Dynamics Of Vortex-induced Vibration Research Articles

Vortex-Induced Vibration of Flexible Cylinders in Cross-Flow

This review provides a comprehensive analysis of the literature on vortex-induced vibration (VIV) of flexible circular cylinders in cross-flow. It delves into the details of the underlying physics governing the VIV dynamics of cylinders characterized by low mass damping and high aspect ratio, subject to both uniform and shear flows. It compiles decades of experimental investigations, modeling efforts, and numerical simulations and describes the fundamental findings in the field. Key focal points include but are not limited to amplitude–frequency response behavior, the relationship between the distributed loading acting on the cylinder and the trajectories and the near wake structures around the cylinder, the existence of traveling waves, the identification of power-in/power-out regions, and the modal overlapping and mode competition phenomena.

An analytical model for estimating the maximum energy harvesting efficiency from vortex-induced vibration

The present work presents an analytical model (AM) based on a nonlinear reduced-order model (ROM) for estimating the maximum efficiency (ηm) of energy harvesting from vortex-induced vibration (VIV) of a circular cylinder. The proposed AM was validated through comparisons against both the origin ROM and experiments over a wide range of parameters. Of interest, it provided a low-cost analytical approximation relating the maximum efficiency ηm to physical parameters. As inspired by the modified Griffin plot, the use of AM allowed the collapse of the maximum efficiency ηm as a function of the combined mass-damping parameter α. Of significance, the presented AM should be not only effective for estimating the maximum efficiency ηm but also useful to shed light on VIV dynamics.

Vortex-induced vibration of flexible riser transporting high-speed spiral flow in deep-sea mining

According to Hamilton's principle and a mechanical decomposition model proposed for high-speed spiral flow, vibration governing equations of flexible riser transporting high-speed spiral flow are developed for vortex-induced vibration (VIV) analysis for lifting pipe system in deep-sea mining. The classic van der Pol oscillator is used to simulate the dynamic characteristics of VIV. The governing equations are then discretized and solved by the finite element method and the Runge-Kuta method. Furthermore, dynamic characteristics of VIV of the flexible riser transporting straight flow and spiral flow are investigated and the effects of the spiral flow incidence velocity and angle controlled by the jet device on VIV responses are evaluated. Also, the VIV dynamics considering different damping ratios are examined. The results show that the rotational angular velocity of the spiral flow would amplify the mean deflection of the in-line (IL) direction, and the incidence velocity has a significant nonlinear effect on the dominant frequency of the riser, which would induce the high-order dominant vibration modes when the incidence velocity is large sufficiently. However, the incidence angle has relatively less effects on the VIV responses of flexible riser. Moreover, the locked interval of VIV is less influenced by damping ratio below 0.1.

Effect of internal flow on vortex-induced vibration dynamics of a flexible mining riser in external shear current

Vortex-induced vibration (VIV) of flexible risers with both internal and external flows has received much attention recently. Hence, VIV dynamics of a fluid-conveying flexible riser subjected to external shear current is investigated. The effect of internal flow velocity and fluid density on VIV response is mainly examined and analyzed. A time domain model is introduced and elaborated. Then the finite element method is adopted to discretize the governing equations. Firstly, the model is validated based on the comparison between the numerical and experimental results. Then the influence of the internal flow velocity and fluid density on VIV dynamics is studied. The results show that multi-frequency response occurs when the flexible riser with various internal flow velocities and densities is subjected to external shear current. Under same shear current velocity, the IL mean deflection is enlarged with the increase of the internal flow velocity and fluid density. In addition, the internal flow velocity and fluid density have an evident effect on the vibrating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions. Moreover, mode and frequency transitions can be observed under different internal flow velocities and fluid densities.

CROSS-FLOW VORTEX-INDUCED VIBRATION OF A FLEXIBLE RISER WITH INTERNAL FLOW IN SHEAR CURRENT

As an important component transporting resources such as oil and mineral ores mixture from the seabed to the surface in ocean engineering, vortex-induced vibration (VIV) of flexible risers can be encountered when the risers are subjected to the external environmental conditions. As VIV can lead to structural fatigue for the riser system, which threatens to the facility safety during deepsea resource exploitation, it is of great significance to investigate VIV mechanism and dynamics. Therefore, VIV dynamics of a flexible fluid-conveying riser undergoing external shear current is studied based on the combination of the Euler-Bernoulli beam theory and the semi-empirical hydrodynamic model. The finite element method and Newmark-β method are adopted to discretize and solve the governing equation. The model is firstly validated by comparing with the experimental data in order to examine the accuracy of the present model. Subsequently, cross-flow (CF) VIV response of the fluid-conveying riser is mainly examined and analyzed while various internal flow velocity and fluid density are considered and changed. The results show that when the flexible riser is subjected to both internal flow and shear current, there appears multi-frequency response for CF VIV. And the CF vibrating frequency and the CF root mean square (RMS) displacement are evidently influenced by the internal flow velocity and fluid density. With the increase of the internal flow velocity and fluid density, the CF vibrating frequency decreases while the RMS displacement shows an increasing trend in CF direction. Furthermore, in addition to the variation of the CF vibrating frequency and RMS displacement, the change of internal flow densities can cause notable mode and frequency transitions.

Random Response of Wake-Oscillator Excited by Fluctuating Wind

Abstract Many wake-oscillator models applied to study vortex-induced vibration (VIV) are assumed to be excited by ideal wind that is assumed to be uniform flow with constant velocity. However, in the field of wind engineering, the real wind is generally described as being composed of mean wind and fluctuating wind. A wake-oscillator excited by fluctuating wind should be treated as a randomly excited and dissipated multi-degree-of-freedom (DOF) nonlinear system. The study of such a system is challenging and so far there is no exact solution available. The present paper aims to carry out the study on the stochastic dynamics of VIV. The stochastic averaging method of quasi-integrable Hamiltonian systems under wideband random excitation is applied to study both the original Hartlen–Currie wake-oscillator model and a modified version excited by fluctuating wind. The probability and statistics of the random response of wake-oscillator in resonant (lock-in) case and in non-resonant case are analytically obtained, and the analytical results are confirmed using numerical simulation of the original system.

Time-domain analysis of vortex-induced vibration of a flexible mining riser transporting flow with various velocities and densities

Vortex-induced vibration (VIV) can be inevitably encountered in deep ocean mining. As the internal flow is transported axially in the flexible riser, complicated VIV dynamics occurs undergoing both the internal and external flows. Therefore, the object here is to explore the effect of the internal flow with different velocities and densities on VIV response under various uniform current. In this study, a semi-empirical time domain prediction method for VIV dynamics of flexible risers considering both internal and external flows is introduced and adopted. The governing equations are discretized and solved by using finite element method. Firstly, validations are made for VIV without internal flow based on the numerical results and experimental data. Comparisons prove that the simulation could reproduce the VIV dynamics of a flexible riser. Then with the increase of the internal flow velocities and densities, the effect of the internal flow on VIV response is examined. It is found that the dominating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions are notably influenced by the internal flow velocity and density. Besides, the drag coefficient and IL mean deflection are detected magnified while the internal flow velocity and density are increased under different external flow velocities. It should be noted that the change of the internal flow velocity and density could trigger new mode response of the flexible riser, leading to mode transition for the IL and CF dominating modes. In addition, VIV dynamics shows a similar changing trend with the increase of the internal flow velocity and density when the flexible fluid-conveying riser is subjected to different external flow velocities.

Block-based adaptive mesh refinement for fluid–structure interactions in incompressible flows

In this study, an immersed boundary (IB) approach on the basis of moving least squares (MLS) interpolation is proposed for analyzing the dynamic response of a rigid body immersed in incompressible flows. An improved mapping strategy is proposed for a quick update of the signed distance field. A CIP-CSL (constraint interpolation profile - semi-Lagrangian) scheme with a compact stencil is adopted for the convective term in momentum equation. Fluid–structure interaction problems can be solved by either the weak or the strong coupling schemes according to the density ratio of the solid and fluid. This research is based on our previous studies on block-structured adaptive mesh refinement (AMR) method for incompressible flows (Liu & Hu, 2018). Present AMR-FSI solver is proved to be accurate and robust in predicting dynamics of VIV (vortex induced vibration) problems. The efficiency of the adaptive method is demonstrated by the 2D simulation of a freely falling plate with the comparison to other numerical methods. Finally, the freely falling and rising 3D sphere are computed and compared with corresponding experimental measurement.

Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement

A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61(3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenomenon due to spontaneous symmetry breaking are observed in this numerical study. The significant characteristic vortex modes in the near-wake region are extracted via dynamic modal analysis and the interference between the gap flow and VIV is found to be mutual. In a vibrating side-by-side arrangement, the lock-in region with respect to reduced velocity becomes narrower due to the interference from its stationary counterpart. The frequency lock-in occurs and ends earlier than that of an isolated vibrating circular cylinder subjected to an identical flow environment. Similar to a tandem cylinder arrangement, in the post-lock-in region, the maximum vibration amplitudes are escalated compared with those of an isolated circular cylinder configuration. On the other hand, subjected to the influence from VIV, the biased gap flow deflects toward the vibrating cylinder quasi-stably during the frequency lock-in process. This behavior is different from the reported bi-stable regime in a stationary side-by-side arrangement. The analyses show that the flip-flop is associated with a characteristic low flip-flopping frequency, which is dependent upon the values of gap ratio, Reynolds number and the symmetry of the gap flow strength in a time-averaged sense. The disappearance of the flip-flop during the frequency lock-in of vibrating side-by-side arrangements is further investigated through a critical-point concept and a critical vortex merging distance.

A harmonic balance technique for the reduced-order computation of vortex-induced vibration

We present a harmonic balance (HB) method to model frequency lock-in effect during vortex-induced vibration (VIV) of elastically mounted circular cylinder and a flexible riser section in a freestream uniform flow. The fluid flow and structure are coupled by a fixed-point iteration process through a frequency updating algorithm. By minimizing the structural residual in the standard least-square norm, the convergence of HB-based fixed-point algorithm is achieved for a range of reduced velocity. To begin with, the HB solver is first assessed for a periodic unsteady flow around a stationary circular cylinder. A freely vibrating circular cylinder is then adopted for the reduced-order computation of VIV at low Reynolds numbers of Re=100 and 180 with one- and two-degrees-of-freedom. The coupled VIV dynamics and the frequency lock-in phenomenon are accurately captured. The results show that the HB solver is able to predict the amplitude of vibration, frequency and forces comparable to its time domain counterpart, while providing a significant reduction with regard to overall computational cost. The proposed new scheme is then demonstrated for a fully-coupled three dimensional (3D) analysis of a linear-elastic riser section undergoing vortex-induced vibration in the lock-in range. The results reveal the 3D effects through isosurfaces of streamwise vorticity blobs distributed over the span of flexible riser section. In comparison to time domain results, the 3D flow-structure interactions are accurately predicted while providing a similar speed up rate that of 2D simulations. This further corroborates that the HB solver can be extended to 3D flow-structure dynamics without compromising efficiency and accuracy.

A study on the effects of axial stiffness and pre-tension on VIV dynamics of a flexible cylinder in uniform cross-flow

In this paper we present the experimental results of a study on the effects of pre-tension and axial stiffness on vortex-induced vibration (VIV) of a horizontally mounted flexible cylinder. The parameters examined included vibration amplitude and its suppression, mean and fluctuating tensions, frequency increase rate, drag and lift coefficients, and in-line (IL) and cross-flow (CF) harmonics. The test model was selected with a low bending-stiffness, low mass ratio (cylinder's mass/mass of replaced water), and high aspect ratio (length/diameter=162). The tests were conducted in the subcritical Reynolds number regime (Re=2000–20,000). The effects of pre-tension and axial stiffness were studied for five different cases in which these parameters were varied. Our results showed that high pre-tension, which reduces vibration amplitude, can significantly raise the lift coefficient. Specifically, a fourfold increase in pre-tension from 73.5N through 294N was found to correspond to an increase of approximately 57% in lift coefficient and a decrease of approximately 30% in vibration amplitude. We also observed that the lock-in bandwidth of amplitude response narrowed with increase in pre-tension, whereas, it broadened with axial stiffness. In contrast to the vibration amplitude bandwidth, the lift bandwidth increased with increase in pre-tension. The fluctuating lift has a secondary peak at the point of maximum fluctuating drag. In addition, high applied pre-tensions delay the excitation of higher modal frequencies compared to lower pre-tensions within the same range of flow velocities. Spectral analysis of all the data showed a broadband frequency response in the lower branch. The ratio of dominant IL-to-CF frequency was almost 2.0 except for the IL lock-in and upper branch regions. In the IL lock-in region the ratio was found to be 1, and in the upper branch the ratio reached 4.0 for the highest pre-tension (294N), accompanied by broadening of the region in which this ratio is over 2.0. The rate of mean and fluctuating tensions increased with increasing axial stiffness and decreased with increasing pre-tension. For constant pre-tension, the increase of axial stiffness resulted in higher frequency increase rates, while the frequency increase rate slowed with the increase of pre-tension. Hence, the parameter TL2/EI may not be a reliable criterion for assessment of the frequency increase rate regardless of pre-tension. Regarding the inference of the VIV response from tension measurements, we found that the fluctuating tension component showed a similar trend with corresponding CF vibration amplitude and increased for higher vibrational modes. In addition, we were able to simply extract excited IL and CF frequencies from tension measurements.

Comments: OTC Winners

Congratulations are due this year’s winners of the Offshore Technology Conference (OTC) awards. The recipients will be honored during OTC, which runs 2–5 May at the Reliant Center in Houston. The OTC Distinguished Individual Achievement Award will recognize J. Kim Vandiver, a professor at the Massachusetts Inst. of Technology. He is being honored for his technical breakthroughs in the dynamics of vortex-induced vibration, which have enhanced the design of structures to with-stand high ocean currents, enabling oil and gas production to occur in progressively deeper water. The 2005 OTC Distinguished Achievement Award for Organizations goes to Kerr-McGee Oil and Gas Corp. and Technip for their pioneering efforts in the Gulf of Mexico in delivering three generations of spar floating production systems in 9 years. This is the second OTC award for Kerr-McGee in recent years. In 2002, the company won the same award for its Neptune Spar project, the first spar production platform. Kerr-McGee and Technip have developed a total of five production spars, using three different designs, over the past decade. The collaboration resulted in the world’s first production spar—now referred to as a “classic” spar design—which was installed at the Kerr-McGee-operated Neptune field in the eastern Gulf of Mexico in 1997. In 2001, the companies developed the world’s first application of truss spars at the Kerr-McGee-operated Nansen and Boomvang gas fields in the East Breaks area of the Gulf of Mexico. Nansen lies in 3,678 ft of water, while Boomvang is in 3,453 ft. Another truss spar for the Gunnison field began production in 2002. Last year saw another world’s first with the development and delivery of the third-generation spar, called a “cell spar,” for the Kerr-McGee-operated Red Hawk field in the Gulf’s Garden Banks Block 877. Kerr-McGee holds a 50% interest in the field, with Devon Energy also taking a 50% share. Red Hawk is a two-well subsea development in 5,300 ft water depth. A sixth spar, using the truss design, is currently under construction for another deepwater project at Kerr-McGee’s Constitution field. The cell spar is designed essentially as an alternative to a long-distance tieback. The design consists of a vertical configuration of seven cylinders that are 20 ft in diameter and form a giant column that supports a 4,700-ton production platform. The spar is anchored to the seafloor by polyester moorings that are lighter, less expensive, and less corrosive than steel cables. Red Hawk’s production is at 120 million ft3/D of gas with expansion capacity of up to 300 million ft3/D. The breakthrough with the Red Hawk spar was its economy and small size. The less expensive cell spars will enable producers to look at deepwater reserves that in the past might have been too small to develop. Reserves previously required approximately 100 mil-lion BOE to justify development, but with smaller production platforms, reserves of less than half that size are now viable. Other producers have begun to adopt Kerr-McGee’s and Technip’s groundbreaking technology. Thirteen spars have been installed in the Gulf of Mexico, and Technip has built 10 of them and is currently constructing another. Technip also just signed a contract with Murphy Oil for the construction of a spar for the Kikeh field in Malaysia, which will be the first spar installed outside the Gulf of Mexico.