Experimental Study on Flow Induced Vibration of a Cylinder with Two Degrees of Freedom Near a Rigid Wall

The flow-induced vibration of a cylinder with two degrees of freedom near a rigid wall under the action of steady flow is investigated experimentally. The vibration amplitude and frequency of the cylinder and the vortex shedding frequency at the wake flow region of the cylinder are measured. The influence of gap-to-diameter ratio upon the amplitude response is analyzed. The experimental results indicate that when the reduced velocity (Vr) is in the range of 1.2 < Vr < 2.6, only streamwise vibration with small amplitude occurs, whose frequency is quite close to its natural frequency in the still water. When the reduced velocity Vr > 3.4, both the streamwise and transverse vibrations of the cylinder occur. In this range, the amplitudes of transverse vibration are much larger than those of streamwise vibrations, and the amplitudes of the streamwise vibration also get larger than those at the range of 1.2 < Vr < 2.6. At the range of Vr > 3.4, the frequency of streamwise vibration undergoes a jump at certain values of Vr, at which the streamwise vibrating frequency is twice as much as the transverse one. However, when the streamwise vibration does not experience a jump, its frequency is the same as that of the transverse vibration. The maximum values of second streamwise and transverse vibration amplitudes increase with increasing gap-to-diameter ratios.

Computational simulation of the flow-induced vibration of a circular cylinder subjected to wake interference

In this work, we considered the flow around two circular cylinders of equal diameter placed in tandem with respect to the incident uniform flow. The upstream cylinder was fixed and the downstream cylinder was completely free to move in the cross-stream direction, with no spring or damper attached to it. The centre-to-centre distance between the cylinders was four diameters, and the Reynolds number was varied from 100 to 645. We performed two- and three-dimensional simulations of this flow using a Spectral/hp element method to discretise the flow equations, coupled to a simple Newmark integration routine that solves the equation of the dynamics of the cylinder. The differences of the behaviours observed in the two- and three-dimensional simulations are highlighted and the data is analysed under the light of previously published experimental results obtained for higher Reynolds numbers.

Flow-Induced Vibrations Of A Cylinder With Two Degrees Of Freedom Near Rigid Plane Boundary

Based on similarity analyses, the flow-induced vibrations of a near-wall cylinder with 2 degrees of freedom are investigated experimentally by employing a hydroelastic apparatus in conjunction with a flume. The cylinder's vibration amplitude, vibration frequency and vortex shedding frequency were measured and analyzed. The effects of gap-to-diameter ratio (e,ID) upon the vibration responses are further investigated. The experimental results indicate that, when the reduced velocity (Vr) is small (e.g. Vr = 1.2 similar to 2.6), only streamwise vibration occurs, and its frequency is quite close to its natural frequency in still water. When increasing Vr (e.g. Vr > 3.4), both streamwise and transverse vibrations of the near-wall cylinder may occur. In the examined range of gap-to-diameter ratio (0.42 < e(0)/D < 2.68), 2 vibration stages (in terms of Vr) of streamwise vibrations usually exist: First Streamwise Vibration (FSV) and Second Streamwise Vibration (SSV). In the SSV stage, the vortex shedding frequency may either undergo a jump to that of the streamwise vibration, or stay consistent with that of the transverse vibration. The amplitudes of transverse vibration are usually much larger than those of streamwise vibration for the same value of e(0)/D. The maximum amplitudes of both streamwise and transverse vibration get larger with the increase of e(0)/D (0.42 < e(0)/D < 2.68).

Multi-mode Vortex-induced Vibration of Slender Cable Experiencing Shear Flow

The dynamic characteristics of slender cable often present serried modes with low frequencies due to large structure flexibility resulted from high aspect ratio (ratio of length to diameter of cable), while the flow velocity distributes non-uniformly along the cable span actually in practical engineering. Therefore, the prediction of the vertex-induce vibration of slender cable suffered from multi-mode and high-mode motions becomes a challenging problem. In this paper a prediction approach based on modal energy is developed to deal with multi-mode lock-in. Then it is applied to the modified wake-oscillator model to predict the VIV displacement and stress responses of cable in non-uniform flow field. At last, illustrative examples are given of which the VIV response of flexible cable in nonlinear shear flow field is analyzed. The effects of flow velocity on VIV are explored. Our results show that both displacement and stress responses become larger as the flow velocity increasing; especially higher stress response companied with higher frequency vibration should be paid enough attention in practical design of SFT because of its remarkable influence on structure fatigue life.

Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.

Experiments on interaction between current-induced vibration and scour of submarine pipelines on sandy bottom

In order to understand the dynamic behavior of submarine pipelines exposed to current and the mechanism of the interaction between current-induced vibration and scour of pipelines on a sandy bottom, an experimental investigation is conducted with a small scale model A test model which can be tested in the flume is set up by taking into account the typical working conditions of the pipelines and by applying the similarity theory. The interactions between the shape of the scour hole and the behavior of the pipeline as well as the flow patterns of the current are detailed, and the interaction mechanism outlined. The effect of vibration of the pipeline on the development of dynamic scour at different stages is found out. The proposed experimental method and test results provide an effective means for design of marine pipelines against scouring.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

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.

PREDICTION OF VORTEX-INDUCED VIBRATION OF FLEXIBLE RISER USING AN IMPROVED WAKE-OSCILLATOR MODEL

Based on improving the wake-oscillator model, an analytical model for vortex-induced vibration (VIV) of flexible riser under non-uniform current is presented, in which the variation of added mass at lock-in and the nonlinear relationship between amplitude of response and reduced velocity are considered. By means of empirical formula combining iteration computation, the improved analytical model can be conveniently programmed into computer code with simpler and faster computation process than CFD so as to be suitable to application of practical engineering. This model is validated by comparing with experimental result and numerical simulation. Our results show that the improved model can predict VIV response and lock-in region more accurately. At last, illustrative examples are given in which the amplitude of response of flexible riser experiencing VIV under action of non-uniform current is calculated and effects of riser tension and flow distribution along span of riser are explored. It is demonstrated that with the variation of tension and flow distribution, lock-in region of mode behaves in different way, and thus the final response is a synthesis of response of locked modes.

Suppression of vortex-induced vibration using moving surface boundary-layer control

Experimental results of flow around a circular cylinder with moving surface boundary-layer control (MSBC) are presented. Two small rotating cylinders strategically located inject momentum in the boundary layer of the cylinder, which delays the separation of the boundary layer. As a consequence, the wake becomes narrower and the fluctuating transverse velocity is reduced, resulting in a recirculation free region that prevents the vortex formation. The control parameter is the ratio between the tangential velocity of the moving surface and the flow velocity (U-c/U). The main advantage of the MSBC is the possibility of combining the suppression of vortex-induced vibration (VIV) and drag reduction. The experimental tests are preformed at a circulating water channel facility and the circular cylinders are mounted on a low-damping air bearing base with one degree-of-freedom in the transverse direction of the channel flow. The mass ratio is 1.8. The Reynolds number ranges from 1600 to 7500, the reduced velocity varies up to 17, and the control parameter interval is U-c/U = 5-10. A significant decreasing in the maximum amplitude of oscillation for the cylinder with MSBC is observed. Drag measurements are obtained for statically mounted cylinders with and without MSBC. The use of the flow control results in a mean drag reduction at U-c/U = 5 of almost 60% compared to the plain cylinder. PIV velocity fields of the wake of static cylinders are measured at Re = 3000. The results show that the wake is highly organized and narrower compared to the one observed in cylinders without control. The calculation of the total variance of the fluctuating transverse velocity in the wake region allows the introduction of an active closed-loop control. The experimental results are in good agreement with the numerical simulation studies conducted by other researchers for cylinders with MSBC. (C) 2012 Elsevier Ltd. All rights reserved.

Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms. [DOI: 10.1115/1.4006755]

One and two degrees-of-freedom Vortex-Induced Vibration experiments with yawed cylinders

Vortex-Induced Vibration (VIV) experiments were carried out with yawed cylinders. The purpose was to investigate the validity of the Independence Principle (IP) for properly describing the flow characteristics and the dynamics of structures subjected to oblique flow. Five yaw angles in relation to the direction perpendicular to the free stream velocity were tested, namely View the MathML sourceθ=0°,10°,20°,30° and 45°. Both the upstream and downstream orientations were tested. The models were mounted on a leaf spring apparatus that allows experiments with one or two degrees of freedom. The Reynolds numbers based on the component normal to the cylinder axis fell in the interval 3×103

The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair

When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini ( J. Fluid Mech. , vol. 661, 2010, pp. 365–401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex–structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept of wake stiffness , a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to Re and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex–structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response

Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

One observed vibration mode for Tainter gate skinplates involves the bending of the skinplate about a horizontal nodal line. This vibration mode can be approximated as a streamwise rotational vibration about the horizontal nodal line. Such a streamwise rotational vibration of a Tainter gate skinplate must push away water from the portion of the skinplate rotating into the reservoir and draw water toward the gate over that portion of the skinplate receding from the reservoir. The induced pressure is termed the push-and-draw pressure. In the present paper, this push-and-draw pressure is analyzed using the potential theory developed for dissipative wave radiation problems. In the initial analysis, the usual circular-arc skinplate is replaced by a vertical, flat, rigid weir plate so that theoretical calculations can be undertaken. The theoretical push-and-draw pressure is used in the derivation of the non-dimensional equation of motion of the flow-induced rotational vibrations. Non-dimensionalization of the equation of motion permits the identification of the dimensionless equivalent added mass and the wave radiation damping coefficients. Free vibration tests of a vertical, flat, rigid weir plate model, both in air and in water, were performed to measure the equivalent added mass and the wave radiation damping coefficients. Experimental results compared favorably with the theoretical predictions, thus validating the theoretical analysis of the equivalent added mass and wave radiation damping coefficients as a prediction tool for flow-induced vibrations. Subsequently, the equation of motion of an inclined circular-arc skinplate was developed by incorporating a pressure correction coefficient, which permits empirical adaptation of the results from the hydrodynamic pressure analysis of the vertical, flat, rigid weir plate. Results from in-water free vibration tests on a 1/31-scale skinplate model of the Folsom Dam Tainter gate are used to demonstrate the utility of the equivalent added mass coefficient.

Dynamic matrix control on wind-induced vibration of spatial latticed structures [Chinese title = 空间网壳结构风振抑制的动态矩阵预测控制分析]

Ameliorated strategies were put forward to improve the model predictive control in reducing the wind induced vibration of spatial latticed structures. The dynamic matrix control (DMC) predictive method was used and the reference trajectory which is called the decaying functions was suggested for the analysis of spatial latticed structure (SLS) under wind loads. The wind-induced vibration control model of SLS with improved DMC model predictive control was illustrated, then the different feedback strategies were investigated and a typical SLS was taken as example to investigate the reduction of wind-induced vibration. In addition, the robustness and reliability of DMC strategy were discussed by varying the model configurations.