Vortex-induced Motion Research Articles

Modelling of the Vortex-Induced Motion of A Single-Column Platform with Non-Linear Mooring Stiffness Using the Coupled Wake Oscillators

A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with nonlinear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8<Ur<15, and the trajectories of the VIM on the xy plane with eight-figure patterns are maintained. The results with different non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.

Modified wake oscillator model for vortex-induced motion prediction of low aspect ratio structures

ABSTRACTFloating structures, such as Spar platform, are likely to experience significant motions while operation due to Vortex-induced Motion (VIM). The main features of VIM include aspect ratio and mass ratio of the structure. This paper focuses on further development of a previously published semi-empirical method called wake oscillator model (WOM) for VIM, which aims to derive a mathematical correlation in modelling all features of the phenomenon. Analytical solution is proposed to coupled WOM and structure oscillator model based on the Van der Pol equation by integrating mass ratio, m* = 4.36, and various low aspect ratios between 0.3 and 2.0. Additionally, a new approach was initiated to embed several empirical parameters linked to the aspect ratio in the existing WOM. It was found the aspect ratio parameter in the modified WOM significantly affected the performance of the model for estimation of VIM on floating structures.

Multi-objective optimization of semi-submersible platforms using particle swam optimization algorithm based on surrogate model

An Innovative Semi-submersible platform Optimization Program (ISOP) has been developed to solve the multi-objective optimization problem for semi-submersible platforms (SEMI). Three types of SEMIs, including semi-submersible floating production unit (SEMI FPU), heave and vortex induced motion (VIM) suppressed semi-submersible (HVS) and semi-submersible floating drilling unit (SEMI FDU) are selected for case studies. The hydrodynamic performances of three types of semi-submersible platforms are analyzed by using panel method and Morison's equation. In order to improve the computing efficiency, the hydrodynamic performances for different hull forms during optimization process are estimated by the surrogate models, which are built by artificial neural network prediction method and Inverse Multi-Quadric (IMQ) radial basis function (RBF). The accuracy of surrogate models is ensured by performing leave-one-out cross validation (LOOCV). The most probable maximum (MPM) heave motion and total weight, representing the safety and economy, respectively, are chosen as the two objectives for optimization. The transverse metacentric height, the MPM surge motion, and the most probable minimum (MPMin) airgap are selected as constraints. Based on surrogate models, multi-objective particle swarm optimization (MOPSO) is employed to search for the Pareto-optimal solutions. A Computational Fluid Dynamics (CFD) tool is adopted to validate the proposed model for the prediction of the motion responses. By comparing the obtained Pareto-optimal solutions with the initial design using simple panel method plus Morison's equation, it is confirmed that the MPM heave motions for SEMI FPU, HVS and SEMI FDU can be suppressed by up to 12.68%, 11.92%, and 14.96%, respectively, and the total weights can be reduced by up to 12.16%, 13.00%, and 24.91%, respectively. Through the detailed analyses of optimization results, the most efficient design strategies for semi-submersible platforms are discussed and proposed.

Coupled CFD-FEM simulation of hydrodynamic responses of a CALM buoy

In this paper, the Finite-Analytic Navier-Stokes (FANS) code is coupled with an in-house finite-element code to study the dynamic interaction between a floating buoy and its mooring system. Hydrodynamic loads on the buoy are predicted with the FANS module, in which Large Eddy Simulation (LES) is used as the turbulence model. The mooring lines are modeled based on a slender body theory. Their dynamic responses are simulated with a nonlinear finite element module, MOORING3D. The two modules are coupled by transferring the forces and displacements of the buoy and its mooring system at their connections through an interface module. A free-decay model test was used to calibrate the coupled method. In addition, to investigate the capability of the present coupled method, numerical simulations of two degree-of-freedom vortex-induced motion of a CALM buoy in uniform currents were performed. With the study it can be verified that accurate predictions of the motion responses and tension responses of the CALM buoy system can be made with the coupling CFD-FEM method.

Numerical Study on the Influence of Mass and Stiffness Ratios on the Vortex Induced Motion of an Elastically Mounted Cylinder for Harnessing Power

Harnessing the power of vortices shed in the wake of bluff bodies is indeed a boon to society in the face of fuel crisis. This fact serves as an impetus to develop a device called a hydro vortex power generator (HVPG), comprised of an elastically mounted cylinder that is free to oscillate in the cross-flow (CF) direction even in a low velocity flow field. The oscillatory motions in turn can be converted to useful power. This paper addresses the influence of system characteristics viz. stiffness ratio (k*) and mass ratio (m*) on the maximum response amplitude of the elastically mounted cylinder. Computational fluid dynamics (CFD) simulations have been used here to solve a two way fluid–structure interaction (FSI) problem for predicting the trend of variation of the non-dimensional amplitude Y/D with reduced velocity Ur through a series of simulations. Maximum amplitude motions have been attributed to the lowest value of m* with Ur = 8. However, the maximum lift forces correspond to Ur = 4, providing strong design inputs as well as indicating the best operating conditions. The numerical results have been compared with those of field tests in an irrigation canal and have shown reasonable agreement.

A new passive control technique for the suppression of vortex-induced motion in deep-draft semisubmersibles

The control of vortex-induced motion (VIM) of deep-draft semisubmersibles has recently emerged as a serious concern in offshore semisubmersible platforms subjected to high ocean currents. With the increased draft of semisubmersibles, the coherent wake vortex fields behind the multi-column platforms become quite significant, which increase the impact of the coupled fluid-structure dynamics on the platform motion. In particular, the effective mitigation of the synchronization of wake vortices in a deep-draft semisubmersible is important for the reliable station-keeping and to extend the fatigue life of risers and mooring systems. The present study aims at the development of a passive control technique for the vortex synchronization of deep-draft semisubmersibles (DDS) via continuous cross-sectional twisting of the rounded square column along the spanwise direction. The computations are performed using a hybrid URAN-LES turbulence model based on the finite volume method. A validation study of the numerical results is performed with the available experimental data for the stationary and vibrating configurations of deep-draft semisubmersible. To begin, we first examine the VIM performance of a single column of the semisubmersible with a twisted angle of 45 °. We next examine the design of twisted column to understand its effect on the vorticity dynamics and the VIM response characteristics. In comparison to the untwisted square-column configuration, the twisted column produces the reduction in the transverse (sway) VIM amplitude up to 90% at the peak lock-in condition. The streamwise (surge) amplitude for the twisted-column semisubmersible is also found to be reduced by approximately 1/3 of the amplitude of the square-column counterpart. The twisted surface on the column results in a continuous spanwise (column-wise) variation of the shear-layer separation points. The three-dimensional (3D) variation of separation lines and the pressure distribution along the twisted and the square columns are analyzed to understand the underlying mechanism of the VIM suppression. We find that the modification of vortex shedding due to the variation in the separation line along the twisted column significantly influences the mean and fluctuating hydrodynamic forces. We extend the twisted column concept to the deep-draft semisubmersibles and demonstrate its effectiveness to produce a remarkable degree of VIM suppression. We explore the effects of the orientation of twisted columns and the incidence angle of the oncoming flow and present the 3D wake vortex structures and the motion histories of the DDS configuration.

Numerical investigation of vortex-induced motions of a paired-column semi-submersible in currents

Vortex-induced motions (VIM) is becoming a noteworthy issue for column-stabilized floating platforms, mainly due to its substantial fatigue damage to risers and mooring system. The VIM of deep-draft semi-submersible is more complex than single column floaters because of the wake interference between columns, as well as the considerable yaw motions. In the present work, a numerical approach for simulating VIM of deep-draft semi-submersible is proposed. Specifically, detached-eddy simulation is used for turbulence modeling and dynamic overset grid technique is used for moving objects. Simulations for stationary drag and VIM of a model-scale paired-column semi-submersible are conducted with the proposed approach. The numerical results are compared with experimental data. Transverse, in-line and yaw motions are allowed during VIM simulations and are further analyzed in frequency domain by Fast Fourier Transform (FFT). Different VIM characteristics are observed at different current velocities. The work done by each component of the structure is also discussed. Flow visualizations are presented for better understanding of the wake interferences during VIM. The accuracy and reliability of the current numerical approach is assessed.

Vortex-induced vibration of floating circular cylinders with very low aspect ratio

Experiments regarding vortex-induced vibration (VIV) on floating circular cylinders with low aspect ratio were carried out in a recirculation water channel. The floating circular cylinders were elastically supported by a set of linear springs. Eight different aspect ratios were tested, namely L/D= 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5 and 2.0. These aspect ratios were selected to cover the aspect ratio range of the main offshore circular platforms, such as spar and monocolumn. The aim was to understand the vortex-induced motions (VIM) of such platforms; due to this, the cylinders were floating, or m∗=1. The range of Reynolds number covered 2800 < Re < 55,400. The amplitude results showed a decrease in amplitude with decreasing aspect ratio in the in-line and in the transverse directions. The frequency results confirm a different behavior for cylinders with L/D≤0.5; in these cases, the cylinder free-end effects were predominant. The resonant behavior was no longer observed for L/D≤0.2. The decrease in Strouhal number with decreasing aspect ratio is also verified, as well as for drag and lift forces. The added mass results help to identify the end of resonance for both directions, in-line and transverse. The amplitude results for the vertical direction, roll, pitch and yaw did not affect the VIV behavior.

Control of vortex-induced motion in multi-column offshore platform by near-wake jets

Vortex-induced motion (VIM) poses a serious challenge in many engineering applications such as offshore structures, floating wind turbines, and high rise buildings. In particular, significant aspects of VIM have to be considered in offshore platforms subjected to high currents. The objective of this numerical study is to investigate the VIM suppression of multi-column floating platforms by injecting steady near-wake jets at the wake side of the columns. Before proceeding to the blowing-jet based flow control method, the transverse VIM amplitude of floating platform is validated with the model test data. We perform a systematic investigation of 3D scaled model with and without prescribed jet flows for varying reduced velocity (Ur) at a fixed mass ratio m*=0.83, the damping ratio ζ=0.01 and the Reynolds number Re=20,000. The numerical investigations are carried out for different near-wake jet configurations at reduced velocity Ur=10. We assess the response characteristics and flow profile patterns to identify a suitable configuration of blowing jet along the columns. We demonstrate that the semi-submersible with elongated near-wake jet configuration is efficient in suppressing VIM in comparison to other near-wake jet configurations and the uncontrolled no-jet case. The vibration amplitudes, the force coefficients and the flow patterns of semi-submersible with the blowing-based control technique are further examined for various mass flow rate coefficients. From our studies, we observe approximately 30% reduction of forces and the amplitudes for the offshore system with the prescribed jet flow compared to the system without near-wake jets. The optimal Vjet/U is estimated to be in the range of 2.5–5, for the effective VIM suppression, where Vjet and U are the prescribed jet flow speed and the free-stream speed, respectively. To understand the underpinning of VIM suppression mechanism, the vortex dynamics and flow patterns in the near-wake region of a freely vibrating semi-submersible platform with the near-wake jet are explored. For this numerical study, we employ a stabilized finite element formulation with an explicit dynamic subgrid-scale model to simulate the fluid-structure interaction subjected to a turbulent wake flow.

Study on Vortex-Induced Motions of A New Type of Deep Draft Multi-Columns FDPSO

A numerical simulation and an experimental study on vortex-induced motion (VIM) of a new type of deep draft multi-columns floating drilling production, storage and offloading (FDPSO) are presented in this paper. The main dimension, the special variable cross-section column and the cabin arrangement of the octagonal pontoon are introduced based on the result. The numerical simulation is adapted to study the effects of current incidence angles and reduced velocities on this platform’s sway motion response. The 300 m water depth equivalent truncated mooring system is adopted for the model tests. The model tests are carried out to check the reliability of numerical simulation. The results consist of surge, sway and yaw motions, as well as motion trajectories. The maximum sway amplitudes for different types of offshore platform is also studied. The main results show that the peak frequencies of sway motion under different current incidence angles and reduced velocities vary around the natural frequency. The analysis result of flow field indicates that the change of distribution of vortex in vertical presents significant influences on the VIM of platform. The trend of sway amplitude ratio curve of this new type FDPSO differs from the other types of platform. Under 45° current incidence angle, the sway amplitude of this new type of FDPSO is much smaller than those of other types of offshore platform at 4.4 ≤ Vr ≤ 8.9. The typical ‘8’ shape trajectory does not appear in the platform’s motion trajectories.

Naoe-FOAM-SJTU Solver for Numerical Study of Vortex-Induced Motions of a Buoyancy Can in Currents

naoe-FOAM-SJTU Solver for Numerical Study of Vortex-Induced Motions of a Buoyancy Can in Currents

Numerical simulation of vortex-induced motion of a deep-draft paired-column semi-submersible offshore platform

Understanding and predicting vortex-induced motion (VIM) of offshore systems for deep seawater applications is crucial to improve the system safety and integrity. We report on experimental tow-tank measurements and numerical simulations of VIM of a deep-draft offshore platform, specifically Paired-Column Semisubmersible (PC-Semi). The study is carried out in model scale (1:54), at subcritical flow regime with Re∼104. Motion of the floating structure has three degrees of freedom: in-line, cross-flow, and yaw. Large periodic cross-flow motion is measured for headings 0°, 11.25°, and 22.5°, for reduced velocities (Ur) between 5 and 10. Considerably smaller cross-flow amplitude is recorded at 45° heading across the Ur range considered.An extensive sensitivity study is performed using computational fluid dynamics (CFD) to capture the transient displacement history of VIM (in-line, cross-flow, and yaw motion components). Amplitude and period of cross-flow (transverse) motion are obtained from statistical analysis of VIM time history and subsequently used as the validation criterion between the CFD simulation and the model tests. Satisfactory agreement between the CFD results and tow-tank measurements is achieved with a Delayed Detached Eddy Simulation – Shear Stress Transport (DDES-SST) formulation. This work provides experimental results and serves as a practical starting point to set up a CFD problem to estimate amplitude and period of cross-flow VIM motion for offshore engineering applications.

Experimental study of the column shape and the roughness effects on the vortex-induced motions of deep-draft semi-submersible platforms

Experiments regarding the VIM of SS platforms with four columns were carried out to investigate the effects of the surface roughness and the column shape. Two different geometry of columns were experimented: rounded-square and circular-cross sections. Each model had the same arrangement of four pontoons in a closed configuration. The range of reduced velocity was from 4 up to 25 covering Reynolds numbers from 7.000 to 80.000. Three angles of incidences for each model were tested, namely 0, 22.5 and 45°. For each model, three different levels of roughness were tested. Regarding roughness effects the results seem to confirm two aspects: the important role played by the separation point near the rounded corners of the rounded-square columns and the roughness effect on the boundary layers of the circular columns. Regarding the effect of the column shape, the results indicated that the heading effects on the VIM of SS strongly depend on the column shape. The characteristic motion periods upheld the resonance behavior for the motions in the transverse direction and yaw motions for the lock-in range. Heave, roll and yaw motions did not impact the VIM behavior in the horizontal plane, and their amplitudes were not considered relevant.

Vortex-Induced Motion Response of Semi-Submersible Platform in Deep Water: II. Investigation on Hull Optimization

Vortex-Induced Motion Response of Semi-Submersible Platform in Deep Water: II. Investigation on Hull Optimization

Vortex-Induced Motion Response of Semi-Submersible Platform in Deep Water: I. Investigation on Key Characteristics

Vortex-Induced Motion Response of Semi-Submersible Platform in Deep Water: I. Investigation on Key Characteristics

Numerical studies on vortex-induced motions of a multi-column deep-draft oil and gas exploration platform

This paper presents numerical studies on vortex-induced motions (VIM) of a multi-column floating oil and gas exploration platform. Numerical computations are performed using an improved delayed detached eddy simulation (IDDES) together with a moving grid approach. The transverse (sway) and yaw motion responses, motion trajectories, motion frequencies and power spectral density of motions are computed and analyzed systematically. After extensive comparisons with experiments, it is confirmed that the present numerical solutions using IDDES agree well with the experimental results and are better than those via delayed detached eddy simulation (DDES). The differences of transverse motion responses between computational results and experiments are less than 10% in the lock-in region. The numerical simulations reveal that the transverse VIM responses occur in a range of reduced velocities from 7.0 to 14.0 at H/D = 1.44 (H and D are the column height and width, respectively). The largest nominal transverse amplitude, around 35% of the column width, occurs for 22.5∘ current incidence. It is found that the VIM responses mainly perform along the platform diagonals for 15∘, 22.5∘ and 45∘ current incidences. The transverse and yaw motion frequencies for 15∘, 22.5∘ and 45∘ current incidences are higher than those for 0∘ current incidence. The energy levels of the yaw motion responses for 15∘, 22.5∘ and 45∘ current incidences are about 10% of that for 0∘ current incidence. Moreover, parametric studies have been performed to examine the effect of submerged column height on VIM. It demonstrates that VIM in transverse direction grows significantly when submerged column height H/D is greater than 1.0. To be more specific, compared to the case with H/D = 1.44, VIM in transverse direction at H/D = 3.0 increase by around 120%.

Internal resonances for heave, roll and pitch modes of a spar platform considering wave and vortex-induced loads in the main roll resonance

We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortexinduced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.

Experimental and numerical study on vortex-induced motions of a deep-draft semi-submersible

An experimental study on vortex-induced motions (VIM) of a deep-draft semi-submersible (DDS) was carried out in a towing tank, with the aim to investigate the VIM effects on the overall hydrodynamics of the structure. In order to study the fluid physics associated with VIM of the DDS, a comprehensive numerical simulation was conducted to examine the characteristics of vortex shedding processes and their interactions due to multiple cylindrical columns. The experimental measurements were obtained for horizontal plane motions including transverse, in-line and yaw motions as well as drag and lift forces on the structure. Spectral analysis was further carried out based on the recorded force time history. These data were subsequently used to validate the numerical model. Detailed numerical results on the vortex flow characteristics revealed that during the “lock-in”, the vortex shedding processes of the upstream columns enhance the vortex shedding processes of the downstream columns leading to the rapid increase of the magnitude of VIM. In addition to the experimental measurements, for the two uniform flow incidences (0° and 45°) investigated, comprehensive numerical data of the parametric study on the VIM characteristics at a wide range of current strength will also serve as quality benchmarks for future study and provide guidance for practical design.

VIM simulation on a cylindrical floating structure

Vortex-induced motion (VIM) on a cylindrical floating structure can be easily found in ocean strong current. Since the VIM on the structure with long-term low-frequency motion causes fatigue damage of the structure’s mooring lines and risers, precise VIM assessment is needed for the safe evaluation of them. In the standard of the International Organization for Standardization ISO19901-7, ‘Specific requirements on stationkeeping systems for floating offshore structures and mobile offshore units’, for instance, a concrete method of assessing VIM displacement is not represented in the standard document, though the requirement on the VIM demands for an assessment on the basis of a proper way. In this paper, a VIM time-domain simulation method on a floating structure with circular cylinder form, that is, for example a Spar, an MPSO (mono-column type floating production storage and off-loading) and so on, is shown using the wake oscillator model. Transverse and in-line VIM are treated for the floater’s motion. The assessment quality of the simulation on the VIM amplitudes of floaters in current is confirmed by model test data.

An experimental study on vortex induced motion of a tethered cylinder in uniform flow

At present, most research achievements are about the response of two or three degrees of freedom vortex induced vibration. Responses of vortex induced motions (VIM) of marine structures with 6-DOF remain to be further studied. In this paper, a model test of a tethered cylinder in uniform flow was carried out. The 6-DOF motion responses with different mass ratios were measured and the motion trajectories, amplitudes and frequencies were investigated. Results show that, the vibration amplitude of the cylinder increases with the reduced velocity at first, and then remain relatively stable. In the “lock in” range, the cross-flow vibration frequency increases with the reduced velocity, and the in-flow vibration frequency increases in a ladder type. Yaw motion was also observed in this experiment, and a strong correlation between yaw motion and cross-flow vibration was found. In the initial branch, yaw motion has only one dominant frequency, while in the “lock in” range, yaw motion appears to have two dominant frequencies, the major frequency is equal to the cross-flow vibration frequency and the minor frequency is half of the transverse vibration frequency. It is also found that in the range of mass ratio applied in this paper (0.272<m*<0.431), the cross-flow vibration amplitude decreases and the yaw amplitude increases with the increase of the cylinder's mass ratio.