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 $m^*\,{=}\,1$.

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.

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.

Controlling parameter for wave types of long flexible riser undergoing vortex-induced vibration

Submerged floating tunnel (SFT) is a popular concept of crossing waterways. The failure of the cable may occur due to vortex-induced-vibration (VIV), and the stability of the cable is crucial to the safety of the entire tunnel. Investigation results in recent years show that the vortex-induced vibration of the flexible cables with large aspect ratio reveals some new phenomena, for example, the vortex-induced wave, multi-mode competition, wide band random vibration, which have brought new challenges to the study of vortex-induced vibration of long flexible cables. In this paper, the dimensionless parameter controlling the wave types of dynamic response of slender cables undergoing vortex-induced vibration is investigated by means of dimensional analysis and finite element numerical simulations. Our results indicate that there are three types of response for a slender cable, i.e. standing wave vibration, traveling wave vibration and intermediate state. Based on dimensional analysis the controlling parameter is found to be related to the system damping including fluid damping and structural damping, order number of the locked-in modes and the aspect ratio of cable. Furthermore through numerical simulations and parameter regression, the expression and the critical value of controlling parameter is presented. At last the physical meaning of the parameter is analyzed and discussed.

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]

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000

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

Two-degree-of-freedom vortex-induced vibration of circular cylinders with very low aspect ratio and small mass ratio

The investigation of vortex-induced vibration on very short cylinders with two degrees of freedom has drawn the attention of a large number of researchers. Some investigations on such a problem are carried out in order to have a better understanding of the physics involved in vortex-induced motions of floating bodies such as offshore platforms. In this paper, experiments were carried out in a recirculating water channel over the range of Reynolds number 6000

Multi-modes approach to modelling of vortex-induced vibration

Acknowledgements A.P. would like to acknowledge the support of the National Subsea Research Institute (NSRI) UK. E.P. and M.W. are grateful for partial support provided by the Italian Ministry of Education, University and Research (MIUR) by the PRIN funded program 2010/11 N.2010MBJK5B

Experimental Study Of Vortex-Induced Vibrations Of A Pipeline Near An Erodible Sandy Seabed

Based on similarity analyses, a series of experiments have been conducted with a newly established hydro-elastic facility to investigate the transverse vortex-induced vibrations (VIVs) of a submarine pipeline near an erodible sandy seabed under the influence of ocean currents. Typical characteristics of coupling processes between pipe vibration and soil scour in the currents have been summarized for Case 1: pipe is laid above seabed and Case 11: pipe is partially embedded in seabed on the basis of the experimental observations. Pipe vibration and the corresponding local scour are usually two coupled physical processes leading to an equilibrium state. The influence of initial gap-to-diameter ratio (e(0)/D) on the interaction between pipe vibration and local scour has been studied. Experimental results show that the critical values of V-r for the initiation of VIVs of the pipe near an erodible sand bed get bigger with decreasing initial gap-to-diameter ratio within the examined range of e(0)/D (-0.25 < e(0)/D < 0.75). The comparison of the pipe vibrations near an erodible soil with those near a rigid boundary and under wall-free conditions indicates that the vibration amplitudes of the pipe near an erodible sand bed are close to the curve fit under wall-free conditions; nevertheless, for the same stability parameter, the maximum amplitudes for the VIV coupled with local scour increase with the increase of initial gap-to-diameter ratio. (c) 2007 Elsevier Ltd. All rights reserved.

Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Two-dimensional Vortex-induced Vibrations of Submerged Floating Tunnel Tethers

A vortex-induced vibration (VIV) model is presented for predicting the nonlinear dynamic response of submerged floating tunnel (SFT) tethers which are subjected to wave, current and tunnel oscillatory displacements at their upper end in horizontal and vertical directions. A nonlinear fluid force formula is introduced in this model, and the effect of the nonlinearity of tether is investigated. First, the tunnel is stationary and the tether vibrates due to the vortices shedding. The calculated results show that the cross-flow amplitude of VIV decreases compared with the linear model. However the in-line amplitude of VIV increases. Next, the periodical oscillation of tunnel is considered. The oscillation caused by wave forces plays the roles of parametric exciter and forcing exciter to the VIV of tether. The time history of displacement of the tether mid-span is obtained by the proposed model. It is shown that the in-line amplitude increases obviously and the corresponding frequency is changed. The cross-flow amplitude exhibits a periodic behavior.

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 carried 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-critical flow regime; (2) with increasing gap-to-diameter ratio (e (0)/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/f (n) ) has a slight variation for the case of larger values of e (0)/D (e (0)/D > 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylinder between the larger gap-to-diameter ratios (e (0)/D > 0.66) and the smaller ones (e (0)/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of V (r) 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 V (r) and the frequency ratio (f/f (n) ) become larger.