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Flow over a cylinder is a fundamental fluid mechanics problem that involves a simple geometry, yet increasingly complex flow patterns as the Reynolds number is increased, most notably the development of a Karman vortex with a natural vortex shedding frequency when the Reynolds number exceeds a value of about 40. The goal of this ongoing study is to numerically investigate the effect of an incoming free-stream velocity pulsation with a mean Reynolds number of 100 on the drag and lift forces over and vorticity dynamics behind a circular cylinder. This paper reports on initial results involving unsteady, laminar and incompressible flows over a circular cylinder. Sinusoidal free-stream pulsations with amplitudes Av varying between 25% and 75% of the mean free-stream velocity and frequencies varying between 0.25 and 5 times the natural shedding frequency fs were considered. Of particular interest to us is the interaction between the pulsating frequency and natural vortex shedding frequency and the resulting effects on drag. Interestingly, at frequencies close to the natural frequency, and to twice the natural frequency, a sudden drop in the mean value of the drag coefficient is observed. The first drop in the drag coefficient, i.e. near f = fs, is also accompanied by a change in the flow and vortex shedding patterns observed behind the cylinder. This change in vortex shedding pattern manifests itself as a departure from symmetrical shedding, and in a non-zero mean lift coefficient value. The second drop, i.e. near f = 2 fs, has similar characteristics, except that the mean lift coefficient remains at zero.

Complex flows through cylinder arrays, such as the case of pull-tubes located in the truss section of a truss spar, are very difficult to describe and analyze. It is especially difficult to predict and correct Vortex Induced Vibration (VIV) response using traditional tools that were developed to analyze single cylinder rather than arrays of cylinders. Computational Fluid Dynamics (CFD) offers the designer the ability to properly analyze these complex problems and increase the reliability of his design. In this study, a full scale truss spar with pull-tubes is modeled using CFD coupled with an FEA structural model of the pull-tubes for a fluid-structure interaction (FSI) computation. The VIV response of the pull-tubes is predicted and analyzed for different current headings and speeds.

Passive turbulence control (PTC) in the form of selectively applied surface roughness is used on a rigid circular cylinder supported by two end-springs in transverse steady flow. The flow-induced motions are enhanced dramatically reaching the limits of the experimental facility and motion mechanism at amplitude to diameter ratio A/D ≅ 3. In comparison to a smooth cylinder, in the fully turbulent shear layer flow regime at Reynolds number on the order of 100,000, PTC initiates VIV earlier at reduce velocity U* ≅ 4, reduces VIV amplitude depending on damping, and initiates galloping at U* ≅ 10 rather than 20. Thus, back-to-back VIV and galloping are achieved expanding the synchronization range of Flow Induced Motion (FIM) beyond U* ≅ 15 and the capabilities of the experimental set-up. The harnessed horizontal hydrokinetic power increased by a factor of four due to increased velocities in the synchronization range without any adjustment of the motion mechanism particulars.Copyright © 2011 by ASME

This paper compares model test data for risers with partial strake coverage to predictions made with the Vortex-Induced Vibration (VIV) prediction program SHEAR7 Versions 4.5 and 4.6. It is shown that new features in Version 4.6 substantially enhance the capability for predicting the VIV response of risers with partial coverage. Experimental data is taken from two large L/D tests: the NDP 38 m long riser tests and the Deepstar-Miami, 500 foot long riser. New methods are described for modeling risers partially covered with helical strakes. Key SHEAR7 parameters are recommended, based on parametric investigations to calibrate the model against the available experimental data. Recommended modeling procedures are described so as to facilitate implementation by SHEAR7 users in their VIV modeling tasks.Copyright © 2011 by ASME

Slender marine risers used in deepwater applications can experience vortex-induced vibration (VIV). It is becoming increasingly common for field monitoring campaigns to be undertaken wherein data loggers such as strain sensors and/or accelerometers are installed on such risers to aid in VIV-related fatigue damage estimation. Such damage estimation relies on the application of empirical procedures that make use of the collected data. This type of damage estimation can be undertaken for different current profiles encountered. The empirical techniques employed make direct use of the measurements and key components in the analyszes (such as participating riser modes selected for use in damage estimation) are intrinsically dependent on the actual current profiles. Fatigue damage predicted in this manner is in contrast to analytical approaches that rely on simplifying assumptions on both the flow conditions and the response characteristics. Empirical fatigue damage estimates conditional on current profile type can account explicitly even for complex response characteristics, participating riser modes, etc. With significant amounts of data, it is possible to establish “short-term” fatigue damage rate distributions conditional on current type. If the relative frequency of different current types is known from metocean studies, the short-term fatigue distributions can be combined with the current distributions to yield integrated “long-term” fatigue damage rate distributions. Such a study is carried out using data from the Norwegian Deepwater Programme (NDP) model riser subject to several sheared and uniform current profiles and with assumed probabilities for different current conditions. From this study, we seek to demonstrate the effectiveness of empirical techniques utilized in combination with field measurements to predict the long-term fatigue damage and the fatigue failure probability.

Vortex-Induced Vibration (VIV) is a complex, non-linear fluid-structure interaction problem with important consequences for offshore risers, tendons and other tubulars. The prevalent approach in the industry is to use semi-empirical formulations to estimate VIV amplitudes, frequencies and the resulting fatigue damage. These semi-empirical techniques estimate VIV response amplitude by considering the balance of power input into the pipe due to vortex-shedding and the loss of power from the pipe due to damping. At the heart of this method are lift coefficient curves, which are used to estimate power input into the pipe. A key difficulty of this method is modeling the response of pipes with mitigation devices (strakes and fairings). This paper discusses the use of negative lift coefficient curves for estimating VIV response from mitigation devices. The author’s show how damping is handled in Shear7 using this approach. Results of comparisons between predicted and measured data show that negative lift curves are an effective means of modeling damping from VIV mitigation devices.Copyright © 2011 by ASME

Flow induced instability has been observed in numerous fields, including the aerospace industry, nuclear reactor components and power generation/transmission. This paper considers the stability analysis of a cantilever pipe excited by the flow of fluid. The developed mathematical model can be used to determine a number of critical flow velocities where the instability may occur. The pipe is modeled as an Euler-Bernoulli beam by considering the effect of fluid mass and the Coriolis acceleration caused by the flow. The required mathematical procedure is presented and it is accompanied by a set of design guidelines for determining the stable and unstable condition for these structures. Parameters to be considered are velocity of the flow, density of the flow, and properties of the pipe as well as its geometry.

Vortex structure behind a flexible rectangular plate with sway motion and flow-induced vibration was experimentally investigated by wind tunnel experiment by using Particle Image Velocimetry (PIV). The flexible rectangular plate, which was made of a polyurethane block, was cantilevered on a flat plate. On the opposite end, top free end showed a sway motion in the downstream direction. Increasing sway angle, the top free end involved the flow-induced in-line vibration which has a small amplitude. This is a typical example of fluid-structure interaction problem. However more experimental research for the effects of the sway motion and the flow-induced vibration on vortex structure behind the rectangular plate is required. In this paper, we focus attention on the phase-averaged vortex structure when the amplitude of vibration is the largest and smallest case. PIV measurement was conducted to clarify the phase-averaged and the instantaneous vortex structure behind the swaying plate. We discussed the effect of sway motion and flow-induced vibration on vortex structure.Copyright © 2011 by JSME

Vibration is an important cause of fatigue damage in subsea piping systems (jumpers, rigid spools, tree pipework etc.). Presently, guidelines are available for a qualitative and quantitative vibration assessment for process pipework, but these are more applicable to topside and refinery piping. Currently, there are limited guidelines specifically developed for vibration assessment for subsea piping. For subsea pipework, additional guidelines may be necessary to check for possible interaction between current induced VIV, wave induced VIV (for shallow waters) and slugging, and other mechanisms that result in flow induced vibration. This paper provides augmented guidelines for subsea piping, which takes into account the interaction between piping and its subsea environment. At the same time, suggestions are provided to trim the guidelines of mechanisms that does not occur subsea. The Likelihood of Failure (LOF) assessment based on the proposed guidelines provides an indication whether further detailed vibration analysis (such as CFD and/or FEA) is necessary. Based on the LOF from this assessment, suitable detailed analysis can be performed to determine the fatigue life. This enhanced methodology enables the user to perform vibration assessment and analysis in the least computational time by identifying 1) the most critical flow conditions over the production life of the field and 2) the most critical vibration mechanisms that should be analyzed. This results in a reduction in the number of conditions or load cases which require detailed analysis, without decreasing the accuracy of the assessment and analysis.Copyright © 2011 by ASME

In recent years, a number of deepwater development projects are running worldwide. As the water depth increases, safety and reliability of the riser is a critical issue. One of the most important matters is vortex-induced vibration (VIV). In the deepwater area with strong current, for example in the Gulf of Mexico, a riser pipe’s VIV motion changes continually due to the change of hydrodynamic conditions. In order to assess safety and reliability of deepwater riser, investigation of the dynamic variation of riser VIV is important. This paper deals with top tensioned riser. To clarify the phenomena of dynamic variation of the riser’s vibration mode, a large-scale experiment using a 28.5 m long model was carried out at the Deep Sea Basin of the National Maritime Research Institute in Japan. In this experiment, the model’s bottom end was fixed, while top end was connected to a tensioner. The current generating system was installed to make flow from water surface to about 5m in depth. A measurement of riser VIV motion in current condition was carried out by changing the model’s top tension from self-weight balanced condition to four times of the self-weight. Vibration mode widely changed from high mode of up to 15th to low mode of 5th. In order to investigate an influence of the change of vibration mode on the riser VIV motion, a series of experiments were conducted with the periodic variation of top tension. It was found that the traveling wave occurred from top to bottom end in a moment of vibration mode changed.Copyright © 2011 by ASME

Measurements have been made of the wake of a circular cylinder at Reynolds number of 105 for a stationary cylinder and a cylinder vibrating +/− 1.25 diameters under natural vortex induced vibration. Wake velocity profiles were taken at 2, 4, 6, 12, 24 and 50 diameters downstream. The stationary cylinder profile reproduces the well known wake deficit law. The vibrating cylinder near wake is wider, deeper and flatter than that of the stationary cylinder. Flow visualization reveals the vortex dynamics in the wake. Correlation is shown with theory.Copyright © 2011 by ASME

In this paper, an experimental study on the in-line and cross-flow vortex-induced vibration (VIV) of flexible cylinders is conducted. The relationship of two-degree-of-freedoms of vortex-induced vibration of flexible cylinders is also investigated. The influence of natural frequency of flexible cylinders on vortex shedding and VIV are studied through the experiment in this paper. Finally, A nonlinear model, with fluid-structure interaction, of two-degree-of-freedom VIV of flexible cylinders is proposed. It is shown that the ratio of the frequencies and amplitudes of in-line and cross flow VIV of the flexible cylinders changes with current velocity and Reynolds number. The natural frequency of flexible cylinder has great influence on the vortex-induced virbation due to the strong fluid-structure coupling effect. Under given current velocity, the natural frequency of flexible cylinder determines its forms of vibration (in circular or ‘8’ form). The ratio of the VIV frequencies is 1.0 beyond the lock in district and 2.0 within the lock in district respectively. And the ratio of the VIV amplitudes is 1.0 beyond the lock in district and 1/3 to 2/3 within the lock in district. The results from this paper indicates that in-line vibration should be considerated when calculating the vibration response and fatigue damage.Copyright © 2011 by ASME

In this paper, model tests of a riser with an aspect ratio of 263 were performed in a towing tank by towing the model with constant speeds. The riser was tested with various configurations of buoyancy, including 0% coverage, 25% coverage, 50% coverage and 100% coverage of the buoyancy modules. Furthermore, for the 25% and 50% coverage conditions, the portion without buoyancy modules of the model was covered with helical strakes of 17.5D/0.25D (pitch/height). In the experiments, the strain information in cross-flow (CF) direction was measured using Fiber Bragg Grating (FBG) sensors. The VIV characters of flexible risers with different buoyancy configurations were studied and compared with each other in detail.Copyright © 2011 by ASME

Small-bore pipes inside manifold structures are designed to be flexible. The piping must absorb thermal and pressure loading, as well as installation tolerances, well growth and in some cases stroking and/or other temporarily imposed displacement controlled conditions. Depending on well conditions and functional requirements the piping is often highly utilised statically. Vortex-induced vibrations (VIV) are on the other hand directly related to the frequency of the piping, and the more flexible a system is, the more prone it is to respond to cyclic loading induced by waves and current. Generally small-bore piping responds easily to VIV since the VIV onset flow velocity is directly proportional to the diameter. Small-bore piping have by default very small diameters, therefore the onset value for VIV is lowered compared to systems with larger diameters. In order to mitigate this environmental loading effect, it is favourable to increase the frequency of the system. Increasing the frequency is however normally done by making the system stiffer, more rigid, which generally is not desirable since this in turn increases the level of static utilisation. The current industry practice for VIV design of small-bore piping systems is to apply onset criteria. Onset criteria are in themselves applicable for small-bore systems, but they are very conservative, and DNV has in projects encountered several systems where a balance between onset of VIV and static utilisation was not obtainable. As temperatures, well growth and operational pressures increase with more complicated well conditions, the challenges with flexibility versus rigidity in small-bore piping will only increase, and previous design methodologies using typical onset criteria will be more difficult to apply successfully. There are many possible solutions to this problem; such as shielding, clever layout design, and/or direct VIV mitigation measures mounted on the pipes. This paper proposes a general methodology for advanced fatigue calculations to decrease the level of conservatism, and introduces some mitigation techniques which have been successfully applied in projects for systems where both onset criteria and fatigue utilisation criteria fail, and where fulfilling them is not possible within the confines of acceptable static utilisation.

A Vortex Induced Vibration (VIV) based hydrokinetic energy system is discussed in this paper. Vibrations induced on a body (facing an external flow) due to the periodic irregularities in the flow caused by boundary layer separation are called as VIV. This separation of the boundary layer from the surface causes vortex formation in the wake region of the cylinder. The lift-force or the transverse oscillation of the vibrating cylinder depends upon the strength and modes of the vortex formed. The VIV energy harvesting system is based on the idea of maximizing rather than spoiling vortex shedding and was discovered in 2004 at the University of Michigan by Bernitsas and Raghavan. The vibrating bodies will in turn be used to harness energy using an efficient power-take-off system. In this paper, we discuss the hydrodynamic design of such a VIV based energy harvesting system using computational fluid dynamics. A fluid structure interaction calculation is performed to determine the forces on the surface of a bluff body due to separation of vortices from the surface. The hydrodynamic forces that act on such a system depend on the cylinder diameter, flow velocity, modes of vortex shedding and arrangement of cylinder(s). A detailed computational study on the effect of different design parameters listed above are first carried on a single cylinder arrangement; this is followed by a more detailed analysis that is extended to multiple cylinders. For a two-cylinder arrangement, the positions in which the cylinders are placed are also found to play an important role, as the vortex shed from one cylinder may be used to enhance the forces of lift on another cylinder present in its wake. Furthermore, the design of a VIV generator requires optimal damping and low mass ratio to enable high energy conversion via an efficient power take-off mechanism. The working and design considerations of the energy converter is outlined starting with a set of basic definitions pertaining to this technology. A tubular linear interior permanent magnet generator (TL-IPM) connected to a power converter is used; a linear generator was chosen to minimize mechanical components, such as gears or cams in the system.Copyright © 2011 by ASME

We outline the procedures used by program VIVA, developed over the last sixteen years to estimate the cross-flow vibration of marine risers in arbitrary currents. The program theory is based on a combination of first principles, extensive hydrodynamic databases, as well as modifications introduced through comparison against experimental and field data. The program was built from the start to handle standing as well as traveling waves, or arbitrary combinations of traveling and standing waves, through the use of complex modes. Considerable effort was expended to develop a hydrodynamic methodology that is suitable for short and long risers and cables, and which provides results in agreement with recent observed mechanisms. In particular, we outline changes to take into account: • the influence of in-line as well as cross-flow oscillations; • the influence of the Reynolds number; • the effect of high force harmonics; • modeling of lock-in in a sheared flow; • modeling of staked sections. The methodology is illustrated through several examples where predictions are compared with field and experimental data.Copyright © 2011 by ASME

A double Birkhoff wake oscillator for the modeling of vortex-induced vibration is presented in which the oscillating variables are assumed to be associated with the boundary layer/near wake and the far wake. The fluid forces are assumed to consist of a potential added mass force and a force due to vortex shedding. In the limit of vanishing incoming flow velocity, the model equations reduce to a form similar to the Morison equation. The results of the double wake oscillator have been compared with forced vibration measurements and free vibration measurements over a range of mass and damping ratios. The model is capable of describing the most important trends in both the forced and free vibration experiments. Specifically, the double wake oscillator is able to model both the upper and lower branch of free vibration.Copyright © 2011 by ASME

The objective of this article is to identify a model able to represent the first harmonic behavior of a rigid cylinder undergoing VIV in the most different cases of a rigid cylinder supported by a spring/damper system. This analysis of the first harmonic behavior is made considering three different non-dimensional variables: the damping coefficient, the reduced velocity and the mass ratio. The challenge is to define a model that represents the changes on the lock-in zone considering the different combination of damping coefficient and mass ratio thus able to represent the different real systems. Two new phenomenological models using the Van der Pol oscillator are studied. They follow the framework of the phenomenological model proposed by Facchinetti et al.Copyright © 2011 by ASME

An investigation was carried out for the fatigue damages due to VIV in a flexible riser evaluated with three different VIV simulation methodologies. One methodology is provided in commercial software Shear7 which is established based on mode superposition. The other two are provided in commercial software OrcaFlex which are established based on global dynamic simulation in time domain. One of the two time-domain methods is referred to as Iwan and Blevings model formed with a wake oscillator, and the other is referred to as Tracking (1) model made with vortex tracking method. Fatigue damages in tensile armoring wires of the riser were evaluated with RMS curvature ranges resulting from the three methodologies separately. A detailed comparison between the damages and between RMS curvature ranges is made and then some discussions and recommendations are presented.Copyright © 2011 by ASME

The present work focusses on the numerical study of Vortex-Induced Vibrations (VIV) of an elastically mounted cylinder in a cross flow at moderate Reynolds numbers. Low mass-damping experimental studies show that the dynamic behavior of the cylinder exhibits a three-branch response model, depending on the range of the reduced velocity. However, few numerical simulations deal with accurate computations of the VIV amplitudes at the lock-in upper branch of the bifurcation diagram. In this work, the dynamic response of the cylinder is investigated by means of three-dimensional Large Eddy Simulation (LES). An Arbitrary Lagrangian Eulerian framework is employed to account for fluid solid interface boundary motion and grid deformation. Numerous numerical simulations are performed at a Reynolds number of 3900 for both no damping and low-mass damping ratio and various reduced velocities. A detailed physical analysis is conducted to show how the present methodology is able to capture the different VIV responses.Copyright © 2011 by ASME

Vortex-Induced-Vibrations (VIV) due to ocean currents can consume a sizable portion of the allotted fatigue life of marine risers. Vibration monitoring and concurrent estimation of fatigue damage due to VIV can significantly enhance the safe and reliable operation of risers. To this end, riser response can be characterized by using sensors (e.g. accelerometers and/or angular rate sensors) to measure the motion of the riser at a few locations. Fatigue damage can be predicted along the entire length of riser from measured data using the method of modal decomposition and reconstruction. In this method the structural response of interest, such as stress and fatigue damage, is expressed by modal superposition, where the modal weights are estimated using measured data and analytical modeshapes. However the accuracy of this method declines as the sensor density (number of sensors per unit riser length) decreases, especially when the riser vibrates in high-order modes and exhibits traveling wave behavior. In this paper, an efficient frequency-domain methodology allowing for accurate reconstruction of the riser response along the entire riser using a limited number of sensors is proposed. We first identify the excited VIV modes (natural frequency and modeshape) using principal vectors of the cross spectral density. Modal decomposition and reconstruction is performed separately for each VIV band surrounding each excited mode. This allows us to use several (as many as the number of sensors) participating modes in each band, and thus improve the accuracy. Since the stress distribution is sensitive to the chosen set of participating modes, we optimize over several candidate sets, selecting the set of modes that result in the lowest prediction error. In order to improve the reconstruction of complex modes, particularly traveling waves, the modeshapes can be augmented with additional basis vectors. The additional basis vectors are obtained by shifting the phase of the normal modes by 90 degrees at every wave number using the Hilbert transform. Though developed in the context of VIV, the method can be used to estimate fatigue damage due to vibrations regardless of the excitation mechanism. The methodology is demonstrated using the NDP (Norwegian Deepwater Program) test data on a 38 meter long slender riser, using data from eight accelerometers. Results show that the proposed algorithm can reconstruct stresses and fatigue damage accurately along the length of the riser in the presence of traveling wave behavior using relatively few sensors.Copyright © 2011 by ASME

In this paper, VIV of a flexible model within full scale Re number regime are studied. The experiments were carried out in the towing tank by towing the flexible model with a constant forward speed. The bending stiffness of the flexible model was specially designed and controlled by a steel core pipe, whose diameter and wall thickness were selected according to the structural naturally frequency, vortex-shedding frequency and strength requirements under VIV conditions. The cylindrical rubber was bundled onto the core pipe to increase the diameter of the pipe to the full scale riser’s diameter, so that the model has the full scale hydrodynamic diameter, and therefore the full scale Re number. The strain information in both IL and CF directions of the model was measured by the optical fiber strain gages. The data was analyzed by the modal super position method. The VIV characters at both IL and CF directions under full scale Re number were studied.Copyright © 2011 by ASME

Rigid subsea jumper systems are typically used as interface between subsea structures and are required to accommodate significant static and dynamic loads. Due to constraints imposed by in-line planar jumpers (e.g. U shaped and M shaped jumpers), the industry is shifting towards the use of multi-planar jumper systems (e.g., Z-shaped jumpers). These multi-planar jumper systems have increased tolerance to end displacements and can be tailored to accommodate cyclic end motions of subsea structures. Multi-planar systems, however, come with unique challenges of their own including the coupling of flexural and torsional responses under vortex induced vibrations (VIV), fluid induced vibration (FIV) and slugging. In particular, the development of hydrodynamic slug flow is a common occurrence in oil and gas pipelines. It is understood to be initiated by instabilities of wave on the gas-liquid interface. It is also understood that slug flows are the source of vibration within pipework when a change of direction occurs e.g. 90° bend at a subsea riser base or top side piping. In standard slug flow vibration analysis, averaged slug frequency and length are used to calculate the force generated. In the case of a multi-planar rigid jumper, several changes of direction occur within a short length of pipe. After each bend the characteristics of the slug flow are modified. It is necessary to accurately capture these changes in order to reproduce the forces generated at critical points along the jumper length. This paper presents a methodology for analyzing slugging induced fatigue that has been developed in an on-going study undertaken by MCS Kenny for design of multi-planar rigid jumper systems. In this methodology, Computational Fluid Dynamics (CFD) is used to accurately simulate the flow within the jumper and provide pressure fluctuations on the internal pipe wall for the vibration analysis. The pressure fluctuations are then incorporated in a Finite Element (FE) model of the jumper system and further used to determine the slugging fatigue damage. CFD (Star-ccm+) and FE (Flexcom, ABAQUS) software programs are used to accurately capture the response of the jumper system. Key conclusions and challenges overcome during the course of this study are presented herein.Copyright © 2011 by ASME

Nuclear power plants have experienced problems related to tube failures in steam generators. While many of these failures have been attributed to corrosion, it has been recognized that flow-induced vibrations contribute significantly to tube failure. In order to avoid these excessive vibrations, tubes are stiffened by placing supports along their length. Various tube/support geometries have been used, but the majority are either support plates (plates with drilled or broached holes) or flat bars. Unfortunately, clearance is often considered necessary between the tubes and their supports to facilitate tube/support assembly and to allow for thermal expansion of the tubes. A combination of flow-induced turbulence and fluidelastic forces may then lead to unacceptable tube fretting-wear at the supports. The fretting wear damage could ultimately cause tube failure. Such failures may require shut downs resulting in production losses, and pose potential threats to human safety and the environment. Therefore, it is imperative to predict the nonlinear tube response and the associated fretting wear damage to tubes due to fluid excitations. Tubes in loose flat-bar supports have complex dynamics due to the possible combinations of geometry. The understanding of tube dynamics in the presence of this type of support and the associated fretting wear is still incomplete. These issues are addressed in this paper through simulations of the dynamics of tubes subjected to crossflow turbulence and fluidelastic instability forces. The finite element method is utilized to model the vibrations and impact dynamics. The tube model simulates a U-tube supported by 16 flat bars with clearances and axial offset. Results are presented and comparisons are made for the parameters influencing the fretting-wear damage such as contact ratio, impact forces and normal work rate. The effect of support clearance and support axial offset are investigated.Copyright © 2011 by ASME

The vortex-induced vibration (VIV) is a classical problem in ocean engineering. Intensive research on this field for flow around a circular cylinder has been observed, due to practical application, mainly the design of risers, cables and pipelines with free span. The relevance of this phenomenon is related to the structure failure, consequence of large displacement or fatigue. In the present study the influence of initial condition on the vortex induced vibration (VIV) of a circular cylinder with two degree of freedom is investigated by the numerical solution of the slightly compressible formulation of Reynolds Average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates. The k–e turbulence model is used to simulate the turbulent flow in the wake of the cylinder. Two different initial conditions have been tested, free-stream and continuous reduced velocity increase (using the previous reduced velocity as initial condition for the next value). Results for the phase angle, amplitude, frequency, and lift coefficient are presented. The numerical results have been compared with experimental data of Jauvtis and Williamson [1]. The results indicate that the history of cylinder movement has a important impact in the amplitude oscillation observed in-line and cross-flow, principally in the reduced velocity range associated with the upper branch. Results obtained for the initial and lower branch seems to be independent of the initial condition. Further investigation are necessary to understand the difference observed such as the absence of the jump in the cross-flow oscillation between the initial and upper branch and the absence of in-line oscillation for reduced velocity in the range of 1–4 and the peak of in-line oscillation at reduced velocity 6.0.Copyright © 2011 by ASME

The Karman vortex induced vibration (KVIV) is observed over a wide range of conditions, and has been regarded as a negative phenomenon until now since it has caused many accidents. Therefore a lot of researches have been conducted to predict and to avoid it. Recently, however, KVIV is regarded as a process to convert energy of natural flows into mechanical energy, and techniques for electricity generation utilizing it are proposed. The electric power of this method is smaller than that of wind and water turbine generations, but this method has possibility to become a smaller and more maintenance-free apparatus than rotary machines. In earlier works, we found that the trailing vortex shed periodically from a cruciform two-circular-cylinder system, and that it induces a cross flow vibration on the upstream cylinder (TVIV) over a wide velocity range, which becomes broader by replacing the downstream cylinder by a strip-plate. Because of this character, an electricity generator utilizing TVIV should be effectively applied to rivers of which velocity usually varies largely. The purpose of this work is to develop a technique to generate electricity utilizing TVIV in water flow. Experiments using a water tunnel and an open-surface water channel are conducted to know conditions of the maximum electric power and to test the performance in a river. The optimum gap-to-diameter ratio is 0.22 since the cylinder vibration amplitude is largest. The optimum resistance of the circuit is the value which makes the virtual damping due to electricity generation nearly equal to the structure damping. The performance test in the water channel shows that the open surface and the turbulence in flow have little influences on the cylinder vibration amplitude and the synchronization velocity range of KVIV. However, TVIV is not observed, maybe because of the large aspect ratio.Copyright © 2011 by JSME

Slender structures immersed in a cross flow can experience vibrations induced by vortex shedding (VIV), which cause fatigue damage and other problems. Engineering VIV models tend to operate in the frequency domain. A time domain model would allow to capture effects beyond the scope of today’s frequency domain empirical codes: interaction between in-line and cross-flow vibrations, higher order frequency components, structural non-linearities, simultaneous actions from other loads like waves and forced motions at boundaries. There is also the potential to capture the chaotic nature of VIV. Such a model was formulated in the present work: for each cross section and at each time step, the recent velocity history is described as a combination of Laguerre polynomials. The coefficients of that combination are used to enter an interpolation function to predict the instantaneous force, allowing to step the dynamic analysis. An offshore riser was modeled in this way: Some analyses provided an unusually fine level of realism, while in other analyses, the riser fell into an unphysical pattern of vibration. It is concluded that the concept is very promising, yet that more work is needed to understand trajectory stability and related issues, in order to further progress towards an engineering tool.Copyright © 2011 by ASME

The vortex induced vibration (VIV) on a circular cylinder with low mass-damping parameter and low Reynolds number is investigated numerically as basis for applications on dynamics of risers used in the offshore oil and gas industry and as a first step before tackling the harder high Reynolds number problem. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. The numerical solution of the Reynolds average Navier-Stokes equations written in curvilinear coordinates is obtained using an upwind and Total Variation Diminishing conservative scheme and the k-e turbulence model is used to simulate the turbulent flow in the wake of the body. Results were obtained for the phase angle, response amplitude, frequency, and lift coefficient for a variation of reduced velocity from 2 to 12 and three different proportional variations of Reynolds number, 2000–6000, 2000–12000, and 2000–24000. The numerical results indicate the strong effect of the Reynolds number range on the response amplitude, lift coefficient, and frequency of oscillation for a low mass-damping parameter.Copyright © 2011 by ASME

A vortex-induced vibration (VIV) inference technology, termed as VIV detector, has been developed at Shell. The underlying idea is to use the tension measurements of a tubular to infer its bending responses due to vortex-shedding. A prototype was developed for monitoring VIV of the tendons of a tension leg platform (TLP). The theoretical frame work, including key parameters and design curves for commonly used offshore tubular, is discussed herein. Examples are provided, which indicate the agreement of the inferred and the measured responses of models in laboratory conditions. The benefits and potential applications to other structures are suggested at the conclusion.Copyright © 2011 by ASME

The characteristics of VIV response of rotating circular cylinders in flow had been investigated by both experiment and numerical simulation. In the experiment, the motions of a flexible circular cylinder pipe installed in a circulation water channel were measured. In simulation, a Discrete Vortex Method had been used to estimate hydrodynamic forces acting on a rigid circular cylinder. When a cylinder rotates in flow, a rotation frequency becomes important added to natural frequency and vortex shedding frequency. The deflection of a flexble pipe peaked when the frequency ratio of rotation frequency to natural frequency was between 1.0 and 1.5. This is similar to increment of oscillation amplitude by a resonance of natural vibration and vortex shedding. The peak oscillation frequency of a rotating circular cylinder in flow decreased with increase in rotation number. The main axis of cylinder oscillation turned in the rotation direction.

A passive control means to suppress flow-induced motions (FIM) of a rigid circular cylinder in the TrSL3, high-lift, flow regime is formulated and tested experimentally. The developed method uses passive turbulence control (PTC) consisting of selectively located roughness on the cylinder surface with thickness about equal to the boundary layer thickness. The map of “PTC-to-FIM,” developed in previous work, revealed robust zones of weak suppression, strong suppression, hard galloping, and soft galloping. PTC has been used successfully to enhance FIM for hydrokinetic energy harnessing using the VIVACE Converter. PTC also revealed the potential to suppress FIM to various levels. The map is flow-direction dependent. In this paper, the “PTC-to-FIM” map is used to guide development of FIM suppression devices that are flow-direction independent and hardly affect cylinder geometry. Experiments are conducted in the Low Turbulence Free Surface Water Channel of the University of Michigan on a rigid, horizontal, circular cylinder, suspended on springs. Amplitude and frequency measurements and broad field-of-view visualization reveal complex flow structures and their relation to suppression. Several PTC designs are tested to understand the effect of PTC roughness, location, coverage, and configuration. Gradual modification of PTC parameters, leads to improved suppression and evolution of a design reducing the VIV synchronization range. Over a wide range of high reduced velocities, VIV is fully suppressed. The maximum amplitude occurring near the system’s natural frequency is reduced by about 63% compared to the maximum amplitude of the smooth cylinder.

The fluid-structure energy transfer of a tensioned beam of length to diameter ratio 200, subject to vortex-induced vibrations in linear shear flow, is investigated by means of direct numerical simulation at three Reynolds numbers, from 110 to 1,100. In both the in-line and cross-flow directions, the high-wavenumber structural responses are characterized by mixed standing-traveling wave patterns. The spanwise zones where the flow provides energy to excite the structural vibrations are located mainly within the region of high current where the lock-in condition is established, i.e. where vortex shedding and cross-flow vibration frequencies coincide. However, the energy input is not uniform across the entire lock-in region. This can be related to observed changes from counterclockwise to clockwise structural orbits. The energy transfer is also impacted by the possible occurrence of multi-frequency vibrations.

The dynamic characteristics of deepwater riser usually present serried modes with lower frequencies, because structural flexibility is very large due to high aspect ratio (ratio of length to diameter of riser). Moreover, in practice flow velocity usually distributes non-uniformly along the riser length. A coupling model, for multi-mode VIV (vortex-induced vibration) of slender riser experiencing non-uniform flow, by means of finite element simulation combined with the hydrodynamic model taking account of the interaction between fluid and structure in time-domain, is proposed. VIV responses of slender risers respectively in uniform, stepped and shear flow are explored. Satisfied agreements with experiment results are observed. Additionally, based on the numerical simulations effects of reduced velocity and modal energy on modal weight are explored. We note that for case of multi-mode vibration the participating modes tend to distribute by groups.

A Monte Carlo analysis using pseudo-random sampling is carried out with the objective of determining the relative importance of each of k = 5 independent input parameters appearing in a typical wake-body model for the vortex-induced vibration of an elastically-mounted rigid circular cylinder in uniform flow. For simplicity, the marginal probability distribution of each parameter is assumed to be a uniform distribution. Furthermore, the standard deviation of each distribution is assumed to be the same. The choice of the uniform distribution is also a reflection of the fact that exact forms for the distributions are not known. The sensitivity analysis indicates that the most important factor from the point of view of the predicted steady-state amplitude of oscillation of the cylinder yo is parameter M, which represents the scaling of the effect of the wake on the structure.Copyright © 2011 by ASME

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid flow, fluid at rest, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. Tube bundles structures are very common in the nuclear industry. The reactor cores and the steam generators are both structures immersed in a fluid which may be submitted to a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influence by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Homogenization models have been developed based on the Euler equations for the fluid. Only inertial effects are taken into account. A next step in the modelling is to build models based on the homogenization of the Navier-Stokes equations. The papers presents results on an important step in the development of such model: the analysis of the fluid flow in a oscillating tube bundle. The analysis are made from the results of simulations based on the Navier-Stokes equations for the fluid. Comparisons are made with the case of the oscillations of a single tube, for which a lot of results are available in the literature. Different fluid flow pattern may be found, depending in the Reynolds number (related to the velocity of the bundle) and the Keulegan-Carpenter number (related to the displacement of the bundle). A special attention is paid to the quantification of the inertial and dissipative effects, and to the forces exchanges between the bundle and the fluid. The results of such analysis will be used in the building of models based on the homogenization of the Navier-Stokes equations for the fluid.Copyright © 2011 by ASME

Technique of wavy wall with the circumferential direction is used to suppressing vortex induced vibration of an elastically mounted circular cylinder which is free to move along the stream-wise (X-Direction) and transverse (Y-Direction) direction. The simulation is performed at low Reynolds number (Re) and based on finite volume method (FVD). The results show that wavy wall is very effective for suppressing VIV by detuning vortex shedding. Transverse response is reduced greatly while applying appropriate frequency and the amplitude is located between 0 and 0.05D (D is the diameter of cylinder) with the increase of reduced speeds and fixed Reynolds number 500. Besides, the difference-value between wavy wall cylinder and standard cylinder increases.Copyright © 2011 by ASME

In service the great majority of structures and components are subjected to stresses of variable amplitude (VA). The fatigue design of welded joints in such structures is based on fatigue data obtained under constant amplitude loading, used in conjunction with a cumulative damage rule to estimate the damage introduced by cycles of varying magnitude in the service stress history. There are two major concerns with fatigue design of deepwater steel catenary risers (SCRs): the validity of cumulative damage rule and the damaging effect of stresses below the constant amplitude fatigue limit (CAFL). It is known that SCRs can experience very high numbers of low stress cycles due to vortex induced vibration (VIV) with the result that the choice of method for accounting for the fatigue damage due to stresses below the constant amplitude fatigue limit can be highly significant in terms of the estimated fatigue life. These two fundamental issues have been addressed in a recent group sponsored project. By successfully establishing a loading spectrum representative of that experienced by risers and developing the testing procedures for VA loading using the resonance testing rigs, the fatigue performance of full-scale girth welded pipes under VA loading were investigated. These loading spectra had the same peak/maximum stress histograms but different minimum stresses. Many tests lasted over 108 cycles to investigate the fatigue damage of small stresses in these spectra. This paper describes the development of the method by which fatigue testing of full-scale girth welded pipes under VA loading had been successfully performed.

The vortex-induced vibration (VIV) phenomenon is a very important issue in ocean and offshore engineering. When bluff bodies are immersed in a current, the boundary layers separate and form shear layers that can interact causing a periodic vortex shedding. In such condition, the forces acting on the body can make it vibrate. In the offshore industry, among other engineering applications, the vibration of structures can cause fatigue problems, reducing the life span of the element. To reduce the vortex-induced vibration effect suppressors can be employed in order to avoid the body to move, or at least, reduce the amplitude of vibration. There is a great number of suppressor types, like strakes, splitter plates, shrouds, etc; and each one has its own flow mechanisms to avoid VIV. Until now there is no simple way to compare the results and effectiveness of each suppressor. The purpose of this work is to define a parameter called suppressor effectiveness, based on the amplitude of vibration and the reduced velocity range, and use the suppressor effectiveness to compare different suppressors. The data used in the comparisons was obtained from experiments by the authors and collected from the literature.Copyright © 2011 by ASME

Vibration and noise of concern were observed at the hood-duct of the exhaust steam turbine at a power generating facility. The field personnel noticed this problem after a startup of the unit which followed the maintenance replacement of the expansion joints. The author was contacted by the field personnel and asked to formally evaluate this problem and advise on the steps needed to eliminate it. Several similar units were scheduled for the same maintenance work. The analysis carried out was based on the acoustic and structural dynamic modeling of the critical parts of the hood-duct system in question. Both the flow induced excitations and mechanical structural responses were considered. The results of the analysis combined with field measurements indicate a vibration generation mechanism which is flow induced in nature and is coupled with the acoustic field and enhanced by the high stream-wise flow velocities. Consequently, there are two categories of solutions identified to the observed problem. The first considers addressing the problem at the source and the second suggests path treatment. Addressing the problem at the source by means of aeroacoustic optimization of the flow path is recommended. Detuning the mechanical response from the flow excitation(s), i.e. the vibration path treatment, involves an aspect of greater or lesser trial and error since the responses of the studied structure depend on many variables; therefore, even the most accurate calculations might not be sufficient to give the expected results. Both recommendations are discussed.Copyright © 2010 by ASME

Jumpers are typically short sections of curved pipe spanning production riser elements on the sea floor. When in areas of significant currents these jumpers are subject to vortex induced vibration (VIV). The complex shape of the jumper means that numerical methods are usually needed to solve for the vibration modes of the jumper. Furthermore, the fluid flow around the jumper is also complex so that traditional methods of VIV analysis used for risers are not applicable to jumpers. Here we use a CFD code in a fully coupled analysis to predict vibration response and strain of a typical subsea jumper. A separate finite element analysis is used to calculate the eigenvalues and eigenvectors of the jumper system for input into the CFD analysis. The resulting method is economical and practical for design analyses.Copyright © 2010 by ASME

The internals in the deaerators of a refinery plant were reported to have experienced a series of failures since their installation in 1985. These failures included development of cracks in the floor plates, damage of supports and breakage of fillet welds. Two possible root causes were initially identified; thermal stresses due to transient conditions and flow induced vibration. The former cause was classified as unlikely since the deaerators were always operating on steady-state conditions. No cyclic operating conditions were imposed on these deaerators. Vibrations however posed as the most likely root cause for the series of failures. The refinery plant inspectors reported that vibrations on the deaerators, although have not been measured, could be physically felt. These vibrations appear to be continuous and increase linearly with load. A finite element analysis was performed to determine the natural frequency of the deaerators. Mode shapes predicted from this calculation show that vibrations could have caused the failures of the internals. Furthermore, the lowest natural frequency of the deaerators appeared to fall within the actual vibration frequency on site (∼20 Hz). Although not confirmed, it is highly suspected that the vibration was excited by the flow (low pressure steam). Several repair options were explored to overcome this problem. These options were concentrated in increasing the stiffness of the steam inlet pipe and the deaerator floor. Finite element assessments demonstrated that the current flexible deaerator floor was the reason for the low natural frequency. An option of introducing reinforcement strips to the bottom side of the floor was identified as the best option to increase the natural frequency of the deaerator and this is expected to overcome the vibration problem. Only one vessel was assessed but the results apply to the other vessels since they are similar in design.Copyright © 2010 by ASME

Pipelines laid on an uneven bottom often have free spans. For cases with long spans, one may have several modes and eigenfrequencies that can be excited by vortex shedding. Furthermore, due to the sag effect of a long free-span, the dynamic properties are different in vertical and in horizontal directions. This causes a complex response pattern in the cross-flow (CF) and in-line (IL) directions. From previous research we know that pure IL response at relatively low current velocities may significantly contribute to fatigue damage. This response type must be studied in addition to the combined IL and CF response. The objective of this paper is to present experimental results from flexible beam experiments where both response types are studied, as well as to present results from an empirical response model for the same cases. The empirical model is based on two types of experiments. The first set of experiments were conducted with a flexible pipe for both single and double span configuration. Pure IL and combined IL and CF motions were observed. In the second set of experiments, forces on a rigid cylinder were measured under forced motions in a current. The motions were found from measurements of cross section in the flexible pipe tests. Hydrodynamic coefficients such as drag, added mass, excitation and damping force coefficients were found and then applied in the empirical response model. In the present paper the results from the flexible beam experiments are presented and also compared with the results from the empirical response model. The results so far are encouraging, but further work and more data are needed in order to have a general and robust response model for combined CF and IL VIV.Copyright © 2010 by ASME

Regarding the Japan Sodium-cooled Fast Reactor, a multi-elbow piping system is adopted for its cold-legs. Flow Induced Vibration (FIV) is considered to be caused by complex flow with very high velocity in the elbows. In this study, pressure measurement test of a single elbow flow is conducted to find out pressure fluctuation characteristic which is related to the elbow turbulent flow and lead potentially to the FIV. Two types of experimental loops, that is, 1/7 and 1/15-scale setup simulating the JSFR cold-leg pipings, are used for pressure measurement, and a distinguishing peak can be seen in the power spectrum density profile of pressure fluctuation obtained where flow separation occurs and at the downstream from it. This characteristics of pressure fluctuation is obtained from the two different scale experiments, and the scale effect is not found in terms of the pressure fluctuation.Copyright © 2010 by ASME

This paper describes a test program that was developed to measure the dynamic response of a bundle of steam generator U-tubes with Anti-Vibration Bar (AVB) supports, subjected to Freon two-phase cross-flow. The tube bundle geometry is similar to the geometry used in preliminary designs for future CANDU® steam generators. This test program is one of the initiatives that Atomic Energy of Canada Limited (AECL) is undertaking to demonstrate that the tube support design for future CANDU steam generators meets the stringent requirements associated with a 60-year lifetime. In particular, the tests will address issues related to in- and out-of-plane fluidelastic instability and random turbulent excitation of a U-tube bundle with Anti-Vibration Bar (AVB) supports. Therefore, the measurements include tube vibration amplitudes and frequencies, work-rate due to impacting and sliding motion of the tubes against their supports, bulk process conditions and local two-phase flow properties. Details of the test rig set-up and the measurement techniques are described in the paper. Moreover, a numerical prediction of the U-tube vibration response to flow was performed with AECL’s PIPO-FE code. A summary of the numerical results is presented.Copyright © 2010 by Atomic Energy of Canada Limited

Long marine risers exposed to ocean currents will experience vortex induced vibrations (VIV), which may cause severe fatigue damage. VIV is, however, generally less understood than other load effects. The offshore oil industry has therefore supported an intensive research activity on VIV during the last two decades. High mode VIV model tests with long flexible riser models were initiated by the Norwegian Deepwater Programme (NDP). A 38 m horizontally towed instrumented riser was tested in uniform and linearly sheared current profiles with varying towing speed. A second series of experiments has been conducted with a motion-controlled rigid cylinder in order to find the hydrodynamic coefficients for realistic cross-section trajectories. The pipe was forced to follow periodic patterns found from the NDP tests with flexible beam. The Reynolds’ number and the non-dimensional frequency, as well the amplitude ratio was kept identical for both types of tests, ensuring that the flow conditions for these two experiments remain the same. The hydrodynamic coefficients calculated from natural trajectories show a general agreement with pure harmonic forced motion tests. A slight change of excitation regions was, however, found for cross-flow response. Another observation is that in-line excitation force coefficients have much higher values than found from pure in-line test.Copyright © 2010 by ASME

Subsea pipelines laid on uneven terrain typically have segments of unsupported spans, referred to as “free spans”. Alternatively, subsea pipelines lying on loose and fine gravel or sand may develop free spans due to sea bottom being scoured out due to current action. This paper is concerned with the numerical simulation of fluid-structure interaction (FSI) to predict the response of free spans exposed to sea bottom currents. When exposed to sea bottom currents these spans may experience vortex-induced vibrations (VIV), which may cause fatigue damage to the pipeline. The VIV response of the pipe span is predicted by coupling a three-dimensional viscous incompressible Navier-Stokes solver with a nonlinear beam finite element solver. Parameters such as turbulence in the flow, proximity of the seabed, pipe sagging due to submerged weight, and pipe-soil interaction, are all accounted for in the FSI simulation. We pay special attention to the effect of seabed / wall proximity on VIV. Design guidelines for free spans are typically based on VIV amplitude and frequency responses for isolated pipes, with little regard to effects of seabed / wall proximity. This may result in overly conservative designs and/or expensive span remediation recommendations, when in reality no span remediation is required. Two examples of field applications are presented.Copyright © 2010 by ASME

In this paper, system level analysis is carried out for a functional HDD with two disks and four sliders operating at spindle speed of 15000 rpm. Full numerical models both for computational fluid dynamics (CFD) analysis and structural Finite Element Analysis (FEA) are developed. The flow induced vibrations of the sliders in all three directions, namely, off-track (X), down-track (Y) and out-of-plane direction (Z) are examined respectively. The numerical simulation results are compared and validated with the experimental results measured with a 3D laser Doppler vibrometer (LDV). Good agreements are observed for the vibrations in the three directions. The airflow patterns and characteristics of the flow induced vibration in HDD for three critical positions of the head gimbal assembly (HGA) parked at the disks identified as ID, MD and OD are investigated. The results reveal that the first slider from top has the highest flow induced vibrations in all the three directions due to the higher turbulent flow close to the top disk surface. Moreover, the results indicate that the slider vibration is interacted with the disk flutter in the HDD. Optimal designs of the HDD disk and air shroud are carried out to reduce the flow induced vibration of the slider, by suppressing the disk flutter and improving the turbulent flow in the HDD. It is demonstrated that significant reduction of flow induced slider vibration could be achieved with the optimal designs of the HDD.Copyright © 2010 by ASME

This paper presents a general theoretical reduced-order model capable of evaluating the multi-mode nonlinear dynamics of marine risers subject to uniform and sheared currents. The main objectives are to predict the vortex-induced vibration responses and parametrically compare between numerical and experimental results. The emphasis is placed on the analysis of cross-flow vibrations due to unsteady lift forces. The nonlinear equations governing riser axial/transversal motions are derived based on a top-tensioned beam model with typical pinned-pinned boundary conditions. The riser geometric nonlinearities owing to possible large dynamic displacements and multi-mode interactions are accounted for. To approximate the space-time varying lift force, the empirical hydrodynamic model, based on a nonlinear van der Pol wake oscillator with a distributed diffusive term, is used. A low-dimensional dynamic model and computationally-robust time-domain tool are then developed to evaluate the multi-mode fluid-riser interactions. These are very useful in dealing with large parametric studies involving varying system parameters. Comparisons of numerical and experimental results are performed by estimating riser response amplitudes and fatigue damage indices. Both linear and nonlinear risers are considered in the present numerical model whereas only linear riser has been considered by a referenced literature in the reconstruction of experimental displacements through measured strains. It is found that riser geometric nonlinearities play a significant role in both numerical simulations and comparisons with experiment post-processed results. In some cases, quantitative/qualitative discrepancies in riser response predictions are remarkable with linear vs. nonlinear models. These may be recognized as one of the factors why recent numerical and experimental comparisons in literature have been unsuccessful.

In this paper we present a computational study of the forces acting on a circular cylinder vibrating both transversely and in-line to a uniform stream. The in-line vibration frequency is equal to twice the transverse frequency. The cylinder thus follows a figure-eight trajectory, emulating the trajectory of a free vortex-induced vibration. We consider three values of transverse oscillation frequency, in the regime of the natural frequency of the Karman street, for a Reynolds number of 400. We find that the fluid forces are greatly influenced by the direction in which the figure-eight is traversed. We also find that the spectrum of the lift force is characterized by the strong presence of odd-numbered higher harmonics. Moreover, depending on the combination of oscillation amplitude and frequency, the lift force exhibits aperiodic time dependence.Copyright © 2010 by ASME

A numerical model in a quasi-three-dimensional fashion is developed in this paper to simulate vortex-induced vibration of a flexible riser (the aspect ratio = 250, mass ratio, m* = 2.9, damping ratio, ζ = 0.01) in uniform current U∞ = [0.06, 0.80] m/s, (Reynolds number, Re = [0.01, 1.28]×104 ). Finite element method are and Finite volume method are applied in the structural and fluid domains respectively. Effects of fluid-structure interaction (FSI) are reckoned in by making use of kinematic equivalence of the relative flow between fluid and the body in inertial and non-inertial frames of reference. It is found transeverse motion and streamwise motion are strongly coupled, they have same changing trend at the same reduced velocity range, the upper branch appears in the range Vrn = U∞ /fn D ≈ 5–7 for the generated nth mode, whilst the lock-in remains in the range Vrn ≈ 3–10, the phase angles decrease from about 90° in the initial branch to less than 45° in the lower branch. The RMS and envelop values of cross-flow displacements are 4∼6 times those of in-line, maximum amplitudes of about 1.2 diameters at cross-flow and 0.25 diameters at in-line have been observed. Standing wave response was observed as Vr1 = 6, the in-line response even contains the first and the second modes at the same time. The strouhal number, St is about 0.17 in the present cases.Copyright © 2010 by ASME