Vortex-induced Vibration Of Cylinder Research Articles

Applying PID control to 2-dof vortex induced vibration of a cylinder

Suppressing a cylinder's vortex-induced vibration (VIV) is an essential means to improve the fatigue life of risers. There is limited research on Proportional integrated derivative (PID) control in cylinder vortex-induced vibration, which has an industrial occupancy rate of over 90%. Therefore, this paper uses PID to study the cylinder's 2-DOF VIV. Firstly, the VIV model of PID control based on a wake oscillator is established and verified. Finally, the control effect of PID on VIV is studied, and some results are obtained. It is feasible to suppress the VIV of the cylinder based on the wake oscillator by PI or PID method. The control force time history curve shows the change of multi-frequency and multi amplitude period of the control force, and the cylindrical trajectory range after control is significantly reduced, which is 68.4%–97.1% lower in X direction and Y direction than that of no-control.

Effects of a detached splitter on the vortex-induced vibration of a 5:1 rectangular cylinder

The present paper examines the vortex-induced vibration (VIV) of a 5:1 rectangular cylinder with a detached splitter in its near wake. The tested gap ratio between the cylinder and the splitter (g/D, where g is the gap between the cylinder rear and the splitter and D is the depth of the rectangular cylinder) ranges from 0.5 to 2.0, with an increment of 0.5. To serve as a reference case, the rectangular cylinder without the splitter is also tested under the same conditions. The test Reynolds number ranges from 32 320 to 56 507. This study delves into the vibration response, pressure distributions, and power spectral densities (PSD) of the cylinder under varying gap ratios. Based on qualitative and quantitative analyses between the cylinder and the splitter using phase average techniques, smoke-wire visualization, and numerical simulation, the different vortex shedding modes according to different gap ratios were identified. Experimental and numerical results show that the detached splitter and its gap ratio play important roles in determining the cylinder VIV properties. For g/D = 0.5, the detached splitter has a sensible mitigation on the cylinder VIV. However, as the gap ratio increases, the VIV response initially recovers to the reference case at g/D = 1.0 and subsequently enlarges at g/D = 1.5 and 2.0. The pressure distribution results showed that the detached splitter demonstrates its effects primarily through fluctuations in the pressure field rather than the mean field. In addition, at g/D = 0.5, a sensibly decayed PSD is observed, while at g/D = 1.0–2.0, an intensified PSD is detected. The underlying mechanism of the detached splitter on the VIV of the 5:1 rectangular cylinder should be attributed to the von Kármán vortex street compared to the reference case.

Effect of a rotatable water-drop plate on vortex-induced vibration of cylinder

To suppress the Vortex-induced vibration (VIV) response, a cylinder with a rotatable water-drop plate is investigated. The influence of the side curves (concave, linear, convex) of the water-drop plate and angle α (α means the angle between the positive half axis of the X-axis and the straight line where the side of the water-drop plate is located, taking 15°, 30°, 45°, and 60°) on the vibration response are studied by adopting uRANS equations and Newmark-β method. It is shown that the water-drop plate has a certain suppression effect on the VIV of the cylinder in the initial and upper branches. A convex plate with a smaller angle is more effective in suppressing the vibrations of cylinders. When the angle decreases to 30°, the suppression effect of the convex plate on the cylinder no longer increases significantly even if the angle continues to be reduced. In the lower branch and desynchronization, the phenomenon of galloping is clearly observed and the amplitude of the cylinder increases continuously.

Vortex-induced vibration characteristics of three cylinders with isosceles-triangle arrangements at low Reynolds number

The geometric factors of multi-cylinders are one of the factors affecting the efficient energy capture of vortex-induced vibration aquatic clean energy. Based on the computational fluid dynamics numerical simulation method and overset mesh technology, an efficient dynamic model of VIV (vortex-induced vibration) of two-dimensional elastic-supported cylinders was established. The influence of different vertex angles on the VIV characteristics in the isosceles-triangle arrangement was investigated. The results show that the upstream cylinder is less affected by the vertex-angle, and the peak value moves to the left in the α-A*y curve of the downstream cylinders. As α increases, the upstream cylinder moves in an 8 shape and moves in the negative direction of the flow direction, while the downstream cylinders move in an O shape and gradually become narrow. The vortex shedding mode of downstream cylinders is mostly the P + S mode, and its amplitude is related to the position of the upstream cylinder's wake vortex effect. The lift and drag coefficients of the downstream cylinders are affected by α, while the dominant frequency of vibration is independent of the change in α and is greatly affected by Re. With the increase in Re, the positive correlation between the lift coefficient and transverse displacement gradually weakens.

Numerical study on vortex-induced vibration of four circular cylinders at low Reynolds number

Vortex-Induced Vibration (VIV) of multiple cylinders has received increasing attention in the ocean engineering field in recent years. In this paper, a two-dimensional numerical model for studying VIV of multiple cylinders is developed. Based on a fixed Cartesian grid with local mesh refinement adopted, the immersed boundary method is utilized to account for the existence of cylinders. Two-degree-of-freedom VIV of a single circular cylinder is simulated to validate the model, and then the model is utilized in the VIV of a four circular-cylinder group with square arrangement. The mass ratio is m* = 2.0, and the spacing ratio L/D is 5.0, where L is the central displacement of two adjacent cylinders and D is the diameter of the cylinders. Reynolds number ranging from 45 to 210 is considered, and the variation of which is achieved by changing the inflow velocity. The corresponding reduced velocity varies from 3 to 14. The influences of Reynolds number on the vibrating frequencies, the response amplitudes, the X–Y trajectories, the vorticity field distribution, and the hydrodynamic coefficients are analyzed in detail. A critical Reynolds number of 105 is observed, at which the X–Y trajectories and the vorticity field distribution change their patterns.

A wind tunnel investigation of the effects of end and laminar/turbulent inflow conditions on cylinder vortex-induced vibrations

The influence of end and inflow conditions on the vortex-induced vibrations of a cylinder is studied on the basis of wind tunnel experiments, combining measurements of the body displacement and flow velocity in its wake. The cylinder of length-to-diameter aspect ratio 5.5 has one end exposed to the current. It is elastically mounted in the cross-flow direction, with low damping. The structure to displaced fluid mass ratio is close to 1000. The behavior of the system is explored over a range of values of the reduced velocity, U⋆, defined as the inverse of the oscillator natural frequency, non-dimensionalized by the inflow velocity (U∞) and the cylinder diameter (D), typically between 4 and 8, at a Reynolds number of the order of 104, based on U∞ and D. Three end conditions are examined: two free-end conditions with either a flat or a hemispherical shape, and a condition where a fixed plate is placed close to the flat end. Three inflow states are considered: a laminar condition and two grid-generated turbulent conditions of different turbulence intensity levels (up to 10%) and comparable integral length scales, around 30% of D. Vibrations characterized by bell-shaped evolutions of their magnitude with U⋆ develop, under flow-body synchronization (lock-in), in all conditions, with peak amplitudes ranging from 4% to 12% of D. The free end causes a shift of the response bell-shaped curve towards higher U⋆ values. The shift may be such that there is no overlap between the vibration domains in the end-plate and free-end conditions. The passage from laminar to turbulent inflow conditions is found to attenuate this shift. A clear reduction of vibration amplitude is observed when the end plate is removed, and the amplitude is further reduced when the flat end is replaced by the hemispherical one. On the other hand, turbulent inflows induce a global enhancement of the vibration amplitudes, which may reach +45% relative to the laminar stream condition. The end/inflow conditions are also shown to impact the regularity of the structural responses.

An analytical study on vortex-induced vibrations of cylinders with variable cross-section in the range of low Reynolds numbers

In the current paper, vortex-induced oscillations of circular cylinders with variable have been investigated. Considering the von-Kármán nonlinear strain-displacement relations and using the displacement coupling model to simulate the system and fluid-structure interaction, the nonlinear differential equations governing the motion have been derived using Hamilton’s principle. To apply the effect of vortices on the system vibrations, the nonlinear Van der Pol oscillator equation has been used. Then, using the Galerkin method, differential equations with partial derivatives are discretized, and nonlinear differential relations are solved by the Runge-Kutta approach. Finally, the response of the system, the phase curves, and the changes in the maximum amplitude according to the fluid velocity are obtained for various parameters, and the results have been discussed. Regarding the obtained results, changes in the cross-section of the beam have a significant effect on the lock-in region and also the maximum deflection of the beam. The maximum dynamic deflection for θ = 2° occurs at the velocity u = 2 , which is equal to 0.927. Also, the lock-in phenomenon is created for the beam with θ = 2.5° and θ = 3° at the velocities u = 2.78 and u = 4.23 , respectively.

Applying LQR to control cross vortex-induced vibration of cylinders based on wake oscillators

Active control of a cylinder's vortex-induced vibration is a research hotspot, and proposing a theoretical model for real-time control of a cylinder's vortex-induced vibration is the foundation of engineering applications. Therefore, this article studies applying the LQR method to control the cross vortex-induced vibration of a single cylinder based on wake oscillators. Firstly, a theoretical control model of the LQR method and wake oscillator was established, and then the model's correctness and numerical solution were verified. Finally, numerical analysis was conducted to investigate the influence of different control parameters on the control of a cylinder's vortex-induced vibration. During the control process, there was no nonlinear bifurcation frequency doubling phenomenon caused by the wake oscillator. Controlling the displacement of a cylinder is more effective than controlling its speed, and the controlled displacement of the cylinder is close to a stationary state, with a lift force close to 2.0. The maximum displacement and lift suppression efficiency is 98.64% and 55.16%. In some cases, the maximum value of hydrodynamic energy at the original system is around 43.85 times that of control systems.

Numerical investigation on VIV of a circular cylinder with multiple small control rods

This study conducts a numerical simulation of the two-degree-of-freedom vortex-induced vibration (VIV) for a circular cylinder attached to multiple small control rods. It systematically investigates the effects of control rod number n, attack angle α, and gap ratio G/D on the vibration responses of the main cylinder. The control rod arrangements are classified into symmetric and asymmetric configurations based on the attack angle variation. The 5, 7, and 9 small control rods present similar impacts on the VIV's characteristics of the circular cylinder. The VIV of the main cylinder is significantly suppressed by the odd number of small control rods in two regions. The 1st excellent VIV suppression (EVS) region locates in the gap ratio of G/D=(0.2, 0.3) for all attack angles. The 2nd EVS region is within a wide range of gap ratios at the 2nd symmetric configuration. The nine control rods at G/D = 1.4–1.5 in the 2nd EVS region can completely suppress the circular cylinder VIV. Meanwhile, the flow structure of the cylinder group is fully symmetric, and vortex shedding cannot be formed behind any circular cylinders.

Data-driven prediction and study of vortex induced vibrations by leveraging hydrodynamic coefficient databases learned from sparse sensors

Semi-empirical models are currently the state-of-the-art industry tool for flexible cylinder vortex induced vibrations (VIV) fatigue prediction. Accurate prediction of the structural response relies entirely on the accuracy of the acquired hydrodynamic coefficient database. The construction of systematic hydrodynamic coefficient databases from rigid cylinder forced vibration experiments can be time-consuming for simple cases and intractable for multi-parametric cases. An alternative approach has been implemented in this work to improve the flexible cylinder VIV prediction by machine-learning optimal parametric hydrodynamic databases using physical experimental measurements. The methodology is applied to a straight riser in uniform flow and extended to non-straight riser configurations and non-uniform incoming flow profiles. Moreover, database inference is extended to using direct sparse sensor measurements along the structure. Specifically, a 19-dimensional parametric hydrodynamic coefficient database is obtained for: (i) straight riser in uniform flow (using sparse strain measurements), (ii) straight riser in sheared flow, and (iii) catenary riser in uniform flow with a 60 deg incidence angle between the catenary plane and the incoming flow stream. The predicted amplitude and frequency responses, using the extracted databases, are compared with observed experimental results.

Two-degrees-of-freedom vortex-induced vibration of cylinders covered with hard marine fouling

Marine fouling quickly covers the submerged surfaces of the man-made structures and affects the flow regime around them. Many important studies have already been conducted on the Vortex-Induced Vibration (VIV) of bluff bodies, but the two-Degree-of-Freedom (2-DoF) VIV of marine-fouled cylinders has received no previous attention. The current towing tank experimental study tries to fill this gap in the context of mechanical sciences. A Poisson Cluster Process (PCP) is used to model aggregated spatial distributions of artificial marine fouling on test cylinders. The Reynolds number ranges between 6.4 × 103 and 5.2 × 104. The results show that in the fouling presence, the super-upper branch disappears from the 2-DoF VIV response of the cylinders. The maximum oscillation amplitudes in the in-line and cross-flow DoFs are reduced up to 37% and 50%, respectively, as compared to those of the smooth cylinder. Marine fouling moderately reduces the maximum lift force coefficient, whereas remarkably decreases the maximum drag force coefficient, the “lock-in” range, the lower branch length, and the reduced velocity (U∗) marking the beginning of the lower branch. The highest mitigation occurs with the most sparsely marine-fouled cylinder examined (33% coverage). The aforementioned fouling effects generally reduce as the fouling coverage ratio increases.

An experimental investigation on the dual-resonance revealed in the VIV of flexible cantilevers with orthotropic bending stiffness

This article presents an experimental investigation on the dynamic behavior of orthotropically stiffened cantilevered flexible cylinders, mounted in vertical configuration, undergoing vortex-induced vibrations (VIV). The investigation was motivated by intriguing results published in 2001, regarding a flexible cylinder with orthotropic bending stiffness, presenting the first natural frequencies ratio parameter f1*=f1x/f1y=4.08 (x and y are the in-line and crosswise directions, respectively), in which a new high amplitude-frequency response branch was revealed in the range U*>12 (amplitudes measured at the free tip), then named “High Speed Mode Branch” (HSMB). The present investigation goes further, by studying the influence of the first natural frequency ratio parameter f1* on VIV. Four cantilevered flexible cylinders were tested, each one presenting a distinct nominal frequencies ratio, namely f1*=1:1, 2:1, 3:1 and 4:1. The experiments were carried out in a recirculating water-channel with the stream flow varied continuously, by slowly increasing the velocity, instead of doing it by steps. An innovative data analysis methodology was developed to deal with the resulting slowly nonstationary signals by combining the Galerkin's projection scheme with the Hilbert-Huang Transform technique. The influence of the first natural frequency ratio parameter is shown as determining the position and width of the reduced velocity range in which dual resonance occurs. Moreover, f1*>1.0 allows higher reduced velocities to be reached, therefore, enabling the appearance of higher modes of crosswise vibration. The HSMB appearance is now recognized as a result of the combination of the first crosswise mode response and the onset of amplitudes related to the second crosswise mode of vibration. The results here presented may serve as a new benchmark data for modeling and simulations involving VIV of flexible cylinders equipped with orthotropic bending stiffness.

Dual-frequency vortex-induced vibrations of long flexible stepped cylinders

Flexible structures within a non-uniform inflow may undergo complex vortex-induced vibrations (VIV) containing multiple frequencies and vibration modes. Therefore, the critical question arises on whether and how a flexible cylinder's structural response and fluid forces undergoing multi-frequency vibrations resemble or differ from mono-frequency vibrations. Therefore, we experimentally studied the problem of dual-frequency VIV of a stepped flexible cylinder, viz., a large-aspect ratio flexible cylinder consisting of two segments with different diameters and rigid cylinder forced vibration experiments. The results show that the maximum in-line (IL) and cross-flow (CF) displacements and the frequency ratio of the stepped cylinder separated by individual frequency resemble those of a uniform cylinder vibrating in the uniform flow at a single frequency. In addition, it is found that forced vibration results from rigid cylinders undergoing multi-frequency IL and CF motion can improve the prediction of the multi-frequency flexible cylinder VIV, provided the amplitudes and phases, as well as the true reduced velocity Vr for each of the dual frequencies match, especially when Vr∈[4,8].

Optimized parametric hydrodynamic databases provide accurate response predictions and describe the physics of vortex-induced vibrations

We address the problem of obtaining accurate predictions of the vortex-induced vibrations (VIV) of flexible structures placed in cross-flow by reconstructing fluid force databases in parametric form. The forces are expressed in terms of hydrodynamic coefficients, which depend on several variables and parameters, including the structural properties and geometry, frequency and amplitude of vibration, and the flow conditions, so that a comprehensive database obtained with systematic experiments would require an intractably large number of tests. Therefore, we develop a method for determining optimal parametric hydrodynamic databases directly from a variety of free- and forced-vibration experiments on both rigid and flexible cylinders, by minimizing the error between the predicted responses using a software driven by the force database, and the measured data. We first describe the process of selecting an appropriate parametrization of the fluid forces as function of reduced frequency and non-dimensional amplitude of vibration, informed by Gaussian-Process-Regression-guided automated experiments. Several examples are selected to demonstrate the method’s ability to acquire optimal hydrodynamic databases, including data sets highlighting the effect of Reynolds number and the addition of in-line motion to cross-flow rigid cylinder VIV. The proposed methodology is further demonstrated to be effective when used with the semi-empirical program VIVA for flexible cylinder VIV, yielding significant improvements in prediction accuracy compared to baseline results. It therefore serves as a potential solution for the development of a digital twin for marine risers, an in-situ, real-time riser response prediction and structural health monitoring system.

Deep learning based on PINN for solving 2 DOF vortex induced vibration of cylinder

Vortex-induced vibration (VIV) exists widely in natural and industrial fields. The main approaches for solving VIV problems are numerical simulations and experimental methods. However, experiment methods are difficult to obtain the whole flow field information and also high-cost while numerical simulation is extraordinary time-consuming and limited in low Reynolds number and simple geometric configuration. In addition, numerical simulations are difficult to handle the moving mesh technique. In this paper, physics informed neural network (PINN) is utilized to solve the VIV and wake-induced vibration (WIV) of cylinder with different reduced velocities. Compared to tradition data-driven neural network, the Reynolds Average Navier-Stokes (RANS) equation, by implanting an additional turbulent eddy viscosity, coupled with structure's dynamic motion equation are also embedded into the loss function. Training and validation data is obtained by computational fluid dynamic (CFD) technique. Three scenarios are proposed to validate the performance of PINN in solving VIV and WIV of cylinders. In the first place, the stiffness parameter and damping parameter are calculated via limited force data and displacement data; secondly, the turbulence flow field and lifting force/drag force are inferred by scattered velocity information; eventually, the displacement can be directly predicted only through lifting forces and drag forces based on LSTM. Results demonstrate that, compared with traditional neural network, PINN method is more effective in inferring and re-constructing the unknown parameters and flow field with different Reynolds numbers under VIV and WIV circumstances.

Effects of force and moment actuation in active two dimensional VIV control of an elastic circular cylinder in power-law fluid flow

The coupled in-line/crosswise (2-DOF) Vortex-Induced Vibration (VIV) control of a flexibly-supported impenetrable circular cylinder immersed in uniform 2D laminar cross-flow of incompressible non-Newtonian power-law fluids is numerically investigated. Two effective active closed-loop control strategies are separately applied and compared in a real-time collaborative simulation framework that interactively connects the Fluent CFD solver with Matlab/Simulink. Numerical simulations reveal the important effects of power-law rheology and controller configuration on the key cylinder response/aerodynamic parameters and flow structure for a wide range of power-law index parameters (0.4≤n≤1.8). In the absence of the control system, the boundary layer thickness, the attached wake size/strength, and the length/thickness of the associated “shear stretching layer” (vortex shedding frequency) are found to noticeably increase (decrease) with increasing the power law index parameter. As the value of power-law index is largely increased, there is a notable shift of the synchronization (lock-in) region into the higher Reynolds number range besides its marked contraction which can passively complement the cylinder VIV control problem in the highly viscous shear-thickening fluid. When the active control system becomes operative, the superior performance and efficiency of the moment-based controller in effective and rapid mitigation of cylinder VIV and weakening of the vortex intensities through a desynchronization type of action with minimum actuator power requirements is demonstrated.

Illuminating the complex role of the added mass during vortex induced vibration

The role of the added mass coefficient in vortex induced vibration (VIV) of the bluff body is complex and elusive. It is certain that decoding the relationship between the added mass and the vibration pattern will benefit the prediction and prevention of VIV. We present a study on VIV of a long flexible cylinder and forced vibration of a rigid cylinder, in a combination of experimental optical measurements and high-fidelity numerical simulation. We focus on uniform flow over a uniform cylinder at a fixed Reynolds number, Red = 900, but systematically varied the motion amplitude in the in-line (Axd) and cross-flow direction (Ayd), as well as the phase angle (θ) between the motions. We show that θ∈[π2,3π2] is associated with negative added mass coefficients in the cross-flow direction (Cmy < 0), and there is a strong correlation between the vortex shedding mode of “2P” or “P+S” and Cmy < 0.

Approach to damping effects of fairings on VIV of flexible cylinder with three-dimensional numerical simulations

Vortex-induced vibration (VIV), which will lead to the fatigue damage on coastal structures like flexible cylinders, has attracted considerable attention. The object of this study is to investigate the VIV phenomenon of flexible cylinder and the damping effects of fairings which could be used as vortex-suppressing devices, with three-dimensional (3D) fluid-structure interaction considered. In this paper, a 3D finite element (FE) model is established with the cylinder simulated by solid elements, the fluid field by the Arbitrary Lagrangian Eulerian (ALE) scheme, and the pipe surface by the moving boundary. Non-uniform mesh in different region and dynamic mesh in the area around the pipe are used to better simulate the pipe and the fluid field. The feasibility of the model is verified. The correlations between the vibration amplitude and the vortex shedding frequency are depicted, with the lock-in phenomenon captured. The displacement responses of the pipe are calculated with the damping effects considered, which is reflected not only in reducing the vibration amplitude of the pipe, but also in raising the flow rates for the lock-in region. This study will provide useful theoretical reference for vibration control of the VIV phenomenon of flexible cylinder.

A numerical study on the flow-induced vibrations of flexible cylinders attached with fixed short fairings

Fairings have been used to suppress the vortex-induced vibrations(VIV) of deep water cylinders in the offshore and marine engineering applications. When properly functioning, they can reduce both the cylinder oscillation amplitude in the cross-flow direction and the fluid drag force in the in-line direction. Plenty research reports can be found on the rigid cylinder VIV suppression performances of fairings while very few research work discuss their VIV suppression performances on flexible cylinders. In the present work, a self-developed high-resolution fluid–structure interaction code based on the computational fluid dynamics is used to simulate the flexible cylinder responses attached with differently covered fixed short fairings. The Reynolds number based on the incoming velocity and the bluff body diameter is 1.68×104. The short fairings are found not to induce strong galloping oscillations in the flexible cylinders while the galloping is prominent in the rigid cylinder cases at large reduced velocities. The different short fairing setups are found to influence the local fluid–structure energy transport distributions and the travelling wave directions in the flexible cylinder responses, which eventually influences the flexible cylinder oscillation amplitude distributions, response frequencies and mode orders.

Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number

Vortex-induced vibration (VIV) is a fluid structure interaction phenomena that can lead to the fatigue failure of high-rise structures. To study the basic principles and method of VIV suppression for a cylinder structure, a two-dimensional simulation model using a cylinder with two degrees of freedom in-line and cross-flow directions is presented herewith. A nonlinear energy sink is added to cylinder structures to assess its impact on vibration suppression. As a result, this study aims to investigate the VIV of cylinder under the action of the NES at low Reynolds numbers. The accuracy of the simulation model is verified by the comparison with the experimental results. Particularly, the VIV response is investigated with different mass ratio $$\beta$$ between the NES and cylinder (namely $$\beta$$ of 0.15, 0.2 and 0.3) at Re = 100 in air environment by analyzing the vibration response, phase diagram, time–frequency and vorticity contours of cylinder and NES oscillator. Three distinct function modes of NES for selected mass ratio $$\beta$$ are also observed. The results indicate that the NES can change between resonance capture states, from weak to strong, when the mass ratio $$\beta$$ increases to a defined value. In this case, the main vibration frequency of the cylinder varies over time, and the motion is in the chaotic state. The NES can also effectively reduce the vibration amplitude in both the in-flow and cross-flow directions.