In-line Vortex-induced Vibrations Research Articles

Coupled in-line and cross-flow vortex-induced vibration responses of a fluid-conveying riser with variable tension in shear flow

When seawater streams around risers, it causes vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF). Accurate prediction of coupled IL and CF VIV behaviors is essential for designing risers. To investigate the VIV of marine risers used in deep-sea oil and gas transportation, this study analyzed the coupled CF and IL VIV characteristics of the riser with axially time-varying tension under the combined effects of internal flow and oceanic linear shear flow. The work established the vibration control equation for the riser considering internal flow velocity, axial top tension, and bending stiffness, which is based on Euler-Bernoulli beam theory. The double Van der Pol diffusion wake oscillator model was used to simulate the vortex-induced forces from the ocean currents, and the internal fluid was considered as a single-phase incompressible liquid. Using the Generalized Integral Transform Technique (GITT), the coupled system of nonlinear partial differential equations was further transformed into a system of nonlinear ordinary differential equations for numerical solution. A parametric study was conducted to analyze the impact of current velocity, internal flow velocity, and diffusion term on the VIV responses, including structural displacement, structural frequency, displacement envelope, and displacement evolution. Numerical results indicate that the vibration modes of the riser are influenced by both CF and IL directions, and the effect of IL can not be ignored. The diffusion term has a significant impact on the vibrations of the riser. The number of vibration modes of the riser is mainly influenced by the increasing current velocity, and for a given current velocity, the vibration of the riser becomes chaotic when the dimensionless internal fluid velocity increased within a certain range.

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.

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.

Reynolds number effect on in-line vortex-induced vibration (VIVx) of a circular cylinder for wider reduced velocity range

Reynolds number effect on in-line vortex-induced vibration (VIVx) of a circular cylinder for wider reduced velocity range

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.

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.

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.

Decomposition of fluid forcing and phase synchronisation for in-line vortex-induced vibration of a circular cylinder

We present a decomposition of the streamwise fluid force for in-line vortex-induced vibration (VIV) to provide insight into how the wake drag acts as a driving force in fluid–structure interaction. This force decomposition is an extension of that proposed in the recent work of Konstantinidis et al. (J. Fluid Mech., vol. 907, 2021, p. A34), and is applied to and validated by our experiments examining a circular cylinder freely vibrating in line with the free stream. It is revealed from the decomposition and linear analysis that two regimes of significant vibration are in phase synchronisation, while they are separated by a desynchronised regime marked by competition between non-stationary frequency responses of the cylinder vibration and the vortex shedding. Of interest, such a near-resonance desynchronisation regime is not seen in the transverse vibration case.

Numerical study on the characteristics of vortex-induced vibrations of a small-scale subsea jumper using a wake oscillator model

Vortex-induced vibrations (VIVs) of a small-scale subsea jumper has been studied numerically using a wake oscillator model. The dynamics of the jumper is described based on the linear Euler–Bernoulli beam theory and a wake oscillator model is uniformly distributed along the jumper to model the hydrodynamic force acting on it. The dynamics of the coupled system has been solved using the finite element method and the responses of the jumper subjected to uniform flows in different directions have been analysed. Some important characteristics of jumper VIVs, such as multi-frequency multi-mode response, single-frequency multi-mode response as well as uncoupled cross-flow and in-line VIVs without dual resonance, have been identified and the underlying mechanism have been explored. One unique character of the jumper mode is that some segmental elements of the jumper would undertake significant rigid body motions in their axial directions. A qualitative comparison shows that these axial rigid body motions of the segmental elements may influence the hydrodynamic force and could play an important role in the reliable prediction of the jumper VIV.

Time-domain prediction of the coupled cross-flow and in-line vortex-induced vibrations of a flexible cylinder using a wake oscillator model

A numerical study, based on a wake oscillator model, has been performed to determine the three-dimensional vortex-induced vibration (VIV) responses of a flexible cylinder subjected to uniform and non-uniform flows. The coupling equations of the structural oscillator and wake oscillator models in the cross-flow (CF) and in-line (IL) directions, have been solved by employing a standard central finite difference method. The structural displacement, structural frequency, response wave pattern, response trajectory for three different aspect ratios, and four different flow profiles have been compared. As the shear parameter β increases, the maximum RMS values for a certain aspect ratio, in both CF and IL directions, display apparent decreasing tendencies. However, for a certain β, the maximum RMS values in CF and IL directions vary slightly with the increased aspect ratio. The VIV displacements in both CF and IL directions exhibit standing wave and traveling wave behaviors, simultaneously. Further, as the shear parameter β increases, the traveling wave behaviors becomes increasingly dominant. The value of dominant frequency of the CF displacement is always half of that of the IL displacement. The dominant frequency participates in the VIV process at all times, whereas, the other peak frequencies intermittently participate in the VIV process.

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part I: model description and validation

This paper is first of the two papers dealing with the nonlinear modelling and investigation of coupled cross-flow and in-line vortex-induced vibrations (VIVs) of flexible cylindrical structures. As a continuation of the previous work (Qu and Metrikine in Ocean Eng 196:106732, 2020) where a new single wake oscillator model was proposed and studied for VIVs of rigid cylinders, the present paper focuses on applying it to flexible cylinders. In this paper, the structure is modelled as an extensible Euler–Bernoulli beam and its 3D nonlinear coupling motion is described in the absolute coordinate system. The single van der Pol wake oscillator model with nonlinear coupling to the in-line motion of the structure, in addition to the classic linear cross-flow motion coupling, is uniformly distributed along the structure to model the hydrodynamic force acting on it. The finite element method has been applied to solve the dynamics of the coupled system, and the experiments of the VIV of a top-tensioned straight riser subjected to a step flow have been taken for the validation of the model. The model has been shown to be able to capture most features of VIVs of flexible cylinders, and a good agreement between the simulation results and the experimental measurements has been observed with regard to the amplitude, frequency and excited mode of both cross-flow and in-line vibrations, as well as the mean in-line deflection due to the amplified in-line force. While it is conventionally expected that the VIV of a flexible cylinder subjected to a uniform flow is dominated by a single frequency, a multi-frequency response is observed in the simulation results over the range of flow velocities through which the transition of the dominant mode of vibration occurs.

Forced Vibration Tests for In-Line Vortex-Induced Vibration to Assess Partially Strake-Covered Pipeline Spans

AbstractHelical strakes can suppress vortex-induced vibrations (VIVs) in pipelines spans and risers. Pure in-line (IL) VIV is more of a concern for pipelines than for risers. To make it possible to assess the effectiveness of partial strake coverage for this case, an important gap in the hydrodynamic data for strakes is filled by the reported IL forced-vibration tests. Therein, a strake-covered rigid cylinder undergoes harmonic purely IL motion while subject to a uniform “flow” created by towing the test rig along SINTEF Ocean's towing tank. These tests cover a range of frequencies, and amplitudes of the harmonic motion to generate added-mass and excitation functions are derived from the in-phase and 90 deg out-of-phase components of the hydrodynamic force on the pipe, respectively. Using these excitation- and added-mass functions in VIVANA together with those from experiments on bare pipe by Aronsen (2007 “An Experimental Investigation of In-Line and Combined In-Line and Cross-Flow Vortex Induced Vibrations,” Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway.), the IL VIV response of partially strake-covered pipeline spans is calculated. It is found that as little as 10% strake coverage at the optimal location effectively suppresses pure IL VIV.

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part II: on the importance of in-line coupling

To illustrate the influence of the in-line coupling on the prediction of vortex-induced vibration (VIV), the simulation results of the coupled cross-flow and in-line VIVs of flexible cylinders- obtained with three different wake oscillator models with and without the in-line coupling- are compared and studied in this paper. Both the cases of uniform and linearly sheared flow are analysed and the simulation results of the three models are compared with each other from the viewpoints of response pattern, fluid force, energy transfer and fatigue damage. The differences between the simulation results from the three models highlight the importance of the in-line coupling on the prediction of coupled cross-flow and in-line VIVs of flexible cylindrical structures.

A full three-dimensional vortex-induced vibration prediction model for top-tensioned risers based on vector form intrinsic finite element method

A novel three-dimensional model is proposed to study vortex-induced vibration (VIV) problems of top-tensioned risers. The model is based on the vector form intrinsic finite element (VFIFE) method and applicable to the fully-coupled cross-flow and in-line riser VIV scenarios. The axial time-varying dynamics and movement at the top end boundary of risers are also considered in the model. By using the VFIFE method, the structure is reduced to a set of particles whose motion satisfies Newton's second law and its response is described by the position change of particles in space. The fluctuating fluid force acting on the structure induced by vortex shedding is simulated using the classical van der Pol wake oscillator equation. In order to intuitively describe the time-varying top tension of the real structure, the real-time changes in top tension caused by the array of tensioners simulated by spring is also considered. The results of numerical simulation on top tension, dominant mode numbers, frequencies, and amplitudes are compared with the experiment to prove that the VFIFE method is feasible and effective in predicting the three-dimensional vortex-induced vibration response.

Prediction of Vortex-Induced Vibration Response of Deep Sea Top-Tensioned Riser in Sheared Flow Considering Parametric Excitations

Abstract It is widely accepted that vortex-induced vibration (VIV) is a major concern in the design of deep sea top-tensioned risers, especially when the riser is subjected to axial parametric excitations. An improved time domain prediction model was proposed in this paper. The prediction model was based on classical van der Pol wake oscillator models, and the impacts of the riser in-line vibration and vessel heave motion were considered. The finite element, Newmark-β and Newton‒Raphson methods were adopted to solve the coupled nonlinear partial differential equations. The entire numerical solution process was realised by a self-developed program based on MATLAB. Comparisons between the numerical calculation and the published experimental test were conducted in this paper. The in-line and cross-flow VIV responses of a real size top-tensioned riser in linear sheared flow were analysed. The effects of the vessel heave amplitude and frequency on the riser VIV were also studied. The results show that the vibration displacements of the riser are larger than the case without vessel heave motion. The vibration modes and frequencies of the riser are also changed due to the vessel heave motion

Experimental investigation on coupled cross-flow and in-line vortex-induced vibration responses of two staggered circular cylinders

In order to better understand the vortex-induced vibration mechanism of multiple cylinders, this article takes a relatively simple case of two staggered circular cylinders as the embarkation point and investigates their vortex-induced vibration characteristics by model test. The experimental Reynolds number ranges from 22,000 to 88,000. The in-line gap L is set as 3.0 D, 3.6 D, 4.2 D and 5.5 D in turn, and the cross-flow gap T is set as 0.7 D, 1.1 D, 1.5 D, 1.9 D, 2.3 D and 2.7 D, respectively. By measuring the vibrating response in model test, the response differences between the two staggered cylinders and the isolated cylinder and the effects of the gaps are discussed. The results indicate that the variation trend of response of the upstream cylinder with reduced velocity is basically similar to that of the isolated cylinder. However, the downstream cylinder shows some great differences. When the in-line gap ratio L/ D is 3.6, the cross-flow amplitude curve of downstream cylinder changes from “single peak” to “double peaks” with the increase in cross-flow gap ratio T/ D, and in-line amplitude curve even shows four different kinds of forms. When L/ D is increasing, maximum amplitudes of the downstream cylinder in two directions also show an increasing trend, and the wake galloping phenomenon even appears in some conditions. Generally, the case of staggered cylinders is a generalized combination of two circular cylinders in tandem and side-by-side arrangements, and this article has extended the research scope of the double-cylinder vortex-induced vibration to arbitrary flow direction.

Study on Vortex-Induced Vibration of Deep-Water Marine Drilling Risers in Linearly Sheared Flows in consideration of Changing Added Mass

In order to more accurately predict the coupled in-line and cross-flow vortex-induced vibration (VIV) response of deep-water marine drilling risers in linearly sheared flows, an improved three-dimensional time-domain coupled model based on van der Pol wake oscillator models was established in this paper. The impact of the in-line and cross-flow changing added mass coefficients was taken into account in the model. The finite element, Newmark-β, and Newton–Raphson methods were adopted to solve the coupled nonlinear partial differential equations. The entire numerical solution process was realized by a self-developed program based on MATLAB. Comparisons between the numerical calculations and the published experimental tests showed that the improved model can more accurately predict some main features of the coupled in-line and cross-flow VIV of long slender flexible risers in linearly sheared flows to some extent. The coupled in-line and cross-flow VIV of a real-size marine drilling riser, usually used in the deep-water oil/gas industry in the South China Sea, was analyzed. The influence of top tension force and seawater flow speed, as well as platform heave amplitude and frequency, on the riser in-line and cross-flow VIV was also discussed. The results show that the platform heave motion increases the VIV displacements and changes the magnitudes of peak frequencies as well as the components of frequencies. The platform heave motion also has a significant influence on the vibration modes of the middle and upper sections of the riser. The impact level of each factor on the in-line and cross-flow VIV response of the riser is different. The improved model and the results of this paper can be used as a reference for the engineering design of deep-water marine drilling risers.

A single van der pol wake oscillator model for coupled cross-flow and in-line vortex-induced vibrations

In this study a new wake oscillator model is proposed to describe the coupled cross-flow and in-line vortex-induced vibrations of an elastically supported rigid cylinder. Different from many other studies where two wake oscillators have been applied, the current model uses only one wake oscillator coupled to both cross-flow and in-line motions. The new model is based on the van der Pol oscillator with the classic acceleration coupling between the wake and cross-flow motion, while the in-line motion is coupled with the wake variable in a nonlinear manner. The predictions of this new model are compared with the existing experimental data and shown to be in good agreement. In addition to the conventional lock-in range that corresponds to reduced velocities between 5 and 8, another lock-in is predicted around reduced velocity of 2.5 due to the in-line vibration. Most importantly, the new model is proved to be able to predict the appearance of the ‘super-upper’ branch at small mass ratios without changing the tuning parameters. The limitations of the model associated with unrealistic predictions of free vibrations with very small mass ratios and those of forced in-line vibrations at high frequencies are also discussed along with a possible remedy.