Test Study on Vortex-Induced Vibration of Deep-Sea Riser under Bidirectional Shear Flow

Abstract

A model test was carried out to reveal the vortex-induced vibration characteristics of a deep-sea riser under bidirectional shear flow. Bandpass filtering and modal analysis were used to process the test strain data, and the amplitude and frequency response characteristics of the vortex-induced vibration of the riser in the bidirectional shear flow field were obtained. The results of the test data analysis show that the dominant frequency of the vortex-induced vibration of the riser model under bidirectional shear flow is locked in the natural frequency of the riser and does not increase with the increase in flow velocity, that the average resistance coefficient of the riser model has little change under different flow velocities because of the distribution characteristics of the “bidirectional shear” flow field, that there is an extreme value of the shear force in the middle of the riser model, and that the Strouhal number in the transverse direction of the vortex-induced vibration under bidirectional shear flow is less than the recommended value of the current vortex-induced vibration prediction software. The obtained results provide basic data for the prediction of vortex-induced vibration and research into the fatigue analysis method of a riser under an internal wave flow field.

1. Introduction

The deep-sea riser is an important link connecting the deep-water floating platform and the submarine pipeline. During the service period, it bears environmental loads such as wind, wave and current for a long time. When the ocean current passes through the riser, it will generate vortex shedding alternately on both sides of the risers. This alternating shedding vortex will generate dynamic pressure on the riser that changes periodically in the in-line (IL) and the cross-flow (CF) directions. This makes the riser vibrate in the IL and CF directions. When the vortex-shedding frequency is locked in the natural vibration frequency of the riser, the vortex-induced vibration (VIV) will be amplified. In addition, the vibration of the riser will conversely affect the vortex structure of the wake flow, so the vortex-induced vibration is a complex process of multi-physical field coupling and interaction. Vortex-induced vibration has a serious impact on the fatigue failure of the riser, which is the main control factor of riser design. The research on VIV mainly adopts numerical simulation and model testing [1,2,3]. One method of VIV numerical simulation is the computational fluid dynamics method of directly solving Navier–Stokes equations, and the other is the semiempirical method of using test data to determine flow parameters, such as the wake oscillator, the single-degree-of-freedom model and the fluid force grouping model. The model test is an effective method for VIV research. The displacement, strain, velocity and acceleration information about a riser can be obtained using a model test. Based on these, the mechanism of the vortex-induced vibration of a riser is deeply analyzed. In recent years, much research work has been conducted at home and abroad to reveal the characteristics of the vortex-induced vibration of a riser caused by different types of flow fields. M. J. Thorsen, S. Savik, and C. M. Larsen (2016) [4] used the semiempirical method of vortex-induced vibration time-domain simulation to give a new hydrodynamic damping formula and found the necessary coefficients from the experimental data. The results show that the model predicts the frequency, mode and amplitude of vibration and has a high authenticity. J. V. Ulvesetter, M. J. Thorsen et al. (2018) [5] proposed a semiempirical prediction tool for CF and IL vortex-induced vibration time-domain analysis. The vertical riser with two different flow profiles was modeled, and the response prediction was compared with the experimental data. The prediction results are good, but there are differences under the combined action of a wave and a current. Victoria Kurushina, Ekaterina Pavlovskaia et al. (2020) [6] developed a new two-dimensional wake-oscillator model. A variety of alternative damping types are used in the fluid equation. The dynamic model takes into account the time history, the frequency response and the variation in the standard deviation of the modal coefficient along the deceleration range. The proposed model reasonably describes the CF displacement amplitude. Wude Xie, Zhenling Liang et al. (2022) [7] studied the dynamic response of flexible pipes for vortex-induced vibration coupled under the CF and IL directions. The numerical results show that the internal fluid density will cause the parametric resonance of the flexible pipe, and the coupling of the CF and IL vibrations of the pipe will make the VIV response differently affected. Chen Weimin, Zheng Zhongqiu et al. (2011) [8] studied the vortex-induced vibration of a riser under unidirectional shear flow. A multimode frequency locking-in calculation method based on the modal energy theory is established. The vortex-induced vibration responses of the riser under the action of internal waves, currents and other different flow fields are compared. The results show that the RMS amplitude and the stress of the response increase in different degrees with the increase in the wave-induced velocity. Gao Yun, Liu Liming et al. (2017) [9] carried out a towing basin test of flexible risers. The effects of the test methods on the trajectory characteristics of the single-mode and multi-mode vortex-induced vibration responses of flexible risers are studied. The results show that the flexible riser has the same trajectory response characteristics as the rigid riser at a low speed, and both of them show the classic “8” shape. At a high speed, the trajectory of the flexible riser becomes chaotic, which is mainly caused by the multi-modal response of displacement. A domestic literature survey found that the research on the vortex-induced vibration mechanism of the riser was basically limited to the research on the vortex-induced vibration of the riser under uniform flow and unidirectional shear flow [10,11,12]_, and the research on the vortex-induced vibration mechanism of the riser under bidirectional shear flow was rarely found.

The marine environment of the South China Sea is complex, one aspect of which is the unique and active deep-sea internal waves. A remarkable characteristic of internal waves is shear flow, and the flow field with the opposite velocity direction will be formed above and below the pycnocline, that is, bidirectional shear flow. The coupling vibration between the riser and the fluid in the bidirectional shear flow field is very complex, and the vortex-shedding frequency varies along the axial direction. The riser is a slender flexible pipe structure, and its modes show low-frequency dense characteristics. Under the action of internal waves and currents, it is easy to produce high-order and multi-modal coupled vortex-induced vibration responses, resulting in serious structural fatigue damage. Therefore, it is necessary to study the vortex-induced vibration characteristics of a riser under bidirectional shear flow. In this paper, the characteristics of the vortex-induced vibration of a riser under bidirectional shear flow are studied using a model test. In the test, the dynamic response data of the riser under vortex-induced vibration were monitored and measured synchronously using fiber Bragg grating strain sensors and force sensors. Based on the measured strain information, modal analysis, noise threshold filtering and time-frequency wavelet transform are used to analyze and summarize the amplitude and frequency response characteristics of the vortex-induced vibration of the riser in a bidirectional shear flow field. The obtained results provide basic data for vortex-induced vibration prediction and fatigue analysis of a riser under an internal wave flow field.

2. Basin Model Test Device and Test Model

2.1. Basin Model Test Device

The overall schematic diagram of the bidirectional shear flow basin model test device is shown in Figure 1. The test device is mainly divided into a double-shear flow simulation mechanical device, a driving device, a riser model and an end-support device.

The test device is installed in a deep-water basin, and the test model is placed horizontally. The driving wheel is driven to rotate using the motor and the gearbox. The driving wheel and the driven wheel are connected with a synchronous belt. The rotation of the driving wheel further drives the driven wheel using friction transmission. The test model is installed and fixed at both ends of the driven wheel and rotates synchronously with the driven wheel to form a bidirectional shear flow field. The schematic diagram of the bidirectional shear flow field is shown in Figure 2. Figure 3 is the schematic diagram of the current vector when the internal wave occurs. The experimental device can simulate the characteristics of bidirectional shear flow when internal waves occur.

The global coordinate system of the bidirectional shear flow pool model test is defined as shown in Figure 1. All measured values in the test are referred to this coordinate system. Wherein, the origin is located at the hinge point of the head of the riser model (the universal joint rotation point). The x-axis direction is the rotation direction of the driven wheel. The y-axis direction is perpendicular to the movement direction, and the z-axis is located along the axis of the riser model. In the test, the transverse flow direction (the CF direction) is the direction along the Y-axis, and the forward flow direction (the IL direction) is the direction along the X-axis.

2.2. Experimental Model and Arrangement of Fiber Bragg Grating Strain Sensor

The riser test model is made up of composite materials.

Table 1. Riser model parameters.

Items	Measured Value	Unit
Length	7.64	m
Hydrodynamic diameter	28.41	mm
Weight per unit length (dry weight)	1.24	kg/m
Bending stiffness EI	58.6	Nm2
Tensile stiffness EA	9.4 × 105	N

shows the parameters of the riser model.

A total of 46 FBG strain sensors were arranged on the test riser model. They were arranged in the four directions of CF1, CF2, IL1 and IL2, in which 9 sensors were arranged in the two directions of CF, and 14 sensors were arranged in the two directions of IL. The arrangement is shown in Figure 4.

2.3. Model Test Cases and Data-Processing Methods

A total of 56 sets of vortex-induced vibration tests under bidirectional shear flow were carried out for different flow conditions. The range of edge flow velocity (the flow velocity at the coordinate origin) was 0.30 m/s to 1.39 m/s, and the increasing step was 0.02 m/s. The experimental water depth was 1.40 m. The pretension applied to the riser model in the test was about 980 N. The measured data in the test included the strain time history of each design measuring point in the CF and IL directions on the riser, the time history of axial pretension and drag force and the encoder signal. The principle of data processing is to use the measured strain value to obtain the displacement vibration mode of the riser and the amplitude and frequency of the vibration response using modal analysis. After determining the displacement function of the whole riser, the hydrodynamic coefficient at the node along the riser length was calculated using the average resistance reverse identification method.

3. Drag Displacement, Resistance and Shear Force Characteristics of the Riser in the IL Direction under Bidirectional Shear Flow

In the test, the riser rotated under the driving of the test device, and with its midpoint as the dividing point, reverse hydrodynamic pressure was generated on the riser. That is, it bore the action of the bidirectional shear flow. The IL vibration and CF vibration in the steady state reflected the vibration characteristics of the riser under bidirectional shear flow. In order to simplify the analysis, the IL vibration and the CF vibration can be studied separately. Based on bandpass filtering and modal analysis, the displacement of each measuring point of the riser can be calculated from its strain data. The calculation results show that the drag displacement and velocity distribution in the IL direction also exhibit the characteristics of antisymmetric distribution. It is 0 at the hinge points at both ends and near the midpoint and reaches the extreme value of drag displacement at about one quarter and three quarters. The test results of the different edge flow velocities show that the maximum drag displacement along the riser length increases with the increase in flow velocity and reaches 0.55 D, as shown in Figure 5.

Based on the inverse identification method of drag displacement and average resistance, the average resistance coefficient and shear force distribution can be obtained. The analysis of the test results shows that the distribution characteristics of the average resistance along the length of the riser are basically the same as those of the drag displacement, and the average resistance along the riser length reaches the extreme value at about one quarter and three quarters of the riser length. Due to the special flow velocity distribution characteristics, there are small average resistance and large resistance coefficients when the midpoint flow velocity approaches 0. It is found that the vortex-induced vibration under bidirectional shear flow will amplify the average resistance coefficient, and the resistance coefficient distributed along the riser length is mostly in the range of 1.5 to 2. This shows that the vortex-induced vibration has the same amplification effect on the resistance coefficient at each position of the riser under bidirectional shear flow. The average value of the resistance coefficient is obtained by calculating the average value of the resistance coefficient distributed along the riser length in the interval from 1 to 2. This average value is taken as the average resistance coefficient of the riser model at this flow rate. The average resistance coefficient of the riser model under different edge flow velocities can be obtained with the same calculation for different flow velocities. The average resistance coefficient under different edge flow velocities is shown in Figure 6. It can be seen from the figure that, under the test condition, the average resistance coefficient does not change much with the increase in the edge flow velocity.

The mean value of the resistance coefficient C_dmean under all flow conditions is 1.3346. This coefficient can be used as the input of the average resistance coefficient in the riser design.

As shown in Figure 7, according to the analysis results of the test data, the distribution of shear force in the IL direction along the riser length under different edge flow velocities has the following two characteristics:

• The shear force of the slender pipe structure under uniform flow is close to 0 at the midpoint, while the shear force of the riser model under bidirectional shear flow reaches the maximum at the midpoint in addition to the maximum shear force distributed at both ends.
• Due to the slow distribution of the average resistance along the riser length in the middle, the riser model is subject to large structural shear near the speed direction change point.

The relationship between shear extreme value and flow velocity under different flow velocities was obtained through experiments. The analysis of the test data shows that the shear extreme value increases with the increase in flow velocity. The calculating formula for the extreme value of shear force can be obtained by linear fitting the test data:

F_SFmax = 0.5C_SFρDLU_max²

(1)

where C_SF is the maximum shear coefficient, taking 0.05519. ρ is the fluid density, D is the riser diameter, L is the length, and U_max is the edge velocity.

4. Vortex-Induced Vibration Characteristics of a Riser in the CF Direction under Bidirectional Shear Flow

During the test, the vortex shedding behind the riser under bidirectional shear flow not only caused the riser structure to vibrate in the IL direction due to the drag force, but it also caused the riser structure to vibrate laterally due to the lift force. When the vortex-shedding frequency locks in the natural frequency of the riser, resonance will occur, and the vibration displacement amplitude of the riser will increase greatly. By changing the edge velocity of the riser model, the vortex-induced vibration characteristics of the riser and the phenomenon of frequency locking-in were studied. By processing the test data, the modal weights of the vortex-induced vibration in the CF direction under different edge flow velocities were obtained. As shown in Figure 8: Section 1 is first-order mode dominance; Section 2 is first-order dominance and second-order participation; Section 3 is second-order dominance and first-order and third-order participation; and Section 4 is second-order and third-order dominance and first-order participation. As the edge flow velocity increases from 0.4 m/s to 1.37 m/s, the vortex-induced vibration mode changes from first-order dominance, first-order dominance, second-order participation, second-order dominance, and first-order and third-order participation.

When the edge velocity is less than 0.52 m/s, the vortex-induced vibration in the CF direction presents a first-order dominant state. When the edge velocity is in the range of 0.52 m/s to 0.85 m/s, the second-order modal participation gradually increases. When the flow velocity exceeds 0.85 m/s, the vortex-induced vibration is dominated by the second-order mode, and the participation of the third-order mode gradually increases. When the experimental flow rate reaches 1.27 m/s, the third-order modal weight is basically close to the second-order modal weight.

Figure 9 shows the dominant frequencies in the CF and IL directions of the riser models under different edge flow velocities. It can be found that the dominant frequency in the CF direction is always locked in the natural frequency under bidirectional shear flow, while the dominant frequency in the IL direction is locked in the natural frequency or twice the dominant frequency in the CF direction under different flow rates. Based on the dominant frequency obtained from the test, the St numbers in the CF direction and IL direction of the vortex-induced vibration under internal wave flow as obtained by linear fitting are 0.10 and 0.24. This provides a reference input parameter for the prediction of vortex-induced vibration under internal wave flow.

In the vortex-induced vibration test of flexible structures under unidirectional shear flow conducted according to the Norwegian Deepwater Project (NDP), the dominant frequency of flexible structures basically increases with the increase in flow velocity. The research in document [8] also shows that under unidirectional shear flow, due to the low-frequency density of the flexible riser structure, high-order frequency locked modes are constantly excited with the increase in flow velocity, and the dominant frequency of the riser structure basically increases with the increase in flow velocity. However, the test data for bidirectional shear flow show that the dominant frequency of the riser structure in the CF and IL directions is locked in the natural frequency of the structure and does not increase with the increase in the flow rate. According to the test data, the distribution diagram of the displacement frequency power spectral density along the riser length under different edge flow velocities is drawn. This distribution diagram proves that under the condition of a small flow rate, the whole riser model presents the first-order dominant mode. Under the condition of a large flow velocity, the power spectral density along the riser length is symmetrically distributed and there is a dominant frequency due to the characteristics of bidirectional shear flow velocity distribution.

Figure 10 shows the change in the maximum RMS dimensionless displacement in the CF direction with the flow rate (the meanings of Sections 1–4 are the same as those in Figure 8). It can be found from Figure 10 that when the riser model presents the first-order dominance, the maximum RMS displacement in the CF direction increases with the increase in the flow rate. When the second-order modes begin to participate in the vortex-induced vibration, the maximum RMS displacement decreases slightly with the increase in flow velocity. When the third-order modes begin to participate in the vortex-induced vibration, the maximum RMS displacement of the riser model begins to increase with the increase in the flow velocity. Therefore, it can be considered that due to the characteristics of velocity distribution, when the dominant order of the vortex-induced vibration transits from odd order to even order, the response amplitude of the riser model under bidirectional shear flow will not increase with the increase in velocity.

5. Displacement Time-Spatial Distribution Characteristics of CF Vibration

Figure 11, Figure 12 and Figure 13 show the time–space distribution of the displacement of the riser model in the CF direction under different dominant modes. As shown in Figure 11, it is a time–space distribution diagram of displacement in the CF direction when the edge velocity is 0.36 m/s. It can be found that at low edge velocity, the vibration of the riser is dominated by the first-order mode, presenting single-mode locking characteristics. At this time, the displacement response of the riser’s vortex-induced vibration presents obvious standing-wave characteristics. When the edge velocity increases by 0.56 m/s, the vortex-induced vibration is dominated by the first-order mode and participated by the second-order mode, and there is a jump between the modal responses. The time–space distribution of the displacement of the riser model shown in Figure 12 shows significant traveling-wave characteristics. Figure 13 shows the time–space distribution of dimensionless displacement in the CF direction under the condition of a large flow rate, and there is also a traveling-wave phenomenon. When the second-order modes or higher-order modes participate in the vortex-induced vibration, the riser model presents multi-modal response characteristics, and the vortex-induced vibration response has very obvious “traveling wave” time–space distribution characteristics.

6. Conclusions

A bidirectional shear flow model test was carried out using a self-developed test device. The dynamic response of the riser under vortex-induced vibration was monitored and measured synchronously using fiber Bragg grating strain sensors and force sensors. Based on the measured strain information, modal analysis, noise threshold filtering and time-frequency wavelet transform were used to analyze and summarize the amplitude and frequency response characteristics of the vortex-induced vibration of the riser. The main conclusions are as follows:

• The maximum displacement amplitude of the vortex-induced vibration of the riser model under bidirectional shear flow is equivalent to that under unidirectional shear flow. The dominant frequency of the vortex-induced vibration of the model under bidirectional shear flow is locked in the natural frequency of the riser and does not increase with the increase in flow velocity.
• Under different edge flow velocities, the average resistance coefficient of the riser model does not change much, and the average resistance coefficient C_dmean is 1.3346, which is slightly higher than the 1.2 recommended by the current specifications.
• The maximum value of the shear force on the riser model under bidirectional shear flow appears at the end of the model (consistent with uniform flow and shear flow), but there is also an extreme value in the middle of the model.
• The Strouhal number in the CF direction of the vortex-induced vibration under bidirectional shear flow is 0.10, which is slightly smaller than the recommended value (0.125 to 0.2) of the current VIV prediction software shear7 and vivana. The Strouhal number in the IL direction is about 0.24.
• The test results show that when the edge velocity is less than 0.56 m/s, the vortex-induced vibration under bidirectional shear flow has the characteristics of a “standing wave”. When the edge velocity increases to 0.56 m/s, the characteristics of a “traveling wave” begin to appear. With the increase in the edge velocity, the characteristics of a “traveling wave” become more obvious.