Cross-flow Vortex-induced Vibrations Research Articles

Numerical analysis of vortex-induced vibration of deepwater drilling riser based on Van der Pol wake oscillator model

Coupled equations of the dynamic model and the Van der Pol wake oscillator model are solved by the central finite difference method for the deepwater drilling riser. The vortex-induced vibration (VIV) response and fatigue life of the riser are calculated and the model validation is performed by comparing with the published experimental and simulation results. The effects of the top tension, current flow velocity, flow velocity profile, internal flow velocity as well as the installation of buoyancy modules on the VIV are discussed. Dynamic response and fatigue life of the riser under In-Line (IL) and Cross-Flow (CF) VIV are preliminarily analyzed. The results show that the VIV of the riser has multiple modes and exhibits a mixed behavior of standing waves and traveling waves. With the increase of top tension and flow velocity profile coefficient, the order of the VIV dominant mode and the peak values of the root mean square (RMS) of VIV displacement decrease, and the fatigue life of the riser is extended. With the increase of current flow velocity, the order of the VIV dominant mode increases and the riser fatigue life decreases. The effect of internal flow velocity on the riser VIV is neglectable. The installation of buoyancy modules can improve the riser stress state and extend the fatigue life. Compared with the CF VIV model, the calculated minimum fatigue life of the riser is extended under the IL and CF coupled VIV model due to the decrease of bending moment and the changing position of fatigue weak point.

Single degree of freedom vortex induced vibration of undulatory seal whiskers at low Reynolds number and various angles of attack: A computational fluid dynamics study

The cross-flow vortex-induced vibration (VIV) response of an elastically mounted idealized undulatory seal whisker (USW) shape is investigated in a wide range of reduced velocity at angles of attack (AOAs) from 0° to 90° and a low Reynolds number of 300. The mass ratio is set to 1.0 to represent the real seal whisker. Dynamic mode decomposition is used to investigate the vortex shedding mode in various cases. In agreement with past studies, the VIV response of the USW is highly AOA-dependent because of the change in the underlying vortex dynamics. At zero AOA, the undulatory shape leads to a hairpin vortex mode that results in extremely low lift force oscillation with a lowered frequency. The frequency remains unaffected by VIV throughout the tested range of reduced velocity. As the AOA deviates from zero, alternating shedding of spanwise vortices becomes dominant. A mixed vortex shedding mode is observed at AOA = 15° in the transition. As the AOA deviated from zero, the VIV amplitude increases rapidly by two orders, reaching the maximum of about 3 times diameter at 90°. An infinite lock-in branch is present for AOA from 60° to 90°, where the VIV amplitude remains high regardless of the increase in reduced velocity.

Large-eddy simulation of vortex-induced vibration of a circular cylinder at Reynolds number 10 000

The canonical scenario of cross-flow vortex-induced vibration (VIV) of a circular cylinder in the turbulent regime, which has been studied by several physical experiments in the literature, is reexamined in this study through high-fidelity large-eddy simulations (LES) at a Reynolds number 104. The VIV response (including vibration amplitude and frequency) and hydrodynamic coefficients predicted by the present LES agree with the experimental results better than previous numerical attempts. In addition, several phenomena reported by previous experimental studies are confirmed numerically for the first time. After validating against the experiments, new VIV characteristics and physical mechanisms are explored with confidence. First, a collective analysis on the frequency spectra of the displacement, lift, and velocity signals provides a complete picture of the frequency response of the system. In contrast, the use of a single signal may miss certain aspects of the frequency response, so that caution should be exercised. Second, spanwise correlation of primary vortex shedding is examined, where relatively low correlations in the upper and lower branches are likely because the vortex shedding patterns involve complex vortex generation and interaction. Third, the effect of mass ratio (m*) of the cylinder on the VIV response is analyzed with a range of m* (=1.4–3.4) relevant to cylindrical structures used in offshore engineering (such as subsea pipelines). The variations in the amplitude response, frequency response, and hydrodynamic coefficients with m* and reduced velocity are examined in detail. The present results suggest that a lighter pipeline is more susceptible to the onset of VIV.

Cross-flow vortex-induced vibrations of a circular cylinder under stochastic inflow at low Reynolds number

The vortex-induced vibrations of an elastically mounted circular cylinder (with mass ratio = 2) in stochastically fluctuating inflow are numerically studied at a Reynolds number of 150. Numerical simulations are carried out on a discrete forcing immersed boundary method (IBM) based in-house fluid–structure interactions (FSI) solver. The existence of gust in the incoming flow causes substantial qualitative and quantitative changes in the vibrating system’s flow and response properties. The oscillation amplitude and extent of lock-in have been found to increase. In the noisy inflow, the vibrating system experiences higher fluid forces than the uniform inflow. A comparison with the vibration characteristics under uniform flow has been conducted to understand the noise’s influence better. Standard vortex-shedding patterns are not detected in the wake. Instead, rich vortex interaction behavior like vortex-merging, vortex-pairing, and formation of mushroom-shaped vortical structures are documented.

VIV of two rigidly coupled side-by-side cylinders at subcritical [formula omitted

Cross-flow vortex-induced vibration (VIV) of two rigidly coupled circular cylinders in side-by-side arrangement at a Reynolds number of 1000 is numerically investigated using direct numerical simulation. A low mass ratio of 1.27 is considered and the nondimensional centre-to-centre spacing ratio is fixed at 2.0. The reduced velocity ranges from 2 to 13. Three response branches are identified and these responses result in different wake and hydrodynamic characteristics. The cases with large amplitudes feature the co-shedding and lower pressure in the gap, while those with small amplitudes are characterised by two parallel vortex streets. Characterisation and quantification of the flow fields of two rigidly coupled side-by-side cylinders undergoing VIV, which have seldom been reported in the existing research, are elaborated on in this study via the statistical analysis in terms of the turbulent wake visualisation, Reynolds stresses, turbulence kinetic energy (TKE) and proper orthogonal decomposition (POD) analysis. It is found that the cases with large amplitudes show a more unstable wake with sharp increases in the Reynolds stresses and TKE in the near wake. Moreover, the large amplitudes are seen to weaken the asymmetry of the wake and the initial POD modes are more energetic. A reformulated version of the novel force decomposition technique is used to realise the measurement of the time-dependent contributions from each mode to the pressure drag. The large amplitude cases are associated with the drag mode and the lift mode, whereas three modes are observed as the amplitude decreases.

Applying Bayesian optimization to predict parameters in a time-domain model for cross-flow vortex-induced vibrations

As the demand for harvesting offshore energy increases worldwide, the need for slender structures, such as marine risers and power cables, will increase. The dominating loads for deep water applications will primarily be caused by current-structure interactions, where vortex-induced vibrations (VIV) are known to be a challenging response type to handle correctly during design. Semi-empirical time-domain models are promising for VIV prediction, but uncertainties related to simplifications in the hydrodynamic load model and empirical parameters lead to over-conservative designs, where the parameters are estimated from model tests within a relatively low Reynolds number range. The aim of this paper is to present an efficient tool to estimate empirical hydrodynamic parameters directly from test data. To illustrate the method, the hydrodynamic parameters were estimated from pure cross-flow VIV model tests in a steady current with Reynolds numbers in the range of 40,000-120,000. The parameters were updated sequentially by using a Bayesian optimization framework, with the aim of minimizing an objective function that incorporates the response errors between time-domain VIV simulations and model test data. It is shown that three empirical parameters can be obtained simultaneously, resulting in small response errors but the optimal parameters were overly sensitive to variations in the flow velocity. The optimal parameters were used to reconstruct the drag amplification related to cross-flow VIV and in forced motion simulations to illustrate how the parameters in the load model would map into the traditional formulation in terms of the added mass and excitation coefficient.

Numerical investigations of the effects of spanwise grooves on the suppression of vortex-induced vibration of a flexible cylinder

Numerical investigations of Vortex-induced Vibration (VIV) suppression of a flexible cylinder with spanwise grooves in the uniform flow have been conducted by viv3D-FOAM-SJTU solver, which imports the thick strip model into OpenFOAM. The Reynolds-averaged Navier-Stokes (RANS) method is adopted to calculate hydrodynamic forces at each fluid strip. The vibrations of cylinder are solved through the Euler-Bernoulli bending beam hypothesis and the Finite Element Method (FEM) in two directions. During simulations, four spanwise grooves are arranged equally around the cylinder with an interval of 90° at two configurations. The spanwise groove keeps a constant width of w = 0.2D and a variable groove depth among 0.08D, 0.12D and 0.16D. Specific comparisons on Root Mean Square (RMS) vibration displacements, vibration modal responses, vibration frequency responses and vortex structures are conducted to analyze suppression effects of the spanwise grooves. Numerical studies indicate that the appropriate choose of groove geometry and arrangement can effectively reduce both crossflow and inline VIV responses.

Cross-flow vortex-induced vibrations of a top tensioned riser subjected to boundary disturbances with frequencies close to vortex shedding

In the present paper, the effects of external disturbances on cross-flow vortex-induced vibrations (VIVs) of a top tensioned riser are investigated based on a wake oscillator model. Two different flow conditions, namely uniform and linearly sheared profiles, and different combinations of disturbance frequency and amplitude were considered. Simulation results showed that synchronization between VIV and disturbance can occur when the disturbance frequency approaches the Strouhal frequency or when the disturbance amplitude is significant. This synchronization leads to a significant increase in riser response and the commonly used industry practice of simulating VIV and disturbance independently and summing both could underestimate the actual fatigue rate in such condition. However, in certain cases where VIV did not lock onto the disturbance, it was found that the disturbance could suppress the VIV and the industry practice tends to overestimate the fatigue rate.

Piezoelectric energy extraction from a cylinder undergoing vortex-induced vibration using internal resonance

A novel concept of utilizing the kinetic energy from ocean currents/wind by means of internal resonance is proposed to address the increasing global energy demand by generating clean and sustainable power. In this work, a non-linear rotative gravity pendulum is employed to autoparametrically excite the elastically mounted cylinder for a wide range of flow velocities. This concept is adopted to increase the oscillation amplitude of the cylinder due to vortex-induced vibration (VIV) in the de-synchronized region for energy harvesting. In this regard, a VIV-based energy harvesting device is proposed that consists of a cylinder with an attached pendulum, and energy is harvested with bottom-mounted piezoelectric transducers. The cylinder undergoes VIV when it is subjected to fluid flow and this excites the coupled fluid-multibody cylinder-pendulum system autoparametrically. In the de-synchronized region, when the vortex shedding frequency becomes two times the natural frequency of the pendulum, an internal resonance occurs. This helps in achieving a higher oscillation amplitude of the cylinder which does not happen otherwise. This study is focused on the two degree-of-freedom (2-DoF) cylinder-pendulum system where the cylinder is free to exhibit cross-flow vortex-induced vibrations subjected to the fluid. The objective of this work is to numerically investigate the effect of a non-linear rotative gravity pendulum (NRGP) on the VIV characteristics and piezoelectric efficiency of the system. The numerical model is based on the wake-oscillator model coupled with the piezoelectric constitutive equation. The influence of the frequency ratio, mass ratio, torsional damping ratio, and ratio of cylinder diameter to pendulum length of the NRGP device on response characteristics due to VIV is also investigated. A detailed comparative analysis in terms of electric tension and efficiency is performed numerically for flows with a wide range of reduced velocities for the cylinder with and without NRGP. A comprehensive study on the implications of internal resonance between the pendulum and a cylinder undergoing VIV on generated electric tension is also reported.

Numerical study on vortex-induced vibrations of a flexible cylinder subjected to multi-directional flows

Vortex-induced vibrations (VIVs) of a flexible cylinder subjected to multi-directional flows have been studied based on a wake oscillator model. The multi-directional flow comprises two slabs of flows in different directions, with each slab having a uniform uni-directional profile. The dynamics of the flexible cylinder is described based on the linear Euler–Bernoulli beam theory, and a wake oscillator model is uniformly distributed along the cylinder to model the hydrodynamic force acting on it. The dynamics of the coupled system has been solved numerically using the finite element method, and simulations have been conducted with the cylinder subjected to multi-directional flows with different angles between the two slabs. A large number of different initial conditions have been applied, and more than one steady-state response has been captured. The steady-state responses exhibit two different patterns: one is characterized by two waves traveling in opposite directions, while the other is dominated by a single traveling wave. The cross-flow VIV primarily occurs in the local cross-flow direction, and a transition of its vibrating direction happens at the interface of the two flows. Such transition is not observed in the inline VIV, and significant vibrations at the double frequency appear in both local cross-flow and inline directions. Energy analysis shows that this transition is boosted by a specific energy transfer pattern between the structure and the flow, which excites the vibration of the cylinder in some directions while damps it in others.

Prediction model for multidirectional vortex-induced vibrations of catenary riser in convex/concave and perpendicular flows

This study presents an advanced numerical prediction model based on nonlinear wake oscillators for the investigation of multidirectional vortex-induced vibration (VIV) responses of a long catenary riser depending on the structural curved configuration versus the incoming flow direction. By considering a uniform free-stream flow aligned with the initial curvature plane of the catenary riser in a convex or concave shape, the normal flow velocity component is nonlinearly sheared owing to the spanwise variation of inclination angles. This is different from the perpendicular flow case in which the normal flow velocity is spatially constant. To capture the influence of flow direction on the three-dimensionally coupled cross-flow and in-line VIV, distributed wake oscillators are introduced and applied to simulate the fluctuating hydrodynamic lift and drag forces that account for the important effects of cylinder inclination, variable vortex excitation frequencies, global–local​ displacement relationships, and relative flow-cylinder velocities. The amplified mean drag force and the axial force depending on the tangential flow velocity are also considered. These empirical hydrodynamic effects are nonlinearly coupled with the equations of riser three-dimensional motion, and the overall governing equations are numerically solved to assess the multimode, multi-frequency and multi-degree-of-freedom responses. Validation of the model is carried out for VIV of flexible straight and curved cylinders based on experimental results in the literature. Parametric investigations are performed by varying the incoming flow velocities in perpendicular, convex and concave configurations for a long catenary riser with a low mass-damping ratio. In-plane (horizontal and vertical) and out-of-plane VIV features are presented and discussed in terms of space–time varying amplitudes, drag-amplified shape reconfigurations, oscillation frequencies, lock-in occurrences, dual resonances, orbital motion trajectories, fluid–structure energy transfer, and multimodal contributions. Overall prediction results highlight the influence of the cylinder geometric configuration versus the incoming flow orientation on multidirectional VIV characteristics that should be recognised and incorporated into practical analysis tools.

A Modified Wake Oscillator Model for the Cross-Flow Vortex-Induced Vibration of Rigid Cylinders with Low Mass and Damping Ratios

The classical wake oscillator model is capable of predicting the vortex-induced vibration response of a cylinder at high mass-damping ratios, but it fails to perform satisfactorily at low mass-damping ratios. A modified wake oscillator model is presented in this paper. The modification method involves analyzing the variation law of the add mass coefficient of the cylinder versus reduced velocity and expressing the reference lift coefficient CL0 as a function of the add mass coefficient. The modified wake oscillator model has been demonstrated to have better accuracy in capturing maximum amplitudes and flow velocity at low mass-damping ratios. However, the modified model at present form is unable to accurately predict the vortex-induced vibration response at high damping ratios. The purpose of this paper is to propose a new modification idea. In order to achieve better results when applying this modification idea to particular objects, it may be necessary to first understand the response law of these kinds of objects.

Development of a Time-Domain Simulation Code for Cross-Flow Vortex-Induced Vibrations of a Slender Structure with Current Using the Synchronization Model

In this paper, the numerical analysis method for the cross-flow vortex-induced vibration (CF VIV) analysis based on the proposed procedure for CF VIV analysis of slender structures is developed. In order to consider the changes in the incoming flow according to the static configuration of the slender structures due to the current, the proposed procedure has three stages. A slender structure is modeled as the lumped-mass line, and the dynamic relaxation method known as the numerical technique for a slender structure with large geometric nonlinearity is applied in the static analysis. The comparison studies with a commercial program are carried out to validate the developed code. The vortex-induced force on slender structures is considered with the synchronization model. To verify the developed CF VIV analysis procedure and numerical method for a slender structure, VIV analysis of the tensioned flexible risers under a uniform and shear current is performed. The simulated results of CF RMS displacement show good agreement with the results of the model test It is found that a tensioned riser vibrates with one dominant frequency in resonance with the nth mode, even though multi-frequencies components of the vortex shedding along the riser due to the shear current occurs.

On the study of vortex-induced vibration of a straked pipe in bidirectionally sheared flow

Helical strakes are widely used to suppress vortex-induced vibration (VIV) in ocean engineering. However, the VIV response and suppression efficiency of the straked pipe are unclear under the recently discovered bidirectionally sheared flow field. Experiments on vortex-induced vibration for a flexible pipe with three kinds of helical strakes were carried out in an ocean basin. The bare pipe model was 28.41mm in diameter and 7.64m in length. Three kinds of helical strakes with different pitch/height (17.5D/0.15D, 17.5D/0.25D,and 17.5D/0.35D) were applied. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. The reduced velocities based on the tested first natural frequency of the bare pipe in water reached 30.79. The cross-flow and in-line VIV amplitudes, VIV suppression efficiency, and fatigue damage are presented in this article. The results showed that the helical strakes can suppress bidirectionally sheared flow-induced VIV significantly at a high reduced velocity regime with fatigue damage suppression efficiency over 99% in the CF and IL directions, but cannot suppress the in-line initial displacement, which was also found in previous studies as a drawback of helical strakes.

Numerical investigation on competitive mechanism between internal and external effects of submarine pipeline undergoing vortex-induced vibration

This work aims to model and explore the competitive mechanism between the internal flow effect (IFE) and external current effect (ECE) on the cross-flow vortex-induced vibration (VIV) of a free-span submarine pipeline transporting an axial internal flow. Considering the coupling between the structure and fluids, the partial differential equations of pipeline system are described by Euler-Bernoulli beam theory coupled with the wake oscillator model. To obtain the VIV response of pipeline at different internal flow and external current velocities, the generalized finite difference method (GFDM) and Houbolt method (HM) are employed for spatial and temporal discretizations for equations, respectively. The results indicates that when the IFE is not accounted, the higher-order VIV modes of the pipe are successively excited by ECE. Of interest is that coupling flutter phenomenon between even-order and adjacent modes will occur. Whereas, when the fluid inside the pipe flows, which means the IFE occurrence to be observed, the coupled flutter phenomenon disappears along with significant enlargement of the amplitude in even-order modes. Meanwhile, the mode transition is associated with internal flow velocity and a continuous change in the external flow velocity.

Numerical investigation of VIV responses of the flexible riser system modelled as tensioned cable subjected to shear flow

The crossflow vortex-induced vibration (VIV) responses of the tensioned cable subjected to the sheared flow velocity profile are investigated numerically using the wake oscillator model. A comparative study is carried out on the VIV response characteristics between the tensioned cable and beam with an aspect ratio (L/D) of 3000. The study was conducted on tensioned cable having different L/D of 2000 and 3000 achieved by varying both diameter and length of the cable. The effect of top tension on the RMS crossflow displacement responses is investigated. The RMS crossflow displacement response is not sensitive to the boundary conditions for the flexible cylinder modeled as a tensioned cable. In contrast, the RMS crossflow displacement response of the lower L/D flexible cylinder modeled as a beam is sensitive to boundary conditions. The standing wave response pattern is observed for the beam with L/D of 500. The standing and traveling wave response patterns are combined for the tensioned cable with L/D = 500. Unlike finite tensioned beams, the higher mode responses are obtained even in the lower aspect ratio for tensioned cables.

Coupling effects of top-end dynamic boundary with a planar trajectory of “8” on three-dimensional VIV characteristics

The top-end dynamic boundary of riser is usually generated by the motion of the moored floating body in marine environment, inducing the oscillation of equivalent fluid velocity and mechanical features of the riser, and further affecting its vortex-induced vibration (VIV). In this paper, the double-degree-of-freedom (2DOF) top-end dynamic boundary with a trajectory of “8”, which widely exists in fluid-structure interactions of ocean engineering, is studied. A series of tests for a riser model with the aspect ratio of 250 are conducted under the combination of the top-end dynamic boundary and uniform flow, whose three-dimensional (3D) VIV characteristics and behaviors are investigated in detail. The effect of amplitude and frequency of “8”-shape dynamic boundary on VIV is discussed, following which the relationship and difference among four top-end boundaries of “8”-shape, in-line harmonic, cross-flow harmonic and static forms are compared and analyzed. The results indicate that some periodically oscillatory phenomena involving time-varying frequency, mode transition and amplitude modulation are induced by the “8”-shape dynamic boundary. The periodic effect of dynamic boundary on VIV shows orthogonality, which means the cross-flow dynamic boundary is mainly responsible to the oscillatory characteristics in in-line VIV while the in-line dynamic boundary corresponds to cross-flow VIV. At the same time, the in-line dynamic boundary has a certain disturbance on the in-line vibration. The amplitude and frequency responses of in-line VIV could be enhanced by “8”-shape dynamic boundary at low or medium reduced velocity, further growing with the increase of boundary amplitude and frequency.

Experimental investigation of vortex-induced vibration of a flexible pipe in bidirectionally sheared flow

The existence of a bidirectionally sheared flow field caused by internal solitary waves has recently been confirmed according to a field survey in the South China Sea. A model test of a tensioned flexible pipe in bidirectionally sheared flow was performed in an ocean basin. The model was 28.41mm in diameter and 7.64m in length. The purpose of the model test was to understand the response performance and obtain benchmark data of vortex-induced vibration (VIV) in bidirectionally sheared flow. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. Reduced velocities based on the tested first natural frequency in water reached 30.79. The cross-flow and in-line VIV amplitudes, response frequencies in statistics and time-domain analysis, traveling wave characteristics, phase synchronization and trajectories are presented in this article. The maximum root mean square (RMS) VIV amplitudes in the test reached 0.51 diameters and 0.18 diameters in the cross-flow and in-line directions, respectively. A relative low Strouhal number of 0.10 was found in the CF direction.

Internal flow effect on the cross-flow vortex-induced vibration of marine risers with different support methods

The present work investigates the effect of internal flow on the vortex-induced vibration (VIV) characteristics of a marine riser under different boundary conditions. A numerical model of the riser structure is established by considering the complex flow fields. The developed model is solved by the finite element theory and Newmark method, and it is verified by the experimental data. The effects of internal flow velocity and density on the vortex-induced dynamic responses with different support methods are studied. The results demonstrate that among different support methods, internal flow effect (IFE) has the greatest influence on the vortex-induced response of the riser with hinged-cantilevered support. In the case of hinged-cantilevered support method, the increment of the internal flow velocity and internal flow density has a negative influence on the vortex-induced vibration of the riser. In the case of fixed at both ends support method, the vibration amplitude and mode of riser decrease with the increment of flow density in riser. For the hinged-hinged support condition, the increment of the internal flow velocity slightly increases the amplitude of the riser and the vibration amplitude of riser decreases with the increase of density. This research may provide an efficient method for the VIV prediction, optimization design and operation control of the marine risers in practical applications.

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

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