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The hydrodynamic forces on the stationary partially submerged cylinder are investigated through towing test with Reynolds number ranging from 5 × 104 to 9 × 105. Three test groups of partially submerged cylinders with submerged depths of 0.25 D, 0.50 D, and 0.75 D and one validation group of fully submerged cylinders are conducted. During the experiments, the hydrodynamic forces on the cylinders are measured using force sensors. The test results show a considerable difference in the hydrodynamic coefficients for the partially submerged cylinders versus the fully submerged cylinders. A significant mean downward lift force is first observed for the partially submerged cylinders in a steady flow. The maximum of the mean lift coefficients can reach 1.5. Two distinct features are observed due to the effects of overtopping: random distributions in the mean drag coefficients and a clear quadratic relationship between the mean lift coefficients and the Froude number appear in the non-overtopping region. However, the novel phenomenon of a good linear relationship with the Froude number for the mean hydrodynamic coefficients is clearly shown in the overtopping region. In addition, fluctuating hydrodynamic coefficients are further proposed and investigated. These results are helpful to have a better understanding of the problem and to improve related structural designs.

The influences of helical strake geometry and vortex-induced vibration (VIV) on the drag coefficients of a long flexible pipe with helical strakes are investigated through uniform flow experiments with the Reynolds (Re) number ranging from 1.1 × 104 to 9.5 × 104. The strains caused by drag forces of a bare pipe and six different straked pipes are measured by fiber bragg grating (FBG) sensors. According to the inverse analysis method and Morison formula, the drag forces and coefficients at each section of the pipe models are identified. Then, the mean drag coefficients of the bare and straked pipes are compared. The results show that helical strakes can effectively stabilize the fluctuation of drag coefficients with Re numbers. An unexpected phenomenon is that helical strakes with pitches of 5 D can reduce the mean drag coefficients. Moreover, the mean drag coefficients of straked pipes are less sensitive to VIV response. Furthermore, an empirical mean drag coefficient prediction formula for straked pipes is proposed, which accounts for the VIV response and geometry of helical strakes. Its applicability is well verified via comparison between predicted and experimental results.

In this study, an efficient time-domain prediction model is developed to predict unsteady flow vortex-induced vibrations (VIV) of flexible risers. The hydrodynamic forces on flexible risers are calculated on the basis of forced oscillation experiments on rigid cylinders. A period identification criterion, based on the spatial and temporal variations of reduced velocity, is proposed to divide the entire vibration process into exciting and damping periods of each exited mode. In exciting periods, assuming that VIV enters an ideal lock-in stage, a non-iterative solving model is established under modal space for response calculations, which efficiently predicts time domain VIV responses. In damping periods, free-decay vibration theory based recurrence formulas are established under modal space, and they get solved stepwise for modal responses. After some slight response adjustments to smooth period transitions, the VIV response time history can be obtained efficiently. This model is validated by steady flow VIV prediction cases, and further applied to predict oscillatory flow VIV experimental results. The prediction cases reveal that this model is able to realize high-speed VIV predictions with satisfactory results and no convergence problems. This model, with high efficiency and stability, is highly suitable for unsteady flow VIV prediction in engineering applications.

The Norwegian Public Road Administration is planning to upgrade Coastal Highway E39 by replacing ferry connections with floating bridges or submerged floating tunnels (SFTs). This study considers a potential pontoon-supported curved SFT designed for crossing Sognefjorden at a submergence of 12 m. It consists of two identical tubes with a diameter of 12.6 m each in a tandem configuration and with a length of approximately 4 km. The natural frequencies of the low-order modes are well within the energy content in the spectra of the second-order difference-frequency wave excitation forces and the vortex shedding-induced forces. In this paper, numerical simulation of wave-induced hydroelastic response and flow-induced vibrations of the twin-tube SFT is performed. Long- and short-crested waves, the first and second order wave loads, are considered. A time-domain approach to simulate crossflow vortex-induced vibration (VIV) and VIV-amplified inline drag forces, partly based on the coefficients obtained experimentally, is established and applied. The focus is on extreme conditions – relating to ultimate strength limit states. The second-order wave load substantially affects the lateral motion and lateral bending moment, as expected. The short-crested waves influence the response in both the lateral and vertical directions by exciting asymmetric eigenmodes. In strong flow conditions, once VIV is excited, the standard deviation of the vertical motion (of about 30% of the diameter) and the bending moment about the horizontal axis is more that an order of magnitude larger than that induced by the wave loads. The simulation of the wave- and flow-induced load effects provides a good reference for the design of SFTs.

Under vessel motion, dynamic responses of compliant risers, like a steel catenary riser, are no longer small displacement and small deformation problems but characterised with large displacement and small deformation instead. It is therefore difficult to directly obtain the riser global motion based on experimental or field-measured local strain or acceleration data. This paper proposes a generalised global motion reconstruction method for large displacement but small deformation problems, assuming that the global motion can be divided into quasi-static motion and dynamic vibration. The proposed methodology is validated numerically and experimentally with satisfactory accuracy. Parameters like sensor location and mode number to be used in the motion reconstruction are optimised and recommended. Uncertainty analysis considering different noise levels is performed to evaluate the robustness of the proposed method. Most importantly, further comparative hydrodynamic analyses indicate the significance ...

In this paper, a time domain prediction method from experimental data is proposed for vortex-induced vibration (VIV) of flexible risers. The nonlinear factors, couplings among axial tension, VIV response in cross flow (CF) direction and the hydrodynamic force, have been taken into account in this method, with a simplified tension variation model and empirical hydrodynamic force model. The hydrodynamic force, including the excitation force in the excitation region and the damping force in the damping region are the function of excitation coefficients, non-dimensional VIV amplitude and frequency based on vibration experiment data. Iterations are performed to achieve balances between the hydrodynamic forces and the VIV responses of a riser. Moreover, a new added mass coefficient of 2.0 from model tests of flexible pipes is applied, where the predicted VIV response frequencies reveal higher accuracy. Comparison between the predicted results and the experimental results under uniform flow of 2.8 m/s and shear flow of 2.0 m/s are conducted, which verifies the feasibility and reliability of the proposed method. In addition, by comparing the prediction results with and without coupling between axial tension and VIV responses, it is found that this coupling effect is of importance to VIV prediction and can improve VIV prediction accuracy, especially under the case of high flow velocity and high vibration mode.

A modal space based direct method is developed for vortex-induced vibration (VIV) prediction of flexible risers. A VIV response solution model is established in modal space, consisting of a hydrodynamic force equation and a dynamic response equation. Adopting a non-iterative root-search method in modal space, the equation set gets solved directly without power-balance iterations. This direct method is compared against conventional empirical models, with its validity and applicability verified. This method entirely gets rid of convergence problems during predictions, which is conducive to practical engineering applications and puts forward fresh ideas for further development of empirical models for VIV prediction.

In this paper, the hydrodynamic coefficients of a horizontal semi-immersed cylinder in steady current and oscillatory flow combining with constant current are obtained via forced oscillation experiments in a towing tank. Three nondimensional parameters (Re, KC and Fr) are introduced to investigate their effects on the hydrodynamic coefficients. The experimental results show that overtopping is evident and dominates when the Reynolds number exceeds 5×105 in the experiment. Under steady current condition, overtopping increases the drag coefficient significantly at high Reynolds numbers. Under oscillatory flow with constant current condition, the added mass coefficient can even reach a maximum value about 3.5 due to overtopping while the influence of overtopping on the drag coefficient is minor.

In this paper, a time-domain hydroelastic method for very large floating structures (VLFS′) in inhomogeneous waves is developed based on Cummins' equation. By discretizing the continuous VLFS into rigid modules connected by elastic beam elements, the inhomogeneous wave effect can be considered by adopting different wave spectra over different regions of the VLFS. In this method, the frequency-domain hydrodynamic coefficients, considering the hydrodynamic interactions between each floating module, are transformed into the time-domain hydroelastic model using Cummins' equation. Moreover, the time-domain wave excitation forces on the modules in different regions are solved using different wave spectra. The hydroelastic responses of a freely floating structure in inhomogeneous regular and irregular waves are investigated. The results show that the inhomogeneity of waves has a significant effect on the bending moments, shear forces and torsional moments of the structure, especially for a wave direction of 90°, in which larger forces may be induced compared with the homogeneous waves.

A method to identify vortex-induced forces and coefficients from measured strains of a Steel Catenary Riser (SCR) undergoing vessel motion-induced Vortex-induced Vibration (VIV) is proposed. Euler–Bernoulli beam vibration equations with time-varying tension is adopted to describe the out-of-plane VIV responses. Vortex-induced forces are reconstructed via inverse analysis method, and the Forgetting Factor Least Squares (FF-LS) method is employed to identify time-varying vortex-induced force coefficients, including excitation coefficients and added mass coefficients. The method is verified via a finite element analysis procedure in commercial software Orcaflex. The time-varying excitation coefficients and added mass coefficients of an SCR undergoing vessel motion-induced VIV are investigated. Results show that vessel motion-induced VIV is excited at the middle or lower part of the SCR and in the acceleration period of in-plane velocity, where most of the excitation coefficients are positive, while during the deceleration period, the excitation coefficients becomes too small to excite VIVs. Parameter γ [1] has strong correlation with excitation coefficients. In addition, time-varying tensions contribute significantly to the variations of added mass coefficients under the condition that the ratio of dynamic top tension to pretension exceeds the range of 0.7–1.3. Moreover, chaotic behaviors are observed in vortex-induced force coefficients and are more evident with the increase of vessel motion velocity. This behavior may attribute to the randomness existing in in-plane velocity and its coupling with out-of-plane vibrations.

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×105. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 105, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.

By using the open source DualSPHysics, the interaction between wave and a triple-cylinder bundle structure is numerically investigated. The wave is generated by applying the predefined function to the wave maker, and the free surface and the velocity of the regular wave and irregular wave are compared with the theoretical data at the measuring point. To verify the feasibility of the numerical method for simulating the fluid-structure interaction, the numerical results of smooth particle hydrodynamics (SPH) model are compared with the experimental and theoretical data, which shows a good agreement. Finally, 95 groups of cases of the interaction between wave and triple-cylinder bundles (TPB) are calculated, and the wave force acting on TPB is explored at different rotation angles. The effects of different wave parameters on the wave force characteristics are further analyzed. The results of a single vertical cylinder are introduced for making a comparison. For the regular wave case, the wave force acting on the structure is higher than that of the irregular wave case. When the rotation angle is 90°, the wave force on the TPB is the maximum; and it reaches the minimum at 180°.

The three-dimensional flow around the four-cylinder and five-cylinder arrays are numerically studied at Re = 3900 by large eddy simulation (LES). By selecting eight spacing ratios (L/D = 2.0–7.0) and three incidence angles (α = 0°–45°), the influence of the center cylinder on the flow characteristics and interference effects of the four-cylinder array is discussed. Different spacing ratios can be divided into three categories with respect to flow regions of the multi-cylinder: small gap flow regime (L/D = 2.0–3.5), critical flow regime (L/D = 3.5–5.0) and large gap flow regime (L/D = 5.0–7.0). For cases with small spacing ratios, the influence of the center cylinder is very notable on the flow characteristics of the four-cylinder array. As the ratio increases, the influence of the center cylinder gradually decreases on the surrounding cylinders in the multi-cylinder array. On the other hand, the direction of the incoming flow also affects the flow characteristics of both four-cylinder and five-cylinder arrays. The development of the shear layer is strongly influenced by the center cylinder for the upstream cylinders at α = 45°. Boundary vortex flux components, flow characteristics and fluid force coefficients change significantly with adding the center cylinder for the four cylinders.

A large-scale model test of a free-hanging water intake riser (WIR) is performed in an ocean basin to investigate the riser responses under vessel motion. Top end of the WIR is forced to oscillate at given vessel motion trajectories. Fiber Brag Grating (FBG) strain sensors are used to measure the WIR dynamic responses. Experimental results firstly confirms that the free-hanging WIR would experience out-of-plane vortex-induced vibrations (VIVs) under pure vessel motion even for the case with a KC number as low as 5. Meanwhile, comparison between numerical results and experimental measurements suggests a significant drag amplification by out-of-plane vessel motion-induced VIV. What’s more, further study on WIR response frequencies and cross section trajectories reveals a strong correlation between vessel motion-induced VIV and local KC number distribution, owing to the small KC number effect. The presented work provides useful references for gaining a better understanding on VIV induced by vessel motion, and for the development of future prediction models.

The drag force coefficients of a flexible riser undergoing vortex-induced vibration (VIV) in sheared flow are investigated for Reynolds numbers (Re) up to 1.2×105. Based on the drag forces theoretically calculated by the beam theory using the strains measured in a scale model test, the properties and distribution of the drag coefficients are investigated, and a new empirical model for estimating the drag coefficient on a flexible riser undergoing VIV is proposed. The results show that VIV leads to non-uniform distribution of the drag coefficient and amplifies the drag coefficient, and the local drag coefficient can reach up to 3.2. For Re values from 1.0×104–1.2×105, the mean drag coefficient is between 1.3 and 2.0 and decreases as Re increases. Furthermore, the empirical drag coefficient prediction model obtained from experiments under low Re is not suitable for high Re. The corrected empirical prediction model, which accounts for the effect of the flow velocity, the VIV dominant mode number and the dominant frequency, can be used to predict riser drag coefficients under VIV more accurately at high Re values up to 1.2×105.

This paper introduces a new method which is based on multi-body hydrodynamics and Euler–Bernoulli beam assumption to study hydroelastic behaviours of very large floating structures (VLFSs). A continuous VLFS is divided into several modules, being multi-module floating structures. The section between two adjacent modules’ centre is seen as a beam element. Based on the above assumption, the six-degree-of-freedom motion of a module's centre is both affected by the hydrodynamic interaction with its adjacent module and restricted by the deformation condition of the equivalent beam between two modules. Then the motion equation of the equivalent multi-module floating structures can be established utilising the potential flow theory and Euler–Bernoulli beam hypothesis. The results calculated by the present method are compared with experimental results and numerically calculated data by three-dimensional hydroelastic theory, which shows rather good agreement.

The behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth-order nonlinear Schrodinger equation. The wavelet analysis method is adopted in order to analyse the time-frequency energy distribution during the generation and evolution of the Peregrine breather. It shows that the peak of the largest amplitudes of the resulting waves can be described in terms of the Peregrine breather-type solution and leads to the solution of the nonlinear Schrodinger (NLS) equation. Meanwhile, strong energy density is found to surge instantaneously and be seemingly carried over to the high-frequency components at the instant when the large, rogue wave occurs.

Because of scale effects and inappropriate hydrodynamic models, the nonlinear hydroelastic response of net cages used for fish-farming cannot be analyzed precisely with traditional model testing or combinations of finite element methods (FEMs) and load models. In this study, an innovative hybrid method is proposed to determine the hydroelastic response of full-scale floater-and-net systems more accurately. In this method, the net for the fish cage was vertically and peripherally divided into similar interconnected sections with different hydrodynamic parameters, which were assumed to be uniformly distributed over each section. A model of a typical section was subjected to various towing velocities, oscillation periods, and amplitudes in a towing tank to simulate the potential motions of all sections in the net under various currents, waves, and floater movements. By analyzing the measured hydrodynamic force from this test section, a hydrodynamic force database for a typical net section under various currents, waves, and floater motions was built. Finally, based on an FEM, the modified Morison equation and the hydrodynamic force database, the hydroelastic behavior of the full-scale fish cage was calculated with an iterative scheme. It is demonstrated that this hybrid method is able to produce correct hydroelastic response for both steady and oscillatory flows. The hydroelastic response of a two-dimensional example of a full-length net panel with steady currents and floater oscillations was studied in detail.

Laboratory tests were conducted on a flexible cylinder to improve the understanding of the response performance of vortex-induced vibration (VIV). The experiment was performed in a towing tank and the relative current was simulated by towing the flexible cylinder in one direction. Based on modal superposition, VIV displacements were obtained from the measured strain. VIV responses from different current cases were analysed, and the response performances, such as the motion trajectory, strain response, and fatigue damage, were studied. The motion trajectory for the flexible cylinder at low velocity displays the typical type-eight figure, very similar to that for a rigid cylinder. However, with increased velocity, the motion trajectory becomes chaotic, induced by the multi-mode VIV responses. Simplified fatigue damage based on the typical steady motion trajectory is usually a little larger than the measured fatigue damage based on the chaotic motion trajectory, but of the same order.

This paper presents theoretical and numerical study on bending properties of unbonded flexible risers. To capture nonlinearities in layer's sliding, the stress component due to slip-stick behavior is considered and energy conservation principle considering sliding-caused heat consumption is employed in the analytical model. Besides, a finite element model estimating mechanics of unbonded flexible risers' bending is proposed. In the finite element model, couplings between bending moment–curvature and axial stress as well as contact interaction among layers and tendons have been considered. The theoretical and numerical results were validated against the corresponding experimental data in literature and mutually compared in analyzing nonlinear bending behavior of flexible risers. Moreover, the impacts of axisymmetric loads on riser's bending behavior have been further investigated.

The drag and added mass coefficients of a flexible pipe undergoing vortex-induced vibration (VIV) in an oscillatory flow are investigated experimentally with maximum reduced velocities ranging from 4 to 7.9 and Keulegan-Carpenter (KC) numbers ranging from 10 to 178. The strain responses are measured by fiber bragg grating sensors. By using displacement reconstruction and inverse analysis methods, displacement response and hydrodynamic force are identified. Then, through least square method, drag and added mass coefficients are extracted. The results show that drag coefficient varies with both the maximum reduced velocity and KC number. It is stable in cases with large KC numbers but significantly amplified in the cases of small KC numbers. The maximum value of the drag coefficient can reach 3.5 at kC

The features of hydrodynamic coefficients including drag and added mass coefficients on a flexible pipe fitted with helical strakes in an oscillatory flow are studied experimentally. The experiment of a flexible straked pipe was conducted in an oscillatory flow with the Keulegan-Carpenter (KC) number varying from 9 to 165 and the maximum reduced velocities ranging from 4 to 8. Strain response in both in-line and cross-flow directions are measured by fiber bragg grating sensors. Using displacement reconstruction and inverse analysis methods, displacement response and hydrodynamic force of the straked pipe are identified. Then, through the least squares method, corresponding drag and added mass coefficients are extracted. The asymmetric features at the acceleration and deceleration stages of hydrodynamic force on a flexible pipe in the in-line direction under oscillatory flow are first observed. Compared with a bare pipe, helical strakes can effectively reduce the higher frequency fluctuating force and enhance the wake effects. The hydrodynamic coefficients on the straked pipe are significantly magnified in the case of a relatively small KC number. The maximum mean drag coefficients can reach approximately 10. The presented work suggests that the risk of helical strakes application should be fully evaluated through flexible pipe experiments in both steady flow and unsteady flow.

This paper presents a time-domain hydroelastic analysis method for bridges supported by floating pontoons in inhomogeneous wave conditions. The inhomogeneous wave effect is accounted for by adopting different wave spectra over different regions along the structure, then the time history of inhomogeneous first-order wave excitation forces on the floating pontoons can be obtained. The frequency-domain hydrodynamic coefficients are transformed into the time-domain hydroelastic model using Cummins' equations. The linear hydroelastic responses of a curved floating bridge with end supports, subjected to irregular waves with spatially varying significant wave heights and peak periods, are investigated. Moreover, sensitive analyses are performed to study the effects of the inhomogeneity on the hydroelastic responses. The primary results indicate that the inhomogeneity of the waves has a significant effect on the dynamic responses of the floating bridge.

A large-scale model test of a truncated steel catenary riser (SCR) was performed in an ocean basin to investigate the riser responses under top vessel motion. Top end of the model was forced to oscillate at given motion trajectories, corresponded with the motion at the truncation point of a full-length SCR under vessel motion. Out-of-plane vortex-induced vibration (VIV) was confirmed under pure top vessel motions, characterized with distinctive time-varying features. Results further indicate that vessel motion-induced VIV was strongly dependent on the KC number and the instantaneous equivalent flow profile. Meanwhile, tension variation was found to be another key factor causing response discrepancy between the ‘lift-up’ and ‘push-down’ phase for the large top vessel motion case. Finally, the relationship between the out-of-plane VIV dominant response frequency, maximum equivalent flow velocity and KC number were unveiled, which provides references for future vessel motion-induced VIV predictions.

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration (VIV) for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line (IL) response is as important as the cross-flow (CF) response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.

The effects of surface roughness on the vortex-induced vibration (VIV) of a flexible cylinder have been studied experimentally. The drag, lift, tension, vortex-shedding frequency, vibration frequency, and displacement response of cylinders with different roughnesses are compared. The results indicate that a pure VIV lock-in phenomenon occurs in the in-line direction earlier than in the cross-flow direction, and thus the VIV response in the in-line direction is larger than in the cross-flow direction in the low-reduced-velocity range. The tension in the cylinder has two peak frequencies. One peak is the dominant frequency, which coincides with the dominant frequency of the drag and is induced by the VIV in the in-line direction. The other peak is at half of the dominant frequency, at the dominant frequency of the lift; it is caused by the VIV in the cross-flow direction. Rough cylinders have a smaller displacement response, a narrower lock-in region, and a higher vortex-shedding frequency than a smooth cylinder.

Vortex-induced vibration (VIV) of a flexible cylinder in oscillatory flow was experimentally investigated in an ocean basin. An intermittent VIV was confirmed to have occurred during the tests. The fatigue damage caused by VIV was calculated based on rainflow counting and a standard S–N curve. There are 3 main observations for fatigue damage from VIV in oscillatory flow: 1) the damage varied significantly with the KC number, which is a unique feature for VIV in oscillatory flow. 2) Fatigue damage at small KC number cases was found to be larger compared to those at large KC numbers owing to the fact that number of vortex shedding cycles per half of the motion cycle is low, and damping within half of the motion cycle will hence become low. The fact that vortices from the previous cycle still are active during the next may also contribute to the large response at small KC numbers. 3) ‘Amplitude modulation’ and ‘mode transition’, two specific features for VIV in oscillatory flow, were found to have a strong influence on fatigue. Fatigue damage has also been calculated by an empirical VIV prediction model assuming that all cases have steady flow at an equivalent velocity. Finally, a simplified method for calculating fatigue damage from VIV in oscillatory flow based on steady flow conditions is proposed. A modification factor diagram is presented, but the scope of the present study is too limited to provide a good basis for a general model for this factor. A general model for how to apply results from constant current analysis to predict fatigue in oscillatory flow will therefore need further research.

Many significant engineering challenges have emerged as the petroleum industry has moved their field development and production activities into increasingly deeper water depths. The design of deepwater marine risers presents the combined challenges to minimize top tensioning requirements, mitigate any flow-induced vibrations, and if possible to increase the expected fatigue life of these slender structural members. As part of the design process to achieve these goals external buoyancy modules and strakes have been employed. To gain insight into the complex multi-mode response behavior a recent experimental study was performed and the analysis of selected data sets is presented. In the experiments a horizontal cylinder with a length to diameter ratio of 263 was fitted with a variety of strake and buoyancy element configurations. The models were towed at uniform speeds ranging from 0.4 to 2.0 m/s and fiber optic strain gages were used to measure both in-line and cross-flow strain response. The resulting time series information was processed utilizing the method of time domain decomposition formulated for strain data input and the introduction of modal assurance criterion to resolve the modal strain information that included frequency, mode shape, and critical damping ratio information. The pre-tensioned cylinder without appendages was used as a base case and the results were basically consistent with expectations. In the case of 0.8 m/s low-tension test, multiple closely spaced non-overlapping peaks were observed in both in-line and cross-flow directions and were identified as being of the same mode with mode shapes distorted away from purely sinusoidal behavior. The test data for the 100% coverage by helical stakes demonstrated the effectiveness of that suppression device over the range of current velocities investigated. The most interesting case was that of a staggered combination of helical strakes and buoyancy element whose total for each type of coverage was equal. This effective asymmetric VIV suppression approach is presented and discussed in detail.

A large-scale model test of a truncated steel catenary riser (SCR) was performed in an ocean basin to investigate the vortex-induced vibration (VIV) and its fatigue damage under pure top vessel motion. The top end of the test model was forced to oscillate at given vessel motion trajectories. Fiber Bragg grating (FBG) strain sensors were used to measure both in-plane and out-of-plane responses. Four different factors have been discussed to understand the VIV responses and fatigue damage results: instantaneous shedding frequency, touch down point (TDP) variation, tension variation and traveling waves. Out-of-plane VIV associated with strong time-varying features was confirmed to have occurred under pure vessel motion. Both KC number and maximum shedding frequency were investigated and indicated that the middle part of the truncated model riser was the ‘power-in’ region for out-of-plane VIV. Meanwhile, fatigue damage caused by out-of-plane VIV was found to be strongly dependent on both top motion amplitude and period. The probability distribution of the maximum damage exhibits 3 critical locations in the test model: TDP, upper sag-bend and top of the SCR. Strong traveling waves, TDP variation and end wave reflection have been proven to cause the maximum damage locations to shift from the ‘power-in’ region to these three positions. Finally, a maximum fatigue damage diagram with top motion amplitude, period and maximum shedding frequency was constructed.

A model test of a free-hanging riser under vessel motion and uniform current is performed in the ocean basin at Shanghai Jiao Tong University to address four topics: (1) confirm whether vortex-induced vibration (VIV) can happen due to pure vessel motion; (2) to investigate the equivalent current velocity and Keulegan–Carpenter (KC) number effect on the VIV responses; (3) to obtain the correlations for free-hanging riser VIV under vessel motion with VIV for other compliant risers; and (4) to study the similarities and differences with VIV under uniform current. The top end of the riser is forced to oscillate or move, in order to simulate vessel motion or ocean current effects. Fiber Bragg Grating (FBG) strain sensors are used to measure the riser dynamic responses. Experimental results confirm that the free-hanging riser will experience significant out-of-plane VIV under vessel motion. Meanwhile, vessel motion-induced VIV responses in terms of response amplitude, response frequency, and cross section trajectories under different test cases are further discussed and compared to those under ocean uniform current. Most importantly, the correlation among VIV response frequency, vortex shedding pairs, and maximum KC number KCmax is revealed. The presented work is supposed to provide useful references for gaining a better understanding on VIV of a free-hanging riser and for the development of future prediction models.

This paper investigates the phase angles of the vibrations and hydrodynamic forces by the model testing of a flexible riser's vortex-induced vibration (VIV) under uniform flow. The VIV displacement of the riser is derived from the measured strains in the cross-flow (CF) and inline (IL) directions. Then, the hydrodynamic forces are obtained by the dynamic equation of an Euler–Bernoulli beam based on the results of VIV displacement. The characteristics of the phase angle of displacement and the hydrodynamic forces are analyzed. The results show that the phase angles of displacement and the hydrodynamic forces are almost identical at different cross sections of the riser under uniform flow. Moreover, within two adjacent vibration nodes in IL direction, the phase angle almost kept constant, while had a 180 deg change at the two sides of each vibration node. When the reduced velocity varies from 5.25 to 7.5, the phase angles of displacement derived from the flexible riser's VIV are 45 deg larger than those from the rigid cylinder's self-excited vibration.

This paper experimentally investigates the nonlinear hydrodynamic forces on a semisubmerged floating collar under full-scale Reynolds number (R) and Keulegan-Carpenter number (KC) oscillatory flow alone and combined with a current. The collar was forced to oscillate harmonically in the direction of the current within a wide range of oscillation amplitudes and frequencies. The first five orders of the horizontal hydrodynamic forces are obtained using Fourier transformation techniques. The influence of the KC, the frequency parameter (β), and the reduced velocity (Vr) on the high-order components of the hydrodynamic force were investigated. The results show that, under oscillatory flows, the first five harmonics of the hydrodynamic force coefficients increase with an increase of KC and β. As the reduced velocity (Vr) increases, the first- and second-order components are greatly affected. These first two order components contribute greatly to the overall hydrodynamic force in the combined flow condit...

Flexible pipe with staggered buoyancy elements such as lazy wave riser and drilling riser has been widely used in ocean engineering. Under the influence of sea current, both of the buoyancy elements and the riser may experience vortex induced vibrations (VIV). However, when VIV occurs, hydrodynamic characteristics of the buoyancy elements and its influence on hydrodynamic force of the bare pipe still need investigation. The purpose of this paper is to reveal the hydrodynamic characteristics of flexible pipe with staggered buoyancy elements undergoing VIV. The crossflow (CF) hydrodynamic coefficients of the flexible pipe with 25%, 50%, and 100% coverage of staggered buoyancy are obtained from model tests, using hydrodynamic forces and coefficients identification method. Then, the characteristics of added mass coefficients and excitation coefficients in CF direction are analyzed. The results show that the added-mass coefficients of bare pipe are relatively larger than those of buoyancy module, while the total mass per unit length (sum of structural mass and added mass) is consistent along the pipe. Similarly, the range of excitation coefficient on the buoyancy elements is smaller than that on the bare pipe, and their ratio is equal to the reciprocal of diameter ratio 2.5.

Experimental investigations were conducted on a flexible riser with and without helical strakes. A uniform current was obtained by towing a riser model in a tank, and the vortex-induced vibration (VIV) suppression of strakes with different heights and pitches was studied. The experimental results indicate that the response characteristics of a bare riser can be quite distinct from those of a riser with helical strakes, and the suppression performance depends on the geometry of the helical strakes. The VIV responses in the cross-flow (CF) and in-line (IL) directions can be coupled via variations in the tensile force. The fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser fitted with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction. The experimental results also confirmed that the strake height has a greater influence on the VIV response than the strake pitch, and the drag exerted...

The objective of the present simulations is to evaluate the applicability of the standard k-e turbulence model in engineering practice in the subcritical to supercritical flow regimes. Two-dimensional numerical simulations of flow around a circular cylinder at Re=1x105, 5x105 and 1x106 , had been performed using Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the standard k-e turbulence model. Solution verification had been studied by evaluating grid and time step size convergence. For each Reynolds number, several meshes with different grid and time step size resolutions were chosen to calculate the hydrodynamic quantities such as the time-averaged drag coefficient, root-mean square value of lift coefficient, Strouhal number, the coefficient of pressure on the downstream point of the cylinder, the separation angle. By comparing the values of these quantities of adjacent grid or time step size resolutions, convergence study has been performed. Solution validation is obtained by comparing the converged results with published numerical and experimental data. The deviations of the values of present simulated quantities from those corresponding experimental data become smaller as Reynolds numbers increases from 1x105 to 1x106. This may show that the standard k-e model with enhanced wall treatment appears to be applicable for higher Reynolds number turbulence flow.