Cross-flow Displacements Research Articles

Vortex-induced vibration prediction of an inclined flexible cylinder based on machine learning methods

Vortex-induced vibration (VIV) is a main cause of fatigue damage to slender flexible structures in offshore engineering, e.g., marine risers, mooring lines, submarine cables and pipelines. In this paper, attempts have been made to predict the VIV response of an inclined flexible cylinder commonly encountered in practice using different machine learning methods. Three different machine learning algorithms (i.e., BP neural network, support vector machine and Gaussian process regression) are employed to establish the prediction models. The data in our previous experimental tests (Xu et al., 2018) are adopted to establish the data set of the present research. The numbers of data samples for constructing the displacement and frequency prediction models in each direction are 10,500 and 500, respectively. The inclination angle, incoming flow velocity, axial tension and the position along the cylinder span are used as the input variables and the output variables are the root mean square values of the in-line and cross-flow displacements and the dominant oscillation frequencies. Compared to the previous studies, the effect of the axial tension and the large inclination cases are considered to establish more comprehensive prediction models. The results show that all the three methods can predict the displacement and frequency responses in the cross-flow and in-line directions with acceptable accuracy. After a detailed comparative analysis of the three machine learning methods, it is found that the BP neural network models tend to result in a certain degree of overfitting and some response characteristics predicted by the GPR models are not consistent with the conclusions from our previous experimental studies. Within the parameter space of the present research, the support vector machine is considered to be the most suitable method for predicting the VIV of the inclined flexible cylinder.

A data-driven reduced-order model based on long short-term memory neural network for vortex-induced vibrations of a circular cylinder

A data-driven reduced-order model (ROM) based on long short-term memory neural network (LSTM-NN) for the prediction of the flow past a circular cylinder undergoing two-degree-of-freedom vortex-induced vibration in the upper transition Reynolds number regime with different reduced velocities is developed. The proper orthogonal decomposition (POD) technique is utilized to project the high-dimensional spatiotemporal flow data generated by solving the two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) equations to a low-dimensional subspace. The LSTM-NN is applied to predict the evolution of the POD temporal coefficients and streamwise and cross-flow velocities and displacements of the cylinder based on the low-dimensional representation of the flow data. This model is referred to as POD-LSTM-NN. In addition, the force partitioning method (FPM) is implemented to capture the hydrodynamic forces acting on the cylinder using the surrounding flow field predicted by the POD-LSTM-NN ROM and the predicted time histories of the lift and drag forces are compared with the numerical simulations.

CFD simulation of vortex-induced vibration of an elastic cylinder in subcritical flow regime using a two-way coupled model validated by experiment

The vortex-induced vibration (VIV) responses of an elastic cylinder have been numerically investigated using the two-way fluid-structure interaction model. The crossflow displacement (y) responses obtained from experiments agree well with that the results obtained from the numerical simulation. Further, the parametric study has been carried out on an elastic cylinder for various reduced velocities (Vr) ranging from 6.25 to 15.00 with an aspect ratio (L/D) of 100 using two way coupled model. The higher-order frequency components were observed in the force coefficients except for Vr of 13.13. In contrast, only a single frequency component was observed in both crossflow and inline displacements, except for Vr of 15.00 in inline response. The infinite lock-in was observed for the crossflow amplitude responses in the Vr range of 6.25–15.00. The finite lock-in was observed in the inline amplitude responses in the Vr range of 6.25–15.00 and reached the maximum amplitude in the Vr range of 9.88–11.49, where the drag force first frequency component is synchronized with the structure's second natural frequency and then decreases up to Vr of 15.00. The drag force frequency component follows harmonics in the limited range of Vr 6.25 to 9.59.

Dual-frequency vortex-induced vibrations of long flexible stepped cylinders

Flexible structures within a non-uniform inflow may undergo complex vortex-induced vibrations (VIV) containing multiple frequencies and vibration modes. Therefore, the critical question arises on whether and how a flexible cylinder's structural response and fluid forces undergoing multi-frequency vibrations resemble or differ from mono-frequency vibrations. Therefore, we experimentally studied the problem of dual-frequency VIV of a stepped flexible cylinder, viz., a large-aspect ratio flexible cylinder consisting of two segments with different diameters and rigid cylinder forced vibration experiments. The results show that the maximum in-line (IL) and cross-flow (CF) displacements and the frequency ratio of the stepped cylinder separated by individual frequency resemble those of a uniform cylinder vibrating in the uniform flow at a single frequency. In addition, it is found that forced vibration results from rigid cylinders undergoing multi-frequency IL and CF motion can improve the prediction of the multi-frequency flexible cylinder VIV, provided the amplitudes and phases, as well as the true reduced velocity Vr for each of the dual frequencies match, especially when Vr∈[4,8].

Experimental Study on Vortex-Induced Vibration Coupling Wake Interference of Multi-Riser Groups with Sensitive Spacing

The “riser group—fluid between risers” is taken as the carrier, and the experiment on vortex-induced vibration of tandem riser groups coupling interference effect under sensitive spacing is performed. The least-square method is used to linearly fit the reduced velocity and main frequency, and the rule of Strouhal numbers is analyzed. Each mode is separated based on the mode decomposition theory, and the mode conversion mechanism is also explored. The concept of “interference efficiency” is introduced to study the dynamic characteristics and response evolutions of different riser groups. The results show that the wake shielding effect widely exists in tandem riser groups, and the interference effect of midstream and downstream risers on their upstream risers is significantly lower than that of upstream risers on midstream and downstream risers. The trajectories of midstream and downstream risers lag behind their upstream risers due to multiple shadowing effects, the vibration frequency range of downstream riser is widened and the dominant frequency is extremely unstable. Compared with the isolated riser, wake interference suppresses the vibration displacement of the midstream and downstream risers in the in-line direction, and enhances the displacement of upstream and midstream risers in the cross-flow direction. The interference effect of the fluid between risers at low velocities is stronger than that at higher velocities, and the cross-flow displacements of upstream risers are always in the interference enhancement region. It is urgent to pay attention to the cross-flow displacement of upstream and midstream risers in tandem riser groups considering the safety design.

The effect of time-varying axial tension on VIV suppression for a flexible cylinder attached with helical strakes

Flexible cylindrical structures, such as top-tensioned risers (TTRs) and tethers of tension leg platforms (TLPs), usually vibrate under the combined excitation of vortex shedding and time-varying axial tension. Helical strakes are widely used to suppress vortex-induced vibration (VIV). The VIV suppression effectiveness of helical strakes for a flexible cylinder under axial tension excitation is still unknown. Model tests were conducted to investigate the effect of time-varying axial tension on VIV suppression for a flexible cylinder fitted with helical strakes. Three tension amplitude ratios (Tv/Tc = 0.1, 0.2 and 0.3, where Tv is the amplitude of the varying tension and Tc is the constant axial tension) and four tension frequency ratios (fv/f1 = 0.5, 1.0, 2.0 and 4.0, where fv is the frequency of the varying tension and f1 is the fundamental natural structural frequency) were considered. The vibration displacements were reconstructed using the measured strains by the modal analysis method. The dominant mode, response frequency and displacement amplitude were determined to show the influence of axial excitation on the dynamic characteristics of the flexible cylinder attached with helical strakes. When the reduced velocity is low, the second-order mode vibrations of the straked cylinder with axial excitation are excited. Due to the axial excitation, the straked cylinder has large cross-flow (CF) and in-line (IL) displacements at low reduced velocities. The displacement contours in the case of fv/f1 = 1.0 are remarkably different from those in other cases. When the reduced velocity increases, the effect of vortex shedding is enhanced. Both fv induced by axial excitation and the fn induced by vortex shedding are prominent, meaning that both vortex shedding and axial excitation affect the vibration of the straked cylinder. Under axial excitation, the IL displacements of the straked cylinder are enlarged, especially in the case of fv/f1 = 1.0. Axial excitation can reduce the VIV suppression efficiency of helical strakes.

Numerical simulation of super upper branch of a cylindrical structure with a low mass ratio

SST (shear stress transport) k-ω and Newmark-β methods are used to comprehensively understand vortex-induced vibration (VIV) characteristics of a cylindrical structure with a mass ratio of 2.6 in a range of reduced velocity from 2.0 to 14.0. The details of drag and lift forces, cross-flow and streamwise displacements, vortex pattern, trajectory, and frequency of VIV are presented and compared systematically with the experimental work of Jauvtis and Williamson that first captured the super upper branch in VIV with the maximum value of 1.5 D (diameter). In this study, the numerical simulation results successfully captured the initial branch, the lower branch, and the super upper branch. Very few research studies have successfully simulated the super upper branch by numerical methods. The vibration amplitude corresponding to the super upper branch is stable and the maximum value of the super upper branch is 1.46 D, which is fairly consistent with the results of the Jauvtis and Williamson experiment. This research also successfully captured the law of trajectory under different reduced velocities. With the reduced velocity increasing, the trajectories switch from an irregular shape to a regular "Figure 8″ shape and then enter into an irregular movement, finally again into a regular movement of a Figure 8 shape or crescent. In the range of the super upper branch, the vibration trajectories gradually change from a Figure 8 shape to a crescent shape with the increase of the transverse vibration amplitude. This work has successfully captured the different vortex patterns corresponding to each branch under different reduced velocities, and found the transitional forms of 2S to 2T, 2T to 2P, and 2P to 2S, respectively.

Experimental investigation on in-plane/out-of-plane vortex-induced vibrations of curved cylinder in parallel and perpendicular flows

This study is motivated by an industrial need to better understand the vortex-induced vibration (VIV) of a curved structure subject to current flows with varying directions whose data for model calibration and validation are lacking. In this paper, new experimental investigations on the two-degree-of-freedom in-plane/out-of-plane VIV of a rigid curved circular cylinder immersed in steady and uniform free-stream flows are presented. The principal objective is to examine how the approaching flow direction versus the cylinder curvature plane affects cross-flow and in-line VIV and the associated hydrodynamic properties. This is achieved by testing the curved cylinder in 3 different flow orientations comprising the parallel flows aligned with the curvature vertical plane in convex and concave configurations, and the flows perpendicular to the curvature plane. The case of varying flow velocities in a subcritical flow range with a maximum Reynolds number of about 50,000 is considered for the curved cylinder with a low mass ratio and damping ratio. Experimental results are presented and discussed in terms of the cylinder response amplitudes, inclination angles, mean displacements, motion trajectories, oscillation frequencies, hydrodynamic forces, relative phases, fluid excitation and added inertia coefficients. Comparisons with other experimental results of curved and straight cylinder VIV are also presented. The experiments highlight the important effects of cylinder curvature versus flow orientation on the combined cross-flow/in-line VIV. The maximum (minimum) responses occur in the perpendicular (convex) flow case whereas the extended lower-branch responses occur in the concave flow case. For perpendicular flows, some meaningful features are observed, including the appearances of cross-flow mean displacements and asymmetric eight-shaped motion trajectories due to multiple 2:1:1 resonances where two out-of-plane and one in-plane dominant frequencies are simultaneously excited. Overall VIV phenomena caused by the system asymmetry should be recognised in a prediction model and design codes to capture the combined effects of curved configuration and approaching flow direction.

Fluid nonlinearities effect on wake oscillator model performance

Vortex-induced vibrations (VIV) need to be accounted for in the design of marine structures such as risers and umbilicals. If a resonance state of the slender structure develops due to its interaction with the surrounding fluid flow, the consequences can be severe resulting in the accelerated fatigue and structural damage. Wake oscillator models allow to estimate the fluid force acting on the structure without complex and time consuming CFD analysis of the fluid domain. However, contemporary models contain a number of empirical coeffcients which are required to be tuned using experimental data. This is often left for the future work with the opened question on how to calibrate a model for a wide range of cases and find out what is working and is not. The current research is focused on the problem of the best choice of the fluid nonlinearities for the base wake oscillator model [1] in order to improve the accuracy of prediction for the cases with mass ratios around 6.0. The paper investigates six nonlinear damping types for two fluid equations of the base model. The calibration is conducted using the data by Stappenbelt and Lalji [2] for 2 degrees-of-freedom rigid structure for mass ratio 6.54. The conducted analysis shows that predicted in-line and cross-flow displacements are more accurate if modelled separately using different damping types than using only one version of the model. The borders of application for each found option in terms of mass ratio are discussed in this work, and appropriate recommendations are provided.

The effect of spacing on the vortex-induced vibrations of two tandem flexible cylinders

Vortex-induced vibrations (VIVs) of two flexible cylinders arranged in tandem are studied using a two-way fluid-structure interaction (FSI) method with different spacing ratios (Sx/D) at Reynolds number Re = 500 using a two-way fluid-structure interaction (FSI) method. The main objective of this study is to investigate the effect of spacing on the hydrodynamic interactions and the VIV responses of these cylinders. The responses of the two flexible cylinders are found to be similar to the classical VIV responses at small Sx/D. Once Sx/D is large enough for the vortices to become detached from the upstream cylinder, the response of the upstream cylinder is similar to the typical VIV response whereas the downstream cylinder undergoes wake-induced vibration. The characteristics of the response of the downstream cylinder in the present study are similar to those of the first two response regimes classified by previous researchers. The third regime is not observed for the flexible downstream cylinder with both ends fixed. The two changes in the phase relation between the cross-flow displacements of the two tandem flexible cylinders are discovered to be linked with the initial-upper branch transition and the upper-lower branch transition, respectively. The correlation lengths of the two flexible cylinders decrease significantly in the transition range between the upper and lower branches. Three modes of vortex shedding (2S, P + S, and 2P) have been identified in the present study. The upper-branch 2P mode is found to be associated with large-amplitude vibration of the upstream cylinder and the P + S mode is observed to be related to large-amplitude vibration of the downstream cylinder for Sx/D = 3.5 and 5. On the other hand, the lower-branch 2P mode leads to small-amplitude vibration of the downstream cylinder in the post-lock-in range at Sx/D = 2.5. The relative phase shifts of the sectional lift coefficients on different spanwise cross sections can be attributed to the variation of the vortex shedding flow along the flexible cylinders, and these phase shifts result in poor phasing between the forces and the displacements that is related to the decrease of the correlation lengths.

Vortex-induced vibrations of a vertical riser with time-varying tension

Numerical simulations of a vertical tensioned riser in a sheared flow are performed, where the riser top end oscillates sinusoidally in the vertical direction. The oscillating top-end motion causes tension variations and changes in the natural frequencies of the riser. The flow around the structure causes vortex shedding, oscillating lift forces and vortex-induced vibrations (VIV). It is well-known that the vortex shedding is affected by structure motion, and may lock on to the riser’s natural frequencies. However, the vortex shedding frequency must remain close to the Strouhal frequency, and may therefore excite different modes of vibration as the riser tension changes. With this in mind, the overall aim of this paper is to investigate how tension variations affect the VIV response. The riser dynamics are simulated in time domain using a non-linear finite element structural model combined with an empirical hydrodynamic load model. The latter includes a synchronization model which simulates how the vortex shedding reacts to the structure motion to obtain lock-in. Simulations are run using different amplitudes and frequencies for the top-end motion, and the resulting cross-flow displacements and bending strains are studied. The results show that, when the riser top-end oscillates, the VIV response contains several modes, and the dominating mode may vary with time. The number of active modes are found to be strongly dependent on the period of the riser tension.

Vortex-induced vibrations of a flexibly-mounted inclined cylinder

The majority of studies on vortex-induced vibrations of a flexibly-mounted rigid cylinder are for the cases where the flow direction is perpendicular to the long axis of the structure. However, in many engineering applications, such as cable stays in bridges and mooring lines of floating offshore wind turbines, the flow direction may not be perpendicular to the structure. To understand the vortex shedding behind a fixed inclined cylinder, the Independence Principle (IP) has been used. The IP assumes that an inclined cylinder behaves similarly to a normal-incidence case, if only the component of the free stream velocity normal to the cylinder axis is considered. The IP neglects the effect of the axial component of the flow, which seems reasonable for small angles of inclination, but not for large angles. In the present study, a series of experiments have been conducted on a flexibly-mounted rigid cylinder placed inclined to the oncoming flow with various angles of inclination (0°<θ<75°) in a range of Reynolds numbers from 500 to 4000 to investigate how the angle of inclination affects VIV. A rigid cylinder was mounted on springs, and air bearings were used to reduce the structural damping of the system. The system was placed in the test-section of a recirculating water tunnel and the crossflow displacements were measured at each flow velocity. Even at high angles of inclination, large-amplitude oscillations were observed. As the angle of inclination was increased, the lock-in range (the range of reduced flow velocities for which the cylinder oscillates with a large amplitude) started at a higher reduced velocity. When only the normal component of the oncoming flow was considered, the onset of lock-in was observed to be at the same normalized flow velocity for all angles of inclination except for 75°. However, the width of the lock-in region, its pattern, the maximum amplitude of oscillations and its corresponding normalized reduced velocity were not following the results of a normal-incidence case entirely. Flow visualizations showed a vortex shedding parallel to the cylinder′s axis for all the angles of inclination considered. The influence of a slight change in the added mass as well as the direction of the inclined cylinder on the response was studied as well.

A conscientious investigation into the effect of Re and mass-ratio on two-degree-of-freedom vortex-induced vibrations

Through a serious application of an overlapping mesh, vortex-induced vibration (VIV) of low-mass-rationale cylinders was computed in the range of 1.0×103<Re<2.0×104. An overlapping mesh is more controllable to deal with the dynamic mesh since there is no necessity to regenerate grids in this complete computational domain. Only boundary nodes are utilized to dispose of all steps each time. It is discovered that the cross-flow amplitudes can increase by approximately 30% in the resonance area when the in-line degree of freedom is taken into account. But the cross-flow amplitudes do not have any change outside the resonance area. In its mass ratio (m *= mass of cylinder/mass of displaced water) ranging from 1.0 to 40, the ratios of in-line amplitudes to cross-flow amplitudes decrease with the increasing m *, especially as m *<2.5, the ratios will be larger than 10%. Moreover, the phase differences between in-line displacements and cross-flow displacements also reduce as m * increases. However, the correlation coefficients between displacements at two directions are so random even a bit low. With regards to vortex mode, the ‘2S’ mode and the ‘2P’ mode are very applicable to the present work. Effect of Re is also investigated, this paper aims to prove that the ratios of amplitudes between two directions have few relations with Re, and then the relationship between relative amplitudes and mass ratios can be decoded hereof.

Characteristics of VIV in multi-degree-of-freedom tensioned beams using a numerical method

The object of this study is to analyze the characteristics of vortex-induced vibration of a slender marine structure with the numerical method. Applying a dynamic analysis method for a slender marine structure based on the 3D finite difference method, we carried out case studies for a tensioned beam model at a constant flow speed. The hydrodynamic forces, in the direction of inline and cross-flow, created by vortex shedding are simultaneously considered based on Morison equation. The frequency of force in the inline direction corresponding to the unstable zone is evaluated. An eigenvalue analysis for different flow speeds of a tensioned beam considering the effect of the tension increase due to the inline and cross-flow drag forces is performed. We found that a revision of the eigenvalue should be considered if the tension along a riser or beam is significantly affected by an environmental or functional load. From a trajectory on the XY plane it was shown that the riser did not move in an exact 8 shape for all flow conditions due to the phase angle difference between inline and cross-flow displacement. It is believed that the phase angles between inline and cross-flow displacements in high modes are different among the nodes.

Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser

This paper compares laboratory measurements of the vortex-induced vibrations of a riser in a stepped current with blind predictions obtained with 11 different numerical models. Results are included on in-line and transverse displacements and curvatures, and dominant frequencies. In general, empirical models were more successful at predicting cross-flow displacements and curvatures than current codes based on CFD. Overall ratios between predictions and measurements of cross-flow displacements were around 95% and 75%, respectively. Predictions of cross-flow curvatures were more scattered, and almost all were unconservative. In-line vortex-induced curvatures, which may cause as much damage as cross-flow curvatures, could not be computed by any of the empirically based codes, and in general those based on CFD were in very poor agreement with the measurements.

Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current

This paper describes measurements of the vortex-induced vibrations of a model vertical tension riser in a stepped current. The riser, 28 mm in diameter, 13.12 m long and with a mass ratio (mass/displaced mass) of 3.0, was tested in conditions in which the lower 45% was exposed to a uniform current at speeds up to 1 m/s, while the upper part was in still water. Its response in the in-line and cross-flow directions was inferred from measurements of bending strains at 32 equally spaced points along its length. Cross-flow vibrations were observed at modes up to the 8th, with standard deviations of individual modal weights greater than 50% of the riser's diameter. Except at the lowest reduced velocities, the response included significant contributions from several modes, all at a frequency controlled by lock-in of the dominant mode. In the presence of multi-mode responses, drag coefficients were up to 120% greater than those for a stationary cylinder at the same Reynolds numbers, and like overall measures of in-line and cross-flow displacements, revealed a strong dependence on the modal composition of the motion.

Direct numerical simulations of emulsion flows

In this paper, three-dimensional boundary integral computer simulations of emulsions in shear flows are described. Results for ordered BCC emulsions with dispersed-phase volume fractions below the critical concentration are presented. Complex rheological features including: shear-thinning viscosities, normal stress differences, and a nonlinear frequency response are also explored. For deformable drops, pairwise collision produces net cross-flow displacements that govern self-diffusion of drops. We compute trajectories of two interacting drops in shearing and present interesting numerical simulations of three dimensional gravity-induced motion of two drops. The results also demonstrate the feasibility of simulating high-volume-fraction emulsions and foam.

Lateral migrations of solid spheres in tube flow

Cross-flow displacements of neutrally buoyant solid spheres under Poiseuille-type flow conditions in narrow channels, at low volume fraction, are described by a phenomenological model within the framework of the Fokker-Planck equation. In this model, the effects of particle-particle and particle-wall interactions are taken into account. In addition to the classical wall effect (depleted layer near the wall), numerical solutions of the derived equations display two opposite lateral migrations towards the wall and the tube axis, and an alignment of the particles in adjacent layers parallel to the flow. These numerical results are then compared with experimental results obtained by Goldsmith and Marlow [18] for erythrocyte suspensions. A good qualitative agreement is observed.