Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Fatigue Life Assessment of Top Tensioned Risers Under Vortex-Induced Vibrations

The fatigue life of top tensioned risers under vortex-induced vibrations (VIVs) with consideration of the effect of internal flowing fluid on the riser is analyzed in the time domain.The long-term stress histories of the riser under VIVs are calculated and the mean stresses,the number of stress cycles and amplitudes are determined by the rainflow counting method.The Palmgren-Miner rule for cumulative damage theory with a specified S-N curve is used to estimate the fatigue life of the riser.The corresponding numerical programs numerical simulation of vortex-induced vibrations (NSVIV) which can be used to calculate the VIV response and fatigue life of the riser are compiled.Finally the influences of the riser's parameters such as flexural rigidity,top tension and internal flow velocity on the fatigue life of the riser are analyzed in detail and some conclusions are drawn.

Numerical simulation of a short flexible pipe subject to forced motion and vortex-induced vibration

A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction （FSI） problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method （Chen and Kim, 2008） was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test （Choi and Hong, 2000） via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn＇t only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.

Nonlinear Coupled in-Line and Cross-Flow Vortex-Induced Vibration Analysis of Top Tensioned Riser

The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations （VIV） of the riser are analyzed in time domain in this papar. The numencal shnulation results of the riser＇s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser＇s VIV. Finally, the effects of the riser＇s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.

Prediction Model for Vortex-Induced Vibration of Circular Cylinder with Data of Forced Vibration

A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions （VIV） of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson＇ s group are in rather good agreement.

Experimental Investigation of Disturbing the Flow Field on the Vortex-Induced Vibration of Deepwater Riser Fitted with Gas Jetting Active Vibration Suppression Device

An experimental investigation on the disturbance effect of jet-type active vibration suppression device on vortexinduced vibration of deep-sea riser was carried out in the wave-flow combined flume.The vibration suppression device was designed in which the jet pipe was horizontally fixed to the front end of the riser.By varying three different excitation spacings and multi-stage outflow velocities,the influence law of the dominant frequency,dimensionless displacement and other dynamic response parameters was studied under different excitation spacings,and the mechanism and sensitive characteristics of the disturbance suppression were explored.The results indicate that the variation of excitation spacing makes gas curtain enter the strong disturbed flow region at different velocities and angles,and the coupling relationship between excitation spacing and reduced velocity is the key factor to enter the strong disturbed flow region to achieve the optimal disturbance suppression.In the strong disturbed flow region,the influence of gas curtain on the dominant frequency is obviously affected by the flow velocity,while the vibration displacement is stable at the same amplitude and is weakly affected by the flow velocity.Gas curtain can effectively disturb the formation of vortex shedding,destroy the strong nonlinear coupled vibration of the riser,and achieve better vibration suppression effect.In the weak disturbed flow region,the vortex length of the riser tail is prolonged,the strong nonlinear coupled vibration of the riser is gradually restored,and the vibration suppression effect of the device gradually decreases.

Investigation of a New Vortex-Induced Vibration Suppression Device in Laboratory Experiments

In order to mitigate vortex-induced vibration (VIV) of marine risers, especially to eliminate the phenomenon of frequency 'lock-in', a new suppression device of crescent-shaped flow spoiler was designed with seven different layout schemes. VIV model tests with six flow levels were conducted in a large wind-wave-current flume. In all cases, vibration responses in both in-line and cross-flow cases were measured. With the installation of suppression devices vibration frequency evolution of a riser was analyzed by Morlet wavelet transform. The principle of VIV suppression was interpreted through vibration characteristics. Fatigue life of the riser was calculated by the Palmgren-Miner rule. Compared with a bare riser, vibration of an outfitted riser with suppression devices disturbed the steady flow, the vibration amplitudes in the two flow directions were reduced, and the riser fatigue life was improved.

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 Deep-Sea Risers of Different Excitation Water Depths

The vortex-induced vibration test of the deep-sea riser was carried out with different excitation water depths in the wave-current combined water flume.By dimensionally changing the multi-stage water depth and hydrodynamic parameters such as outflow velocity at various water depths,the dynamic response parameters such as dominant frequency,dimensionless displacement and vibration trajectory evolution process of the riser under different excitation water depths were explored to reveal the sensitive characteristics of the dynamic response of vortexinduced vibration of the risers under different excitation water depths.The results show that different excitation water depths will change the additional mass of the riser and the fluid damping and other parameters,which will affect the spatial correlation and stability of the vortex shedding behind the riser.In the lock-in region,the distribution range of the characteristic frequency becomes narrow and centered on the lock-in frequency.The increase of the excitation water depth gradually advances the starting point of the lock-in region of the riser,and at the same time promotes the excitation of the higher-order vibration frequency of the riser structure.Within the dimensionless excitation water depth,the dominant frequency and dimensionless displacement are highly insensitive to the excitation water depth at high flow velocity.The change of the excitation water depth will interfere with the correlation of the non-linear coupling of the riser.The“8-shaped”gradually becomes irregular,and the vibration trajectories of the riser show“O-shape”,“X-shape”and“Crescent-shape”.

Experimental evidence for the mechanism of subcritical vortex-induced vibration

The vortex-induced vibration(VIV)of circle cylinder can occur at subcritical Reynolds numbers as low as 20,which is called subcritical VIV.Recent numerical research suggests that the interaction of fluid mode and structural mode is the primary cause of its occurrence.Due to the limitations of experimental techniques and data analysis methods,researchers failed to find experimental evidence to support this view.To this end,we conducted subcritical VIV tests in a rotating channel and discovered that the flow is unstable when subcritical VIV occurs.Subsequently,an experimental data-driven model for unsteady flow is constructed.By coupling the unsteady flow model with the structural dynamic equations,we constructed the FSI model for subcritical VIV.By performing linear stability analysis on the FSI model,we found that there are two key modes in the FSI system,namely fluid mode and structural mode.These two modes will couple when the structural natural frequency is close to the characteristic frequency of the flow,resulting in the instability of structural mode and thus inducing subcritical VIV.This experimental finding clarifies that subcritical VIV is essentially flutter as a result of structural mode instability,providing the first experimental evidence for the mechanism of subcritical VIV.

An overview of vortex-induced vibration(VIV)of bridge decks

A brief overview of vortex-induced vibration(VIV)of circular cylinders is first given as most of VIVstudies have been focused on this particular bluff cross-section.A critical literature review of VIV of bridge decks thathighlights physical mechanisms central to VIV from a renewed perspective is provided.The discussion focuses on VIVofbridge decks from wind-tunnel experiments,full-scale observations,semi-empirical models and computational fluidsdynamics(CFD)perspectives.Finally,a recently developed reduced order model(ROM)based on truncated Volterraseries is introduced to model VIVof long-span bridges.This model captures successfully salient features of VIVat“lockin”and unlike most phenomenological models offers physical significance of the model kernels.

Application of fiber Bragg grating based strain sensor in pipeline vortex-induced vibration measurement

The vortex-induced vibrations(VIV)is an important topic of study in many different scientific and engineering fields.While VIV can be of benefit in some cases,oftentimes,it is an undesirable phenomenon that can be quite dangerous.In particular for offshore pipelines,VIV can lead to fatiguing of the pipe structure and can cause disastrous consequences if left unchecked.A number of different methods have been applied to the measurement of VIV,especially for the elongated,thin cylindrical structures.The use of fiber optic fiber Bragg gratings(FBGs)in particular has gained popularity over the recent years due to their distinct properties.However,FBGs are also very fragile and are susceptible to failure when placed in harsh environments without protection.In this paper,56 FBGs encapsulated in stainless steel tubes were applied to the measurement of VIV in a28-m model pipeline under controlled and uncontrolled conditions.Tests show that the encapsulated sensors possessed good sensitivity as well as fatigue life(>80000 cycles).The measurements from FBGs were also high enough to allow frequency domain analysis of the pipeline VIV under the two conditions.The authors conclude that the encapsulated FBGs are a viable tool for the study of VIV in pipeline structures.

Numerical simulations of vortex-induced vibrations of a flexible riser with different aspect ratiosin uniform and shear currents

This paper aimed at describing numerical simulations of vortex-induced vibrations（VIVs） of a long flexible riser with different length-to-diameter ratio（aspect ratio） in uniform and shear currents. Three aspect ratios were simulated： L/D= 500, 750 and 1 000. The simulation was carried out by the in-house computational fluid dynamics（CFD） solver viv-FOAM-SJTU developed by the authors, which was coupled with the strip method and developed on the OpenFOAM platform. Moreover, the radial basis function（RBF） dynamic grid technique is applied to the viv-FOAM-SJTU solver to simulate the VIV in both in-line（IL） and cross-flow（CF） directions of flexible riser with high aspect ratio. The validation of the benchmark case has been completed. With the same parameters, the aspect ratio shows a significant influence on VIV of a long flexible riser. The increase of aspect ratio exerted a strong effect on the IL equilibrium position of the riser while producing little effect on the curvature of riser. With the aspect ratio rose from 500 to 1 000, the maximum IL mean displacement increased from 3 times the diameter to 8 times the diameter. On the other hand, the vibration mode of the riser would increase with the increase of aspect ratio. When the aspect ratio was 500, the CF vibration was shown as a standing wave with a 3-（rd） order single mode. When the aspect ratio was 1 000, the modal weights of the 5-（th） and 6-（th） modes are high, serving as the dominant modes. The effect of the flow profile on the oscillating mode becomes more and more apparent when the aspect ratio is high, and the dominant mode of riser in shear flow is usually higher than that in uniform flow. When the aspect ratio was 750, the CF oscillations in both uniform flow and shear flow showed multi-mode vibration of the 4-（th） and 5-（th） mode. While, the dominant mode in uniform flow is the 4-（th） order, and the dominant mode in shear flow is the 5-（th） order.

NONLINEAR FLUID DAMPING IN STRUCTURE-WAKE OSCILLATORS IN MODELING VORTEX-INDUCED VIBRATIONS

A Nonlinear Fluid Damping （NFD） in the form of the square-velocity is applied in the response analysis of Vortex-Induced Vibrations （VIV）. Its nonlinear hydrodynamic effects on the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-in, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is in good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

PREDICTION OF VORTEX-INDUCED VIBRATION OF LONG FLEXIBLE CYLINDERS MODELED BY A COUPLED NONLINEAR OSCILLATOR:INTEGRAL TRANSFORM SOLUTION

The Generalized Integral Transform Technique （GITT） was applied to predict dynamic response of Vortex-Induced Vibration （VIV） of a long flexible cylinder. A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder, leading to a coupled system of second-order Partial Differential Equations （PDEs） in temporal variable. The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations （ODEs）, which was numerically solved by using the Adams-Moulton and Gear method （DIVPAG） developed by the International Mathematics and Statistics Library （IMSL）. Numerical results were presented for comparison to those given by the finite difference method and experimental results, allowing a critical evaluation of the technique performance. The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated, which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.

MULTI-MODE OF VORTEX-INDUCED VIBRATION OF A FLEXIBLE CIRCULAR CYLINDER

The vortex-induced vibration of a flexible circular cylinder is investigated at a constant Reynolds number of 1000. The finite-volume method on moving meshes is applied for the fluid flow, and the Euler-Bernoulli beam theory is used to model the dynamic response of a flexible cylinder. The relationship between the reduced velocity and the amplitude response agrees well with the experimental results. Moreover, five different vibrating modes appear in the simulation. From the comparisons of their vortex structures, the strength of the wake flow is related to the exciting vibrating mode and different vortex patterns arise for different vibrating modes. Only 2P pattern appears in the first vibrating mode while 2S-2P patterns occur in the other vibrating modes if monitoring at different sections along the length of the cylinder. The vibration of the flexible cylinder can also greatly alter the three-dimensionality in the wake, which needs further studies in our future work, especially in the transition region for the Reynolds number from 170 to 300.

Identification of Hydrodynamic Forces on a Flexible Pipe Near Plane Boundary Subjected to Vortex-Induced Vibrations

Formally,use of system identification techniques to estimate the forces acting on the beam may give information on hydrodynamic forces due to vortex-induced vibrations(VIVs),but no results from such attempts for submarine pipeline spans have been reported.In this study,a pipe model with a mass ratio(mass/displaced mass) of 2.62 is tested in a current tank.The gap ratios(gap to pipe diameter ratio) at the pipe ends are 2.0,4.0, 6.0 and 8.0.The response of the model is measured using optical fiber strain gauges.A modal approach linked to a finite element method is used to estimate the hydrodynamic forces from measurement.The hydrodynamic force at the dominant response frequency is the major concern,and the lift force and added mass coefficients are calculated.Response calculations are performed using force coefficients from the inverse force analysis and the calculated results are in accordance with the experimental data.

Vortex-induced vibration response of a circular cylinder surrounded with small rods

In this paper,cross-flow vortex-induced vibration(VIV)responses of a circular cylinder surrounded with different control rods have been investigated in a wind tunnel.The number of rods n is set equal to 3 and 6,and the ratios of diameters d/D(where d is the diameter of small rods,D is the cylinder diameter)are assumed to 0.10,0.16 and 0.20.The spacing ratios of s(s=G/D,where G is the gap distance between the main cylinder surface and the control rod surface)are selected as 0.2,0.4 and 0.6 respectively.The Reynolds number based on the main cylinder is in the region of Re=4000–42000.Results show that the VIV can be significant suppressed if placing the control rods in appropriate arrangement.And the gap between the rod and the main cylinder plays a more important role in the VIV amplitude response.When the spacing ratio between the rod and main cylinder is 0.2,VIV can be best suppressed by 96.7%.However,rods do not always suppress VIV and the responses can be more severe in other spacing ratios(s=0.4,0.6).And typical vortex shedding frequency lock-in phenomenon can be observed.When the spacing ratio is 0.2,other than the natural frequency component,St frequency is also presented in the frequency spectrum of wake velocity.

Suppression of vortex-induced vibrations of a flexible riser by adding helical strakes

3-D computational fluid dynamics/ computational structure dynamics (CFD/CSD) numerical two-way coupling simulations are conducted for a flexible rise in order to study the dynamic response performance of the riser with and without helical strakes exposed to the vortex-induced vibration (VIV). The VIV responses of a PVC riser without helical strakes are computed and compared with experimental data, to verify the accuracy of the present two-way coupling method. Subsequently, the dynamic behaviors of a short PVC riser with different kinds of helical strakes are studied. The vibration amplitudes along the riser, the trajectories of the riser's monitor point and the vortex shedding contours are obtained in a series of simulations. The helical strakes5 VIV suppression mechanisms are found involving the breaking of the vortex structures and the reduction of the vortex shedding frequency of the bare riser. Moreover, a good suppression effect can be achieved by attaching the helical strake structure with a reasonable geometrical configuration (such as the appropriate strake height, strake pitch, the number of starts and strake coverages) to the flexible riser. The effect is also diverse at different reduced velocity (Ur). The remarkable effect is found at Ur = l for the short riser, with about 97% reduction in the transverse vibration response.

VIV analysis of pipelines under complex span conditions

Spans occur when a pipeline is laid on a rough undulating seabed or when upheaval buckling occurs due to constrained thermal expansion. This not only results in static and dynamic loads on the flowline at span sections,but also generates vortex induced vibration (VIV),which can lead to fatigue issues. The phenomenon,if not predicted and controlled properly,will negatively affect pipeline integrity,leading to expensive remediation and intervention work. Span analysis can be complicated by:long span lengths,a large number of spans caused by a rough seabed,and multi-span interactions. In addition,the complexity can be more onerous and challenging when soil uncertainty,concrete degradation and unknown residual lay tension are considered in the analysis. This paper describes the latest developments and a'state-of-the-art' finite element analysis program that has been developed to simulate the span response of a flowline under complex boundary and loading conditions. Both VIV and direct wave loading are captured in the analysis and the results are sequentially used for the ultimate limit state (ULS) check and fatigue life calculation.