow (USO) and after that evolves to stable flow (STB), as the liquid superficial velocity increases from 0.06 m/s to 0.30 m/s. For SS3, the pressure peaks occur when the long liquid slug is generated and the riser base is filled with liquid, while the pressure troughs appear when the liquid slug is pushed upwards and the riser base is occupied by gas (Fig. 7a). The corresponding vibration shows the same period as the pressure fluctuation, and the phase difference between the two directional responses is 180°. When it comes to unstable oscillation flow, the monitored pressure reaches peaks as liquid flows through the riser base, while    the pressure falls to the troughs as gas flows through the same position (Fig. 7b). However, due to the continuous gas-liquid flow, the pressure amplitude is reduced significantly compared with the severe slugging. The vibration amplitude is also reduced correspondingly and the vibration period is shortened. For stable flow, the pressure amplitude is further reduced due to the shorter liquid slug (Fig. 7c). The same trend is observed in the vibration response. The pressure peaks and troughs could be distinguished by the flow regime at the riser base. When the riser base is occupied by liquid, the pressure reaches peaks, while pressure troughs occur when gas penetrates into the liquid slug. Therefore, the pressure at the riser base reflects the flow pattern and flow process in the riser (Fabre et al., 1990;Mokhatab, 2007;Malekzadeh et al., 2012a;Li et al., 2013), and the pressure fluctuation has effect on vibration.
The frequency of pressure fluctuation is plotted together with the dominated vibration frequency in Fig. 8. It can be seen that the horizontal vibration frequency basically follows the trend of pressure frequency. As the incoming gas and liquid flow along the x direction, the pressure fluctuation in the riser inlet directly affects the flow-induced vibration in this direction. In the z direction, the pressure frequency has the same trend as the vibration frequency of the upper part, which is close to the first-order natural frequency at v m ≥0.46 m/s. When the mixture velocity is in the range of 0.46-0.80 m/s, the vertical vibration of the upper part is dominated by a lower frequency while the vibration of the lower part is dominated by a higher frequency. It indicates that the pressure fluctuation mainly affects the firstorder vibration.

Vibration response
The time histories of vibration response at the midspan of the riser are shown in Fig. 9. Compared with the response in xoz plane, the displacement along the y direction is far smaller, so it is not plotted in the figure. It illustrates that the vibration induced by the internal two-phase flow mainly occurs in the vertical plane, unlike the out-of-plane vibration caused by external currents (Zhu et al., 2016).
As depicted in Fig. 9, the vibration responses in the x and z directions present similar trend. The response be-comes weaker as the liquid flow rate increases. When the gas superficial velocity is 0.10 m/s, the maximum vibration amplitude in the x direction reaches 1.3D at v SL =0.06 m/s, while it is reduced to 0.5D at v SL =0.30 m/s. The vibration response in the z direction is smaller than that in the x direction owing to the approaching direction of gas-liquid flow. The maximum amplitude decreases from 0.3D at v SL =0.06 m/s to 0.1D at v SL =0.30 m/s. This obvious reduction of vibration amplitude is attributed to the flow regime changing from severe slugging to transition flow or stable flow (Fig. 4). Severe slugging gives rise to gas compression (energy aggregation) and rapid liquid blowout (momentum release), exciting larger vibration. However, the vibration frequency becomes higher with the increasing liquid flow rate, and the higher the gas flow rate gets, the larger the increment of frequency is. When the severe slugging occurs, the cycle of severe slugging is relatively long, resulting in the lower frequency of flow instability, although the flow fluctuation in the riser is relatively large. Consequently, the vibration induced by severe slugging exhibits a lower frequency with a larger amplitude. When the flow pattern evolves into the oscillation flow, the gas and liquid flow out continuously so that the frequency of flow instability is relatively high. Additionally, the higher the gas flow rate becomes, the faster the liquid slug will be pushed upward in the riser, resulting in the increase of vibration frequency. As shown in Fig. 9, the vibration amplitude fluctuates over time when the unstable oscillation flow occurs in the riser, indicating that the riser undergoes multi-frequency response. The unstable and variable slug length along the riser (Fig. 3) is the main reason.
The vibration velocity and acceleration show the similar fluctuation as the displacement. As the liquid superficial velocity increases, the vibration displacement is reduced so that the velocity and acceleration in the same period also decrease. However, the maximum velocity occurs at the zero displacement, i.e. the phase angle between the velocity and displacement is 90°. Additionally, the maximum acceleration occurs when the velocity is reduced to zero, corresponding to the maximum displacement.
In order to present the whole response of the flexible riser, Fig. 10 plots the root mean square (RMS) displacements (X rms and Z rms ) along the riser. The vertical vibration ZHU Hong-jun et al. China Ocean Eng., 2018, Vol. 32, No. 6, P. 633-645 exhibits two peaks along the riser with a node close to the midspan, indicating that the response is dominated by the second mode. The asymmetry distribution of amplitude along the span is mainly attributed to the geometric nonlinearity of the riser. The first peak appears at the lower part of the riser (#4 marking, l i /L=0.18). As the angle between the local riser and vertical line varies along the axis of the riser, the maximum vertical vibration occurs at this segment with a relatively small horizontal angle. The second peak appears at #13 marking (l i /L=0.59), where the horizontal vibration experiences the peak amplitude. It illustrates that the responses along the two directions have a mutual effect. Owing to the catenary configuration, the lower part of riser would move upwards along the z axis if the upper part has a positive displacement along the x axis, and vice versa . Unlike the vertical vibration, the other peak of horizontal vibration occurring near the riser base is very small. Thus the horizontal vibration is dominated by the first mode, confirmed in Fig. 8 where the dominated frequencies of most part in many cases are close to the first natural frequency.
As shown in Fig. 10, at v SG ≤0.30 m/s, both of the horizontal and vertical vibration displacements decrease gradually as the liquid superficial velocity increases. Small gas flow rate means small lift energy. Thus the liquid slug is shortened as the liquid flow rate increases, resulting in smaller excitation force on the riser. However, the displacements are not reduced monotonically at v SG >0.30 m/s. At v SG =0.40 m/s, the vibration experiences an enhancement as the liquid superficial velocity increases from 0.06 m/s to 0.12 m/s, after that the vibration becomes weaker as the liquid superficial velocity further increases. At v SG ≥0.50 m/s, the most vigorous vibration shifts to appear at v SL =0.18 m/s. It indicates that the slug-induced vibration is enhanced firstly and then weakened as the liquid flow rate increases at v SG >0.30 m/s. This trend is similar to the VIV of a flexible riser whose vibration amplitude increases firstly and then decreases as the external flow velocity increases (Zhu et al., 2016), as depicted in Fig. 11. The equivalent reduced velocity for the internal flow is v m /(f n D). The vigorous slug-induced vibration occurs at the moderate reduced velocity, corresponding to the flow regime transition. Fig. 12 plots the response trajectories of six typical markings along the flexible riser. The size of the trajectories is magnified by 10 times for clear identification. The lower part close to the riser base vibrates vertically, exhibiting vertical-line-shaped orbits. As the position moves upwards, the horizontal amplitude becomes larger. Therefore, the trajectories of #6 and #9 markings present spindle or elliptic shape. When the marking moves to the upper part of the riser where the angle between the local segment and vertical line is relatively small, the trajectories evolve back to line-shaped figures. However, the horizontal amplitude is far larger than the vertical one. It is noted that the vibration trajectories induced by the internal gas-liquid two-phase flow are not as symmetry as the VIV trajectories caused by external currents (Zhu et al., 2016). The flow instability of severe slugging or unstable oscillation flow is the main reas-on. Besides, the unsynchronized vibration in the two directions also contributes to the asymmetric orbits.
As depicted in Fig. 13, both of the horizontal and vertical displacements show a slight increase when the mixture velocity is smaller than 0.46 m/s. However, the corresponding vibration frequencies increase gradually to the first-order natural frequency (f 1n ) as the mixture velocity increases from 0.16 m/s to 0.46 m/s. Similar to the VIV, this stage is called an initial branch (Khalak and Williamson, 1999;Jauvtis and Williamson, 2004). As the mixture velocity increases from 0.46 m/s to 0.80 m/s, the vibration displacements undergo an obvious increase. Both horizontal and vertical displacements reach their maximum values at v m =0.80 m/s. The horizontal vibration frequency is locked at the first-order natural frequency in this range (0.46 m/s≤ v m ≤0.80 m/s). However, the vertical frequency in the lower part of the riser further grows to almost the second-order  natural frequency (f 2n ), while the frequency in the upper part is still locked at the first-order one. It explains the specific locations of the two peaks of vertical displacements (Fig. 10). Additionally, it indicates that the responses of different parts of the riser are dominated by different frequencies. The lower part vibrates more strongly along the z direction, illustrating the second-order dominant mode. This stage is defined as a build-up branch. When the mixture velocity further increases from 0.8 m/s, the displacements become smaller. This stage is named as a descending branch, similar to the lower branch of VIV. Therefore, the slug-induced vibration has similar characteristics as the vortex induced vibration, as both of them belong to flow-induced vibration.
The maximum vibration displacement is the main concerned parameter in practice. Fig. 14 shows the maximum vibration displacement versus the gas-liquid ratio (R GL ). In order to predict the vibration displacement, semi-empirical equations are obtained by fitting the experimental results.
The root mean square errors of X rms-max and Z rms-max are 10.32% and 9.64%, respectively. It should be noted that the semi-empirical equations are based on the test data in this small-diameter tube. More validations are required to extrapolate the results to large-diameter pipelines.

Summary
Based on the experimental results, some aspects on the flow regime, pressure and the corresponding vibration displacements are summarized as follows: (1) Severe slugging type 3 (SS3) with gas penetration occurring prematurely was observed at v SL ≤0.18 m/s. The slug length is shortened as the gas superficial velocity increases. Compared with the fixed riser, free-vibration riser benefits the liquid accumulation and hence the long slug. The pressure at the riser base undergoes cyclic fluctuation with the peak and trough occurring at the end of slug-production and at the end of liquid blowout, respectively. The pressure fluctuation has an obvious effect on the riser vibration, as one of the vibration frequencies is the same as the pressure frequency. Owing to the long period and large flow fluctuation, the vibration induced by severe slugging presents a low frequency with large amplitude.
(2) Unstable oscillation flow characterized by variable slug length was generated at v SL ≥0.24 m/s and v SG ≥0.2 m/s. As compared with SS3, the pressure fluctuation experiences lower period and smaller amplitude, and the fluctuation period is further shortened as the gas superficial velocity increases. The vibration amplitude is also reduced correspondingly and the vibration period is shortened.
(3) Relatively stable slug was formed at v SL ≥0.24 m/s and v SG <0.2 m/s. The base pressure fluctuates in the minimum amplitude and the minimum period among the three ob-

Conclusions
Experimental tests were carried out to investigate the gas-liquid two-phase flow in a free-hanging flexible riser and the slugging-induced vibration. Small-diameter tube was employed based on the Froude number criterion. From the results and discussion presented above, the following conclusions can be drawn: (1) Three flow regimes are observed in the considered cases. When the liquid superficial velocity is smaller than 0.18 m/s, severe slugging type 3 with slug length smaller than the tube length is found in the riser. As the liquid superficial velocity increases, unstable oscillation flow characterized by aerated slug and variable slug length, and relatively stable slug were observed.
(2) The base pressure demonstrates the flow regime and flow process in the riser. Additionally, the pressure fluctuation affects the riser vibration as the lower vibration fre- ZHU Hong-jun et al. China Ocean Eng., 2018, Vol. 32, No. 6, P. 633-645 643 quency follows the pressure frequency. Among the three flow regimes, severe slugging leads to the longest period and the largest amplitude of pressure fluctuation.
(3) The slug-induced vibration mainly occurs in the plane of the riser, although the responses in the two directions are out of sync. The vibration response is sensitive to the flow regime. The vibration induced by severe slugging exhibits large amplitude with a low frequency, but the amplitude decreases and the frequency increases as the flow regime evolves into unstable oscillation flow. Similar to external flow-induced vibration, three branches of response are identified and defined as initial branch, build-up branch and descending branch.
This experimental study is an attempt to gain some insights on the slug-induced vibration of a free-hanging flexible riser. Further extensive studies are needed to evaluate the slug-induced vibration in larger diameter pipelines and to examine the response of a flexible riser under the combined effect of internal gas-liquid flow and external current, in order to provide references for practical production.