A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

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.

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.

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.

Shear flow induced vibrations of long slender cylinders with a wake oscillator model

A time domain model is presented to study the vibrations of long slender cylinders placed in shear flow. Long slender cylinders such as risers and tension legs are widely used in the field of ocean engineering. They are subjected to vortex-induced vibrations（VIV） when placed within a transverse incident flow. A three dimensional model coupled with wake oscillators is formulated to describe the response of the slender cylinder in cross-flow and in-line directions. The wake oscillators are distributed along the cylinder and the vortex-shedding frequency is derived from the local current velocity. A non-linear fiuid force model is accounted for the coupled effect between cross-flow and in-line vibrations. The comparisons with the published experimental data show that the dynamic features of VIV of long slender cylinder placed in shear flow can be obtained by the proposed model,such as the spanwise average displacement,vibration frequency,dominant mode and the combination of standing and traveling waves. The simulation in a uniform flow is also conducted and the result is compared with the case of nonuniform flow. It is concluded that the flow shear characteristic has significantly changed the cylinder vibration behavior.

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.

Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.

Theoretical and Experimental Investigation of Flexural Vibration Transfer Properties of High-Pressure Periodic Pipe

According to the theory of phononic crystals, the hydraulic pipeline is designed to be a periodic structure composed of steel pipes and hoses to suppress the vibration of the hydraulic system with band gaps. We present theoretical and experimental investigations into the flexural vibration transfer properties of a high-pressure periodic pipe with the force on the inner pipe wall by oii pressure taken into consideration. The results show that the vibration attenuation of periodic pipe decreases along with the elevation of working pressure for the hydraulic system, and the band gaps in low frequency ranges move towards high frequency ranges. The periodic pipe has good vibration attenuation performance in the frequency range below 1000 Hz and the vibration of the hydraulic system is effectively suppressed. A11 the results are validated by experiment. The experimental results show a good agreement with the numerical calculations, thus the flexural vibration transfer properties of the high- pressure periodic pipe can be precisely calculated by taking the fluid structure interaction between the pipe and oil into consideration. This study provides an effective way for the vibration control of the hydraulic system.

Prediction of Streamwise Flow-Induced Vibration of A Circular Cylinder in the First Instability Range

The streamwise flow-induced vibration of a circular cylinder with symmetric vortex shedding in the first instability range is investigated, and a wake oscillator model for the dynamic response prediction is proposed. An approach is applied to calibrate the empirical parameters in the present model; the numerical and experimental results are compared to validate the proposed model. It can be found that the present prediction model is accurate and sufficiently simple to be easily applied in practice.

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.

Behavior of Vortex-Induced Vibration of A Circular Cylinder Near A Deformable Wall with Two Degrees of Freedom in Steady Flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder＇s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.

Safety estimation of high-pressure hydraulic cylinder using FSI method

Hydraulic cylinder is a primary component of the hydraulic valve systems.The numerical study of hydraulic cylinder to evaluate the stress analysis,the life assessment and the performance of operation characteristics in hydraulic cylinder were described.The calculation of safety factor,fatigue life,piston chamber pressure,rod chamber pressure and the change of velocity of piston with flow time after the beginning of hydraulic cylinder were incorporated.Numerical analysis was performed using the commercial CFD code,ANSYS with unsteady,dynamic mesh model,two-way FSI(fluid-structure interaction)method and k-εturbulent model.The internal pressure in hydraulic cylinder through stress analysis show higher than those of the yield strength.

A Numerical Investigation of Vortex-Induced Vibration Response and Fatigue Damage for Flexible Cylinders Under Combined Uniform and Oscillatory Flow

Vortex-induced vibration(VIV)for flexible cylinders under combined uniform and oscillatory flow is a challenging and practical issue in ocean engineering.In this paper,a time domain numerical model is adopted to investigate the characteristics of cross-flow VIV response and fatigue damage under different combined flow cases.Firstly,the adopted VIV model and fatigue analysis procedure are validated well against the published experimental results of a4-m cylinder model under pure oscillatory flows.Then,forty-five combined flow cases of the same cylinder model are designed to reveal the VIV response characteristics with different non-dimensional oscillation period T^*and combined ratio r.The combined flow cases are classified into three categories to investigate the effect of r on cylinder’s dynamic response,and the effect of T*is described under long and short period cases.Finally,fatigue analysis is carried out to investigate how the structural fatigue damage varies with the variations of r and T^*.The captured characteristics of structural response and fatigue damage are explained through the VIV mechanism analysis.

Passive Control of Flow-Induced Vibration(FIV)by Helical Strakes for Two Staggered Flexible Cylinders

Helical strake is a widely-used device for passive flow-induced vibration(FIV)control of cylindrical structures.It is omnidirectional and can effectively reduce FIV response amplitude.Studies on the passive FIV control for cylindrical structures are mainly concerned with a single isolated cylinder,while the influence of wake interference between multiple cylinders on FIV suppression devices is less considered up to now.In engineering applications,multiple flexible cylinders with large aspect ratios can be subjected to complex flow forces,and the effects of wake interference are obvious.The FIV suppression effect of helical strake of a common configuration(17.5D pitch and 0.25D height,where D is the cylinder diameter)in two staggered cylinders system is still unknown.This paper systematically studied the FIV response of multiple cylinders system fitted with the helical strakes by model tests.The relative spatial position of the two cylinders is fixed at S=3.0D and T=8.0D,which ensures the cylindrical structures in the flow interference region.The experimental results show that the helical strakes effectively reduce the FIV response on staggered upstream cylinder,and the suppression efficiency is barely affected by the smooth or straked downstream cylinder.The corresponding FIV suppression efficiency on the downstream cylinder is remarkably reduced by the influence of the upstream wake flow.The wake-induced vibration(WIV)phenomenon is not observed on the staggered downstream cylinder,which normally occurs on the downstream straked cylinder in a tandem arrangement.

Flow-Induced Vibration Fatigue Damage of A Pair of Flexible Cylinders in A Staggered Array

Flow-induced vibration(FIV)of a group of long,flexible cylinders involves a complex interaction between fluid and structures.Although a substantial number of studies have been devoted to assessing FIV response behaviours,fatigue damage features of staggered flexible cylinders are not fully understood.Moreover,the wake-induced flutter constitutes an intricate hydrodynamic behaviour that frequently occurs when one cylinder is in the vicinity of another one.Unfortunately,existing studies on the fatigue damage caused by wake-induced flutter are incapable of achieving better results.This paper,therefore,estimates the FIV fatigue damage of two staggered flexible cylinders with an aspect ratio of 350 and a mass ratio of 1.90 based on normal S−N curves according to Det Norske Veritas(DNV)regulations.Twelve staggered cases(cross-flow spacing ratios of 2.0,3.0,4.0,and 6.0 and in-line spacing ratios of 4.0,6.0,and 8.0)are discussed for comparison,and fatigue damage caused by wake-induced flutter is thoroughly considered.Fatigue damage results indicate that the variation of the cross-flow(CF)spacing ratio has a greater influence than that of the in-line(IL)spacing ratio on the CF fatigue damage of the upstream cylinder.Lower IL fatigue damages of the upstream cylinder are observed when reduced velocity V_(r)≥15.03 due to the wake flow patterns with different IL spacing ratios.Moreover,wake interference,especially wake-induced flutter,predominates the fatigue damage characteristics of the downstream cylinder.When V_(r)=8.77−11.27,wake-induced flutter enhances the IL fatigue damage of the downstream cylinder and slightly affects that of the upstream body.Furthermore,wake-induced flutter causes considerable IL fatigue damage disparity between the two staggered cylinders by suppressing the IL fatigue damage of the upstream cylinder when V_(r)≥20.04.

Flow-Induced Vibration of Four Cantilever Cylinders Arranged in A Square Configuration

Flow-induced vibration(FIV)of four separately mounted cantilever cylinders are experimentally investigated in a water flume.The four cylinders with top ends screwed vertically into a turntable platform are subjected to uniform flows with Reynolds number ranging from 3840 to 16520.A non-intrusive measurement with high-speed cameras is employed to simultaneously capture the time-varying in-line and cross-flow vibrations in the reduced velocity range of 3.0-12.9.Experimental results highlight the continuous adjustment of flow regime caused by the spatial-temporal alteration of cylinders.Consequently,the space-time varying flow interference contributes to the occurrence of multiple response frequencies.The transition from a dominant frequency to a broad-band response illustrates the enhancement of wake interference.The combination of wake flow interactions results in the irregular oscillation trajectories and the appearance of a response trough with the associated switching in vortex shedding mode.The dual-resonance phenomenon is observed in the four cylinders due to the complicated wake-structure interaction.The greatest mechanical energy possessed by the four cylinders in an in-line square arrangement is mainly resulted from the downstream cylinders,signifying the positive role of wake excitation in extracting hydrokinetic energy from ambient flow.

Flow-Induced Stream-Wise Vibration of Circular Cylinders

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

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.

An improved HSFR method for natural vibration analysis of an immersed cylinder pile with a tip mass

Immersed cylinder piles are usually modelled as immersed carrying a tip mass and rotary moment of inertia. In this paper, an immersed cylinder pile along transversal modes of vibration are of water and structural damping are included in the formulation. cantilever cylinder columns the equations of motion of developed. Compressibility Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.