Tension and Drag Forces of Flexible Risers Undergoing Vortex-Induced Vibration

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×10⁵. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 10⁵, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.     

A practical approach to predicting cross-flow and in-line VIV response for deepwater risers

In this study, a practical model is proposed to predict cross-flow (CF) and in-line (IL) vortex-induced vibrations of a flexible riser in time domain. The hydrodynamic force as a function of non-dimensional amplitude and frequency is obtained from the forced vibration experimental data of a two-dimensional cylinder. An empirical nonlinear damping model is used to simulate the hydrodynamic damping outside the experiment's range. Coupling effect of CF and IL-VIV is taken into account by implanting a magnification model for the IL hydrodynamic force associated with CF amplitude, and by increasing the non-dimensional amplitude corresponding to the IL hydrodynamic coefficient in the second excitation region. The experimental models of flexible riser under the uniform and sheared current are simulated to validate the proposed model. The predicted displacement, curvatures, excited modes and fatigue damage show reasonable agreement with the measured data.     

基于能量竞争载荷模型的海洋立管双向涡激振动时域预报方法研究

海洋立管是深海油气开发中用于连接海底井口和水面浮体的唯一通道。立管在洋流作用下极易发生涡激振动（vortex-induced vibration,简称VIV）,发展快速经验性涡激振动时域预报方法对立管的安全设计具有重要意义。通过柔性立管模型试验,结合载荷重构方法和最小二乘法,识别建立了能量竞争载荷模型下的经验水动力载荷系数模型。应用识别建立的经验水动力载荷系数模型,发展形成了海洋立管顺流向及横流向双向涡激振动时域预报方法。将预报结果与试验结果对比,结果表明：基于能量竞争载荷模型的海洋立管双向涡激振动预报方法能够有效预报海洋立管涡激振动主导模态、主导频率、流向平均位移响应和涡激振动位移响应等力学行为特性。研究成果对发展更为有效的涡激振动预报手段具有有益参考。     

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations (VIV) of cylinders. In this paper, a novel in-line (IL) and cross-flow (CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.     

Analytical solution of mean top tension of long flexible riser in modeling vortex-induced vibrations

The vortex-induced vibration (VIV) of flexible long riser with combined in-line and cross-flow motion has been studied using a wake oscillator in this paper. The analytical solution of mean top tension of long flexible riser is evaluated and compared with experimental results, and good agreement is observed to verify its validity. Then the nonlinear coupled dynamics of the in-line and cross-flow VIV of a long tension-dominated riser were analyzed through wake oscillator model with the consideration of variation of the mean top tension. The in-line and cross-flow resonant frequencies, lift and drag coefficients, dominant mode numbers, amplitudes and instantaneous deflections are reported and compared with experimental results, and excellent agreements are observed. The comparison of mode numbers between the calculation with and without consideration of variation of mean top tension shows that the proposed analytical solution of the mean top tension can produce a better prediction of multi-mode VIV.     

Time domain prediction approach for cross-flow VIV induced fatigue damage of steel catenary riser near touchdown point

Previous steel catenary riser (SCR) models targeted for VIV prediction are truncated at touchdown point (TDP) where simple constrain and rotation stiffness are generally applied. In this study, a time domain approach accounting for the SCR–soil interaction is proposed to predict the cross-flow (CF) VIV induced fatigue damage of a SCR near TDP. The hydrodynamic force is simulated based on the forced vibration test data as a function of the non-dimensional amplitude and frequency, and an empirical damping model. When the non-dimensional frequency associated with the calculated frequency falls in the excitation region, the natural frequency closer to the frequency corresponding to the maximum excitation force is taken to be the dominant frequency, and applied to obtain the excitation force. The SCR–soil interaction model takes into account the trench shape, and the mobilization and release of the soil suction. Fatigue damage is linearly accumulated by using the rain-flow counting methodology. To validate the proposed models, simulation for a riser model test is carried out, and the envelopes of RMS displacement, curvature, and fatigue damage are compared. Further works focus on the sensitivity of VIV induced fatigue damage near TDP to the seabed parameters, such as mudline shear strength, shear strength gradient and soil suction, and some conclusions are obtained.     

Experimental Investigation on Vortex-Induced Vibration of Steel Catenary Riser

Steel catenary riser(SCR) is the transmission device between the seabed and the floating production facilities. As developments move into deeper water, the fatigue life of the riser can become critical to the whole production system, especially due to the vortex-induced vibration(VIV), which is the key factor to operational longevity. As a result, experimental investigation about VIV of the riser was performed in a large plane pool which is 60 m long, 36 m wide and 6.5 m deep. Experiments were developed to study the influence of current speed and seabed on VIV of SCR. The results show that amplitudes of strain and response frequencies increase with the current speed both in cross-flow(CF) and in-line(IL). When the current speed is high, multi-mode response is observed in the VIV motion. The amplitudes of strain in IL direction are not much smaller than those in CF direction. The seabed has influence on the response frequencies of riser and the positions of damage for riser.     

Experimental Investigation on Vortex-Induced Vibration of Steel Catenary Riser

Steel catenary riser (SCR) is the transmission device between the seabed and the floating production facilities. As developments move into deeper water, the fatigue life of the riser can become critical to the whole production system, especially due to the vortex-induced vibration (VIV), which is the key factor to operational longevity. As a result, experimental investigation about VIV of the riser was performed in a large plane pool which is 60 m long, 36 m wide and 6.5 m deep. Experiments were developed to study the influence of current speed and seabed on VIV of SCR. The results show that amplitudes of strain and response frequencies increase with the current speed both in cross-flow (CF) and in-line (IL). When the current speed is high, multi-mode response is observed in the VIV motion. The amplitudes of strain in IL direction are not much smaller than those in CF direction. The seabed has influence on the response frequencies of riser and the positions of damage for riser.     

Stress Wave Propagation Analysis on Vortex-Induced Vibration of Marine Risers

To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony''s method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the "global" dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.     

The effect of yaw angle on VIV suppression for an inclined flexible cylinder fitted with helical strakes

Experimental studies were carried out to investigate the response features of an inclined flexible bare cylinder as well as a straked cylinder in a towing tank, with the main purpose of further improving the understanding of the effect of yaw angle on vortex-induced vibration (VIV) suppression. Four yaw angles (a = 0°, 15°, 30°, 45°), which is defined as the angle between the cylinder axis and the plane orthogonal to the oncoming fluid flow, were tested. The cylinder model was towed along the tank to generate a uniform fluid flow. The towing velocity was in the range of 0.05–1.0 m/s with an interval of 0.05 m/s. The corresponding Reynolds number ranged from 800 to 16000. The strakes selected for the experiments had a pitch of 17.5D and a height of 0.25D, which is generally considered as the most effective configuration for VIV suppression of a flexible cylinder in water. The experimental results indicate that VIV suppression effectiveness of the inclined flexible straked cylinder is closely related to the yaw angle. The displacement amplitudes are significantly suppressed in both cross-flow (CF) and in-line (IL) directions at a = 0°. However, with increasing yaw angle, the suppression efficiencies of the CF and IL displacement amplitudes gradually decrease. In addition, the CF dominant frequencies of the straked cylinder obviously deviate from those of the bare cylinder at a = 0° and 15°. This deviation is substantially alleviated with increasing yaw angle. The IL dominant frequencies show less dependency on the yaw angle. Similar trends are also observed on the dominant modes of vibration and the mean drag coefficients.     

Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents

Many studies have tackled the problem of vortex-induced vibrations (VIV) of a vertical riser with a constant tension and placed in uniform currents. In this study, attention is focused on the cross-flow VIV modelling, time-domain analysis and prediction of variable-tension vertical risers in linearly sheared currents. The partial-differential equation governing the riser transverse motion is based on a flexural tensioned-beam model with typical pinned-pinned supports. The hydrodynamic excitation model describing the modulation of lift force is based on a distributed van der Pol wake oscillator whose nonlinear equation is also partial-differential due to the implementation of a diffusion term. The variation of empirical wake coefficients with system parameters and the water depth-dependent Reynolds number is introduced. Based on the assumed Fourier mode shape functions obtained by accounting for the effect of non-uniform tension, the Galerkin technique is utilized to construct a low-dimensional multi-mode model governing the coupled fluid-riser interaction system due to VIV. Numerical simulations in the case of varying sheared flow profiles are carried out to systematically evaluate riser nonlinear dynamics and highlight the influence of fluid-structure parameters along with associated VIV aspects. In particular, the effects of shear and tensioned-beam (tension versus bending) parameters are underlined. Some comparisons with published experimental results and observations are qualitatively and quantitatively discussed. Overall parametric analysis and prediction results may be worthwhile for being a new benchmark against future experimental testing and/or numerical results predicted by an alternative model and methodology.     

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration(VIV) for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line(IL) response is as important as the cross-flow(CF) response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.     

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration (VIV) for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line (IL) response is as important as the cross-flow (CF) response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.     

Application of Helical Strakes for Suppressing the Flow-Induced Vibration of Two Side-by-Side Long Flexible Cylinders

Helical strakes have been widely applied for suppressing the vibration of flexible cylinders undergoing vortexshedding in offshore engineering. However, most research works have concerned on the application of helical strakes for the isolated flexible cylinder subjected to vortex-induced vibration(VIV). The effectiveness of helical strakes attached to side-by-side flexible cylinders in vibration reduction is still unclear. In this paper, the response characteristics of two side-by-side flexible cylinders with and without helical strakes were experimentally investigated in a towing tank. The configuration of the helical strakes used in the experiment had a pitch of 17.5D and a height of 0.25D(where D is the cylinder diameter), which is usually considered the most effective for VIV suppression of isolated marine risers and tendons. The center-to-center distance of the two cylinders was 3.0D. The uniform flow with a velocity ranging from 0.05 m/s to 1.0 m/s was generated by towing the cylinder models along the tank. Experimental results, including the displacement amplitude, the dominant frequency, the dominant mode,and the mean drag force coefficient, were summarized and discussed. For the case where only one cylinder in the two-cylinder system had helical strakes, the experimental results indicated that helical strakes can remarkably reduce the flow-induced vibration(FIV) of the staked cylinder. For the case of two straked cylinders in a side-by-side arrangement, it was found that the performance of helical strakes in suppressing the FIV is as good as that for the isolated cylinder.     

Vortex modes and vortex-induced vibration of a long,flexible riser

Investigations of the velocity and vorticity fields in the wake of a flexible riser with a length to diameter ratio of 181 were conducted in a towing tank at moderate Reynolds numbers in the range of 9400–47,000. Wake velocity measurements were made with the riser freely vibrating in both in-line and cross-flow directions. The motion and wake field of the riser, undergoing free vibration, were simultaneously measured by accelerometers installed inside the riser and by using a digital particle image velocimetry (DPIV) system. The vortex-induced vibration (VIV) results show that the riser freely oscillated at multiple vibration frequencies and amplitudes at each Reynolds number. Mixed vortex modes, ‘2S’, ‘2P’ and ‘P+S’, were observed in the near wake of the riser at different instants of time. The occurrence of these vortex modes depended on the Reynolds number, dominant frequency and mean amplitude. At lower Reynolds number, the single stable mode ‘2S’ dominated the wake. With the increase of Reynolds number, the percentage of the ‘2S’ modes decreased while the percentage of ‘2P’ modes increased steadily except at Reynolds numbers of 14,100 and 47,000. The ‘P+S’ modes occurred mostly at a Reynolds number of 14,100 accompanied by more ‘2P’ modes and less ‘2S’ modes. At this Reynolds number, the frequency of the VIV was very close to the natural frequency of 0.72 Hz, which was obtained from a riser decay test in steady water and the average amplitude to diameter ratio reached 0.95, the highest found in these tests.     

Cross-flow vortex-induced vibration reduction of a long flexible cylinder using 3 and 4 control rods with different configurations

Control rod is one of the common passive control methods to suppress the vortex-induced vibration (VIV) of cylindrical structures. In this paper, the experimental study is conducted to detailed understand the performance of multiple control rods in suppressing the cross-flow (CF) VIV for a long flexible cylinder. The influence of the spatial arrangement of 3 and 4 control rods on CF VIV response of the main cylinder is investigated in a towing tank. It is observed that the attack angle θ is a very significant parameter to affect the vibration response, dominant frequency and the VIV suppression efficiency of the main cylinder. Based on the suppression efficiencies analysis of VIV response in the present experimental investigation, the spatial arrangement of 3 control rods with θ = 40° and 4 control rods with θ = 30° is the best choice for suppressing the CF VIV response of the main flexible cylinder. Overall, the use of 4 control rods could reduce VIV more effectively than the application of 3 control rods.     

An Experimental Study on Dynamics Features of Three Side-by-Side Flexible Risers Undergoing Vortex-Induced Vibrations in A Uniform Flow

A vortex-induced vibration(VIV) experiment on three side-by-side risers subjected to a uniform flow was carried out in a combined wave-current flume. The dynamic features of interference effect on three side-by-side risers were investigated by varying fluid velocity and inter-riser spacing. The distributions of dimensionless displacement,dominant frequency, and displacement trajectory of the model risers were measured using mode decomposition and wavelet transform techniques. The coupled interference of inter-riser fluid to adjacent risers at different spacings was disclosed by introducing the "interference ratio" concept. The results show that at spacings smaller than 6.0 D, the three model risers display appreciable deviations in their displacement responses in cross-flow or in-line direction,attributable to the strong proximity disturbance and wake interference between the risers. When the spacing is increased to 8.0 D, wake interference still makes great difference to the dynamic response of the risers in both directions. As reduced velocity increases, the three risers show higher agreement with an isolated riser in overall dominant vibration frequency in CF direction than that in IL direction at all spacings and the side risers, although symmetrically placed, do not vibrate symmetrically, as a result of the steady deflection of clearance flow within the riser group. Interference effect results in a remarkable unsteady mode competition within the risers; quantitation of the interference levels for the three risers at different spacings with interference ratio revealed that under low flow velocities and large spacing ratios, clearance flow constitutes a non-neglectable interferer for three side-by-side risers.     

Instantaneous multi-mode identification and analysis of vortex-induced vibration via a mode decomposition method

The dynamic characteristics of marine risers/pipes often present serried modes with various frequencies due to high levels of structural flexibility and slenderness, especially when the flow velocity is non-uniformly distributed along the span. Therefore, the vortex-induced vibration (hence VIV) for slender risers/pipes is usually characterized by multi-mode motions. In this paper, by means of a newly developed empirical mode decomposition (EMD) method which contributes to more efficient instantaneous multi-mode identification and analysis, new characteristics of a multi-mode “lock-in” vibration process of a large-scale flexible pipe subject to shear flow were discussed. Because the two-degree vibration along the span can be analyzed simultaneously, the effects of multi-mode VIV were investigated systematically. From the given illustrative examples, it was found that the vibration energy diffusion between the fluid and the structure, and among the participating modes, may be repeatable and reversible, or even irreversible, which causes VIV to be highly intricate. The coexistence of multiple modes, energy transfer, and mode switching/jump is observed when the reduced velocity is relatively high. The multi-dominant mode phenomenon is also found in both cross-flow (CF) and in-line (IL) VIVs. Energy transfers between the CF and IL directions occasionally occur, and CF VIV is apt to dominate the vibration process, because it is superior to IL VIV with the increment of the reduced velocity.     

Study on Pure IL VIV of A Free Spanning Pipeline Under General Boundary Conditions

Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line (IL) vortex-induced vibrations (VIV) analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.     

On splitter plate coverage for suppression of vortex-induced vibrations of flexible cylinders

Experimental results show how vortex-induced vibration (VIV) amplitudes of flexible cylinders can be reduced up to a 90% by covering less than half of the length of the cylinder with splitter plates elastically mounted to the surface of the cylinder.The VIV amplitude reduction takes place along with drag coefficient reductions of up to a 50% for the reduced velocities investigated.