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.

Suppression of Vortex-Induced Vibration Caused by A Terebridae-Inspired Cylinder with Different Helical Angles

Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural forms are shown,including the traditional smooth cylinder(P0),and the Terebridae-inspired cylinder with the helical angle of 30°(P_(30)),60°(P_(60)),and 90°(P_(90)).Computational fluid dynamics(CFD)method is adopted to solve the flow pass the Terebridae-inspired structures,and the vibration equation is solved using the Newmark-βmethod.The results show that for P_(30),P_(60) and P_(90),the VIV responses are effectively suppressed in the lock-in region,and P_(60) showed the best VIV suppression performance.The transverse amplitude and the downstream amplitude can be reduced by 82.67%and 91.43%respectively for P_(60) compared with that for P0,and the peak of the mean-drag coefficient is suppressed by 53.33%.The Q-criterion vortices of P_(30),P_(60),and P_(90) are destroyed,with irregular vortices shedding.It is also found that the boundary layer separation is located on the Terebridae-inspired ribs.The twisted ribs cause the separation point to constantly change along the spanwise direction,resulting in the development of the boundary layer separation being completely destroyed.The strength of the wake flow is significantly weakened for the Terebridae-inspired cylinder.

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.

Experimental Study on Vortex-Induced Vibration of Rough Risers with Coupling Interference Effect Under Side-by-Side Arrangement

A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.

Experimental Study on Vortex-Induced Vibration of Rough Risers Coupling with Interference Effect in Tandem Arrangement

In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference effects on the riser,a VIV experiment of rough risers in tandem arrangement was conducted in a wave−current combined flume.The experiment characterized the risers’roughness by arranging different specifications of attachments on the surface of the risers.Three rough risers with different roughness and smooth risers were arranged in tandem arrangement,with the rough risers arranged downstream.The experimental results indicate that the suppression of the attachments on the downstream risers’vibration are more significant both in the CF and IL directions as the reduced velocity increases.For the downstream riser,the amplitude response of rough riser is more significantly weakened compared with the smooth one at high reduced velocity.For the upstream risers,changes in the roughness and spacing ratio have an impact on their‘lock-in’region.When the roughness of downstream risers is relatively large(0.1300)and the spacing between risers is small(S/D=4.0),the reduced velocity range of‘lock-in’region in the CF direction of upstream risers is obviously expanded,and the displacement in the‘lock-in’region is severer.

Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.

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.

Experi mental Study on Vortex-Induced Vibrations of Submarine Pipeline near Seabed Boundary in Ocean Currents

Unlike most previous studies on vortex-induced vibrations of a cylinder far from a boundary, this paper focuses on the influences of close proximity of a submarine pipeline to a rigid seabed boundary upon the dynamic responses of the pipeline in ocean currents. The effects of gap-to-diameter ratio and those of the stability parameter on the amplitude and frequency responses of a pipeline are investigated experimentally with a novel hydro-elastic facility. A comparison is made between the present experimental results of the amplitude and frequency responses for the pipes with seabed boundary effects and those for wall-free cylinders given by Govardhan and Williamson （2000） and Anand （1985）. The comparison shows that the close proximity of a pipeline to seabed has much influence on the vortex-induced vibrations of the pipeline. Both the width of the lock-in ranges in terms of Vr and the dimensionless amplitude ratio Amax/D become larger with the decrease of the gap-to-diameter ratio e/D, Moreover, the vibration of the pipeline becomes easier to occur and its amplitude response becomes more intensive with the decrease of the stability parameter, while tire pipeline frequency responses are affected slightly by the stability parameter.

Numerical and Physical Investigation on Vortex-Induced Vibrations of Marine Risers

As a project supported by the National Natural Science Fotmdation of China, a model experiment on the vortex-induced vibration of practical risers transporting tluid in currents was conducted in the Physical Oceanography laboratory of ocean University of China in 2005. Because most of the offshore oil fields in China are in shallow water, the experiment was focused on the risers in shallow water. The similarity theory was used in the experiment to derive the experimental model from the practical model. Considering the internal flowing fluid and external marine environment, the dynamic response of the marine riser was measured. Corresponding numerical simulation was performed with the finite element method. Ccnaparisons were made between the results from the experiment and numerical simulation.

Numerical Prediction of Vortex-Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration （VIV） of top tensioned riser （Till）, the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti＇ s wake oscillator model. Then Galerkin＇ s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and file corresponding numerical programs are compiled which solve the coupled equations directly in the time domain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7 is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers. The effect of internal flow on the dynamic characteristics and dynmnic response of the riser is analyzed and several valuable conelusions are drawn.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.

Numerical Study on the Effect of Current Profiles on Vortex-Induced Vibrations in a Top-Tension Riser

In this paper, numerical simulations of vortex-induced vibrations in a vertical top-tension riser with a length-to-diameter ratio of 500 using our in-house code viv-FOAM-SJTU are presented. The time-dependent hydrodynamic forces on two-dimensional strips are obtained by solving the Navier-Stokes equations, which are, in turn, integrated into a finite-element structural model to obtain the riser deflections. The riser is discretized into 80 elements with its two ends set as pinned and 20 strips are located equidistant along the risers. Flow and structure are coupled by hydrodynamic forces and structural displacements. In order to study the effects of the shear rate, of the current profiles on the vortex-induced vibrations in the riser, vibrations, with varying shear rates, in both the in-line and cross-flow directions, are simulated. In addition to the time domain analysis, spectral analysis was conducted in both the temporal and spatial domains. Multi-mode vibration characteristics were observed in the riser. The relationship between dominant vibration mode number and the shear rate of current profiles is discussed. In general, the overall vibrations in the riser pipe include contributions from several modes and each mode persists over a range of shear rates. Moreover, the results suggest that with a larger shear rate the position of the maximum in-line time-averaged displacement will move closer to the end where the largest velocity is located.

Simulation of Vortex-Induced Vibrations of A Cylinder Using ANSYS CFX

In this paper, vortex-induced vibrations of a cylinder are simulated by use of ANSYS CFX simulation code. The cylinder is treated as a rigid body and transverse displacements are obtained by use of a one degree of freedom spring damper system. 2-D as well as 3-D analysis is performed using air as the fluid. Reynolds number is varied from 40 to 16000 approx., covering the laminar and turbulent regimes of flow. The experimental results of （Khalak and Williamson, 1997） and other researchers are used for validation purposes. The results obtained are comparable.

Vortex-Induced Vibrations of A Long Flexible Cylinder in Linear and Exponential Shear Flows

A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration(VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to linear and exponential shear flows. The coupling equations of a structural vibration model and wake oscillator model were solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, structural wavenumber, standing wave behavior,travelling wave behavior, structural velocity, lift force coefficient and transferred energy from the fluid to the structure with different flow profiles were compared. The numerical results show that the VIV displacement is a combination of standing waves and travelling waves. For linear shear flow, standing waves and travelling waves dominate the VIV response within the low-velocity and high-velocity zones, respectively. The negative values of the transferred energy only occur within the low-velocity zone. However, for exponential shear flow, travelling waves dominate the VIV response and the negative energy occurs along the entire length of the cylinder.

Synergetic Analysis and Possible Control of Vortex-Induced Vibrations in a Fluid-Conveying Steel Catenary Riser

This work aimed to demonstrate possibilities for both active and passive control of the vortex-induced vibration and fatigue life of steel catenary risers via an analysis of the self-organization and evolution of the structural vibration based on synergetic theory. An analysis of the complex interrelated and synergistic relationship between the order parameter and the fast variable was performed, and the master equation of the nodal displacements was established as the order parameter for the evolution of the riser's structural vibration. Passive control methods include modifying the structure's elastic modulus, the internal fluid velocity, the top tension and the structural damping ratio, while an active control involves adjusting the external flow rate. Optimized parameters were obtained by analyzing the non-steady state solution of the master equation. The results show that the fatigue life greatly increases as the riser's elastic modulus decreases. In contrast, the fatigue life decreases with an increase of the internal fluid velocity. With an increase of the top tension, the vibration amplitudes and the number of modes may decrease, resulting in fewer bending stress cycles and a longer fatigue life. Furthermore, the structural damping ratio should be as large as possible. Finally, an active and passive control of the riser structure's response to vortex-induced vibration and its fatigue life can be achieved by carefully modifying the parameters mentioned above. The results may provide a theoretical framework for engineering practice concerning the design and control of steel catenary riser structures which are affected by vortex-induced vibration.

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.

Simplified Prediction Model for Vortex-Induced Vibrations of Top Tensioned Risers

According to the characteristics of deepwater top tensioned risers, a simplified model is presented to predict the multi-modal response of vortex-induced vibration （VIV） in non-uniform flow based on energy equilibrium theory and the exporimental data from VIV self-excited and forced oscillations of rigid cylinders. The response amplitude of each mode is determined by a balance between the energy fed into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainders. Compared with the previous prediction models, this method can take fully account of the intrinsic nature of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping effect, etc. Moreover, it is the first time to propose the accurate calculating procedure for VIV amplitude correction factor by solving energy equilibrium equation and a closed form solution is presented for the case of a riser of uniform mass and cross-section oscillating in a uniform flow. The predicted values show a reasonable agreement with VIV experiments of riser models in stepped and sheared currents.

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.

Vortex-Induced Vibrations of A Free-Spanning Pipe Based on A Nonlinear Hysteretic Soil Model at the Shoulders

The pipe-soil interactions at shoulders can significantly affect the vortex-induced vibrations (VIV) of free-spanning pipes in the subsea. In this paper, the seabed soil reacting force on the pipe is directly calculated with a nonlinear hysteretic soil model. For the VIV in the middle span, a classic van der Pol wake oscillator is adopted. Based on the Euler-Bernoulli beam theory, the vibration equations of the pipe are obtained which are different in the middle span and at the two end shoulders. The static configuration of the pipe is firstly calculated and then the VIV is simulated.The present model is validated with the comparisons of VIV experiment, pipe-soil interaction experiment and the simulation results of VIV of free-spanning pipes in which the seabed soil is modelled with spring-dashpots. With the present model, the influence of seabed soil on the VIV of a free-spanning pipe is analyzed. The parametric studies show that when the seabed soil has a larger suction area, the pipe vibrates with smaller bending stresses and is safer.While with the increase of the shear strength of the seabed soil, the bending stresses increase and the pipe faces more danger.

Mode Transitions in Vortex-induced Vibrations of a Flexible Pipe near Plane Boundary

A pipe model with a mass ratio（mass/displaced mass） of 4.30 was tested to investigate the vortex-induced vibrations of submarine pipeline spans near the seabed.The pipe model was designed as a bending stiffness-dominated beam.The gap ratios（gap to diameter ratio） at the pipe ends were 4.0,6.0,and 8.0.The flow velocity was systematically varied in the 0-16.71 nondimensional velocity range based on the first natural frequency.The mode transition between the first and the second mode as the flow velocity increases was investigated.At various transition flow velocities,the research indicates that the peak frequencies with respect to displacement are not identical along the pipe,nor the frequencies associated with the peak of the amplitude spectra for the first four modes as well.The mode transition is associated with a continuous change in the amplitude,but there＇s a jump in frequency,and a gradual process along the pipe length.