Random vortex induced vibration response of suspended flexible cable to fluctuating wind

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled equations.The first equation is a partial differential equation governing the cable vibration.The second equation is a wake oscillator that models the lift coefficient acting on the cable.The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic one.In the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration.In the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind.Using the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration system.Depending on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration.By applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted.Then,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations.Some numerical simulation results confirm the obtained analytical results.It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration.Thus,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

Dynamic Properties of Steel Catenary Riser near Touchdown Point Under Coplanar Vessel Heave and Vortex Induced Vibration

The present study establishes a simple numerical model for the coupled response of a steel catenary riser(SCR) subjected to coplanar vessel motion and vortex-induced vibration(VIV). Owing to the large deflection of the SCR, the geometric nonlinearity is considered in this model. The hydrodynamic force comprises the excitation force and hydrodynamic damping, where the excitation force that only exists when the non-dimensional frequency is located in the lock-in range, is associated with the VIV. The hydrodynamic force model is validated based on the published VIV test data.As for the seabed resistance at the touchdown zone(TDZ), integrated with an initial seabed trench, the hysteretic feature is modeled. Based on the model, the study emphasizes on the coupled response characteristics near the touchdown point(TDP) induced by coplanar vessel heave and VIV, and analyzes the sensitivity of the coupled response to the heaving amplitude and frequency. It is found that with the increase of the heave amplitude and frequency, the VIV can be obviously mitigated, but the heave-related response in the coupled analysis seems to be close to that in the heave-only simulation. Finally, the fatigue damage near TDP is parametrically investigated based on the separate analysis and the coupled analysis. The results demonstrate that the coupled effect plays a significant role in the fatigue assessment near TDP. Besides, the proportion of the coupled effect accounting for the total fatigue damage decreases with the increasing seabed stiffness, while increases with the increasing seabed trench depth.

INVESTIGATION OF VORTEX SHEDDING INDUCED HYDRODYNAMIC VIBRATION IN VORTEX STREET FLOWMETER

Vortex street flowmeter has been used in steady flow measurement for about three decades The benefits of this type of flowmeter include high accuracy,good linearty,wide measuring range,and excellent reliability However,in unsteady flow measurement,the pressure disturbance as well as the noise from the system or surrounding can reduce the signal to noise ratio of the flowmeter seriously Aimed to use vortex street flowmeters in unsteady flow measurement,the characteristics of the vortex shedding induced hydrodynamic vibration around the prism bluff body in a vortex street flowmeter are investigated numerically and by expriments The results show that the hydrodynamic vibrations with 180° phase shift occur at the axisymmetric points of the channel around the bluff body The most intense vibration occurs at the points on the lateral faces close to the base of the prism The results provide therefore a useful reference for developing an anti interference vortex flowmeter using the different ial sensing technique.

Vortex-induced Vibration of Elastically Connected Multiple Circular Cylinders in a Side-by-side Arrangement in Steady Flow

Vortex-induced vibration(VIV)of multiple circular cylinders elastically connected together in a side-by-side arrangement subject to steady flow is investigated numerically at a low Reynolds number of 150 and a mass ratio of 2.Simulations are conducted for two-,five-and ten-cylinder systems over a wide range of reduced velocities.The aim of the study is to identify the high-amplitude response range of the reduced velocity for the multiple degree of freedom vibration system and identify the difference between the responses of the single-and multiple-degree-of-freedom vibrations.Unlike the single cylinder case,distinct lock-in between the response frequency and any of the structural natural frequencies in a wide range of reduced velocity is not observed in the multiple-cylinder cases.Instead,the response frequency increases continuously with increasing reduced velocity.High response amplitudes are found when the response frequency is between the first and the highest modal frequencies.In a multiple-cylinder system,the single-mode response,where the vibration is dominated by one mode,can be only found in low reduced velocity range.In the single-mode branch,the dominance of a single mode shape in the response can be clearly identified except at the boundary reduced velocity between two modes.The maximum response amplitude occurs in the multiple-mode response and interaction between the vortices in the wake of the cylinders is strong when the response amplitudes are high.

A NEW WAKE OSCILLATOR MODEL FOR PREDICTING VORTEX INDUCED VIBRATION OF A CIRCULAR CYLINDER

This article proposes a new wake oscillator model for vortex induced vibrations of an elastically supported rigid circular cylinder in a uniform current. The near wake dynamics related with the fluctuating nature of vortex shedding is modeled based on the classical van der Pol equation, combined with the equation for the oscillatory motion of the body. An appropriate approach is developed to estimate the empirical parameters in the wake oscillator model. The present predicted results are compared to the experimental data and previous wake oscillator model results. Good agreement with experimental results is found.

Calculation of Maximum Allowable Free Span Length and Safety Assessment of the DF1-1 Submarine Pipeline

The DFI-1 submarine pipeline was investigated using a dual-frequency side-scan sonar and a swath sounder system. More than a hundred scour pits under the pipeline were found, most of which have caused the span of the pipeline to increase and threatened its safety. The maximum allowable free span length （MAFSL） of the pipeline was determined through the limitations re- garding maximum allowable stress under static or quasi-static loads and the onset of Vortex Induced Vibrations （VIV） under different hydrodynamic actions. The results show that the MAFSL under static conditions is 56m. However, the MAFSLs are 30m and 20m under ordinary weather conditions and hurricane-induced currents for the 100-year return period, respectively, to avoid VIV as cal- culated by using the highest safety class factor. It is suggested that spanning pipelines longer than 20 m should be supported. Addi- tionally, eight successive spans which may also threaten the pipeline were proposed. The most hazardous scour pits are along the pipeline section from KP42 to KP51.

VORTEX INDUCED VIBRATIONS OF FINNED CYLINDERS

This article presents the results of a numerical simulation on the vortex induced vibration of various fumed cylinders at low Reynolds number. The non-dimensional, incompressible Navier-Stokes equations and continuity equation were adopted to simulate the fluid around the cylinder. The cylinder （with or without fins） in fluid flow was approximated as a mass-spring system. The fluid-body interaction of the cylinder with fins and uniform flow was numerically simulated by applying the displacement and stress iterative computation on the fluid-body interfaces. Both vortex structures and response amplitudes of cylinders with various arrangements of fins were analyzed and discussed. The remarkable decrease of response amplitude for the additions of Triangle60 fins and Quadrangle45 fins was found to be comparable with that of bare cylinder. However, the additions of Triangle00 fins and Quadrangle00 fins enhance the response amplitude greatly. Despite the assumption of two-dimensional laminar flow, the present study can give a good insight into the phenomena of cylinders with various arrangements of fins.

Reynolds and Mass-Damping Effect on Prediction of the Peak Amplitude of A Freely Vibrating Cylinder

The Reynolds effect and mass-damping effect on the peak amplitude of a freely vibrating cylinder is studied by using forced oscillating data from Gopalkrishnan＇ s research in 1993, in which all experimental cases were carried out at a fixed Reynolds and the tested cylinder was recognized as a body that had no mass and damping. However, the Reynolds and roass-damping are the very important parameters for the peak amplitude of a freely vibrating cylinder. In the present study, a function F is introduced to connect the forced oscillation and free vibration. Firstly the peak amplitude AG^＊ can be obtained from the function F using forced oscillation data of Gopalkrishnan＇ s experimental at Re = 10^4, and then the Reynolds effect is taken into account in the function f（Re）, while the mass-damping effect is considered in the function K（ α ）, where a is the mass-damping ratio. So the peak amplitude of a freely vibrating cylinder can be predicted by the expression： A ^＊ = K（ α ）f（ Re ）AG^＊ . It is found that the peak transverse amplitudes predicted by the above equation agree very well with many recent experimental data under both high and low Reynolds conditions while roass-damping varies. Furthermore, it is seen that the Reynolds number does have a great effect on the peak amplitude of a freely vibrating cylinder. The present idea in this paper can be applied as an update in the empirical models that also use forced oscillation data to predict the vortex induced vibration （VIV） response of a long riser in the frequency domain.

Kinetic energy based model assessment and sensitivity analysis of vortex induced vibration of segmental bridge decks

In this paper, semi 3D models for segmental Bridge decks are created in ABAQUS CFD program with the support of MATLAB codes to simulate and analyze vortex shedding generated due to wind excitation through considering the stationary position of the deck. Three parameters （wind speed, deck streamlined length and dynamic viscosity of the air） are dedicated to study their effects on the kinetic energy of the system in addition to the shapes and patterns of the vortices. Two benchmarks from the literature Von Karman and Dyrbye and Hansen are considered to validate the vortex shedding aspects for the CFD models. Good agreement between the results of the benchmarks and the semi 3D models has been detected. Latin hypereube experimental method is dedicated to generate the surrogate models for the kinetic energy of the system and the lift forces. Variance based sensitivity analysis is utilized to calculate the main sensitivity indices and the interaction orders for all the three parameters. The kinetic energy approach performed very well in revealing the rational effects and the roles of each parameter in the generation of vortex shedding and predicting vortex induced vibration of the deck.

The Coupling VIV Analysis of SCRs with Rigid Swing

With the development of deepwater oil and gas exploration, Steel Catenary Risers(SCRs) become preferred risers for resource production, import and export. Vortex induced vibration(VIV) is the key problem encountered in the design of SCRs. In this study, a new model, the rigid swing model, is proposed based on the consideration of large curvature of SCRs. The sag bend of SCRs is assumed as a rigid swing system around the axis from the hanging point to the touch down point(TDP) in the model. The torque, produced by the lift force and the swing vector, provides the driving torque for the swing system, and the weight of SCRs provides the restoring torque. The simulated response of rigid swing is coupled with bending vibration, and then the coupling VIV model of SCRs is studied in consideration of bending vibration and rigid motion. The calculated results indicate that the rigid swing has a magnitude equal to that of bending vibration, and the rigid motion affects the dynamic response of SCRs and can not be neglected in the VIV analysis.

An experiment study of vortex induced vibration of a steel catenary riser under steady current

The vortex induced vibration(VIV)of marine risers has been investigated by many researchers in experimental studies of a straight flexible riser model as well as a rigid cylinder to reveal the dynamic response characteristic and the mechanics behind it.However,due to the limitation of experimental apparatus,very few studies are about the VIV of a steel catenary riser(SCR)which is with a complex geometry.To investigate the VTV features and to further develop the corresponding numerical predictions of a SCR under steady current,a large-scale model test of a SCR was towed in an ocean basin at various speeds.Fiber Bragg grating strain sensors are instrumented on the riser model to measure both in-plane and out-of-plane responses.The characteristics of oscillating amplitude and dominating frequency response,the phenomenon of mode competition and travelling wave and the fatigue damage of the steel catenary riser in inline and cross-flow direction under steady current are analyzed.

Optimization Design of Fairings for VIV Suppression Based on Data-Driven Models and Genetic Algorithm

Vortex induced vibration(VIV)is a challenge in ocean engineering.Several devices including fairings have been designed to suppress VIV.However,how to optimize the design of suppression devices is still a problem to be solved.In this paper,an optimization design methodology is presented based on data-driven models and genetic algorithm(GA).Data-driven models are introduced to substitute complex physics-based equations.GA is used to rapidly search for the optimal suppression device from all possible solutions.Taking fairings as example,VIV response database for different fairings is established based on parameterized models in which model sections of fairings are controlled by several control points and Bezier curves.Then a data-driven model,which can predict the VIV response of fairings with different sections accurately and efficiently,is trained through BP neural network.Finally,a comprehensive optimization method and process is proposed based on GA and the data-driven model.The proposed method is demonstrated by its application to a case.It turns out that the proposed method can perform the optimization design of fairings effectively.VIV can be reduced obviously through the optimization design.

Numerical Study on Vortex Induced Vibration of a Flexible Plate Behind Square Cylinder with Various Flow Velocities

The vortex induced vibration(VIV) of a flexible plate behind the square head with various flow velocities is simulated. The closely coupling approach is used to model this fluid-structure interaction problem.The fluid governed by the incompressible Navier-Stokes equations is solved in arbitrary Lagrangian-Eulerian(ALE)frame by the finite volume method. The structure described by the equations of the elastodynamics in Lagrangian representation is discretized by the finite element approach. The numerical results show that the resonance occurs when the frequency of vortex shedding from square head coincides with the natural frequency of plate. And the amplitude of both the structure motion and the fluid load keeps increasing with the time. Furthermore, it is also found that in particular range of flow velocity the vibration of the plate would reach a periodical state. The amplitude of plate oscillating increases with the growth of velocity, while the frequency is locked.

Subsea rigid jumper design and VIV fatigue evaluation

The purpose of this paper is to present a design procedure for subsea rigid jumper system including strength and fatigue analysis. Special attention gives to a methodology based on DNV-RP-F105 to evaluate jumper fatigue damage caused by vortex induced vibration (VIV). Jumper strength analysis is to determine the jumper con-figuration which can accommodate various load conditions and all possible span lengths driven by installation tole-rances of connected subsea structures. Fatigue analysis includes two parts:thermal fatigue and VIV fatigue. This paper presents the procedure of VIV fatigue damage calculation. An example is given to illustrate above methodologies.

Discharge and flow characterizations of the double-side sliding discharge plasma actuator

We investigate the discharge and flow characterizations of a double-side siding discharge plasma actuator driven by different polarities of direct current(DC)voltage.The discharge tests show that sliding discharge and extended discharge are filamentary discharge.The irregular current pulse of sliding discharge fluctuates obviously in the first half cycle,ultimately expands the discharge channel.The instantaneous power and average power consumptions of sliding discharge are larger than those of the extended discharge and dielectric barrier discharge(DBD).The flow characteristics measured by a high-frequency particle-image-velocimetry system together with high-speed schlieren technology show that the opposite jet at the bias DC electrode is induced by sliding discharge,which causes a bulge structure in the discharge channel.The bias DC electrode can deflect the direction of the induced jet,then modifying the properties of the boundary layer.Extended discharge can accelerate the velocity of the starting vortex,improving the horizontal velocity profile by 203%.The momentum growth caused by extended discharge has the largest peak value and the fastest growth rate,compared with sliding discharge and DBD.However,the momentum growth of sliding discharge lasts longer in the whole pulsed cycle,indicating that sliding discharge can also inject more momentum.

Numerical study of free end effect of cylinder with low aspect ratios on vortex induced motion

In this paper,numerical simulation is conducted via our in-house solver,vim-FOAM-SJTU,developed on open-source software,OpenFOAM.Flow around static rigid cylinders and elastically mounted rigid cylinder constrained to free stream with free end are numerically investigated.Some significant conclusions are made by analyzing the different results between cases with and without free end.The turbulence model is implemented with a shear stress transport-based(SST-based)improved delayed detached eddy simulation(IDDES)approach in the vim-FOAM-SJTU.Firstly,The paper starts with the application of the vim-FOAM-SJTU solver to flow past fixed cylinder with free end at Reynolds number 43000.The numerical results are compared with experimental data.Comparison are satisfactory which implies the validity and accuracy of the current computational fluid dynamics(CFD)solver.The flow visualization in the vicinity of free-end is discussed.Subsequently,the solver is utilized to simulate the free end effect associated with the VIM of a cylinder submerged in current.The motion responses under different inflow velocities are studied.The relationship between transverse motion frequency,in-line motion frequency is discussed.Lastly,the effect of the free end on the vortex of the wake field is analyzed by comparing the 3-D vorticity diagrams of the free end cylinder.The responses of circular cylinder with or without free end are compared.

A review on flow-induced vibration of offshore circular cylinders

As a fundamental fluid-structure interaction(FSI)phenomenon,vortex-induced vibrations(VIVs)of circular cylinders have been the center of the FSI research in the past several decades.Apart from its scientific significance in rich physics,VIVs are paid great attentions by offshore engineers,as they are encountered in many ocean engineering applications.Recently,with the development of research and application,wake-induced vibration(WIV)for multiple cylinders and galloping for VIV suppression attachments are attracting a growing research interest.All these phenomena are connected with the flow-induced vibration(FIV).In this paper,we review and give some discussions on the FIV of offshore circular cylinders,including the research progress on the basic VIV mechanism of an isolated rigid or flexible cylinder,interference of multiple cylinders concerning WIV of multiple cylinders,practical VIV suppression and unwanted galloping for cylinder of attachments.Finally,we draw concluding remarks,give some comments and propose future research prospects,especially on the major challenges as well as potentials in the offline/online modelling and prediction of real-scale offshore structures with high-fidelity CFD methods,new experimental facilities and applications of artificial intelligence tools.

Nonlinear perturbation developments in flow around a vibrating cylinder

We investigate the flow around a circular cylinder vibrating with a prescribed magnitude and frequency at Reynolds number 230.The Navier-stokes equations and the adjoint equations are solved to search for the 3-D nonlinear optimal initial perturbation,which is amplified by the attached shear via the Orr mechanism and then activates wake instabilities.The energy growth and the spanwise distributions of the nonlinear optimal perturbation vary significantly with the initial phase to introduce the perturbation.As the initial perturbation energy increases,linear amplification,nonlinear saturation and nonlinear growth are sequently observed.The last one is owing to the generation of a spanwise homogeneous mode,which modifies the pressure distributions on the cylinder surface and induces an extra lift force.Interestingly,at all the initial phases,this force is opposite to the acceleration of the cylinder,illustrating the potential to reduce the magnitude of vibration.