In-line Research Articles

Analysis of the vortex-induced vibration response characteristics of riser under the soft suspension evacuation condition

This paper establishes a nonlinear dynamic model for a suspended riser under the condition of considering realistic configurations, based on the principles of virtual work and Hamilton's variational principle. The nonlinearity of the model is manifested by considering vortex-induced vibration in the cross flow (CF) and in-line (IL) directions, as well as large deformations, taking into account the variable diameter of the riser in the compliant riser system. The model is discretized using the finite element method and solved using the Newmark-β method. Experimental validation is conducted to verify the effectiveness of the model. Utilizing the parameters of a riser in a well in the South China Sea, the paper explores the influence of different environmental and structural parameters on the VIV response characteristics of a compliant riser. Results show that the vibration frequency is controlled by both the bare tube and buoyant block when the buoyant block coverage rate is 25%, which can significantly inhibit VIV. With the increase of flow velocity, the VIV energy jumps from low order to high order, and the riser mode also transitions from low order to high order. The increase in suspension length transfers the vibration energy from high to low frequency, thus realizing energy transition and mode shape transformation. With the increase in LMRP weight, the vibration and natural frequencies of the riser increase synchronously, the vibration amplitude decreases, and the mode shape remains unchanged.

Observed wake branches from the 2-DOF forced motion of a circular cylinder in a free stream

The combined in-line (IL) and cross flow (CF) vibration of flexibly mounted cylinders in a free stream due to vortex-induced vibration (VIV) demonstrates significantly more complex dynamics than purely CF vibrations. In this study, the forces on a circular cylinder undergoing combined IL and CF motion in a free stream are investigated through an expansive series of forced motion experiments with force measurement and quantitative flow visualization. The motion of the cylinder is parameterized using sinusoidal motions with variation of the non-dimensional IL amplitude, non-dimensional CF amplitude, CF reduced velocity, and phase between IL and CF motion, while the Reynolds number is held constant at 7620. The resulting database of experimental measurements consists of 9555 variations of the governing motion parameters. The decomposed force coefficients are reported and mapped over the range of parameters. We observe a number of interesting wake-dependent parameter space features, such as regions of multiple branch responses, where the wake may exhibit multiple mode behaviors for the same cylinder motion parameters. Multiple branch regions are observed throughout the experimental data space.

Experiments on flow-induced vibration of four flexible cylinders with large aspect ratio in a square configuration

A system consisting of four cylinders positioned in the quadrilateral arrangement represents the prevalent and fundamental constituent within pipe bundles and tube banks in numerous engineering scenarios. This research presents a laboratorial study on flow-induced vibration (FIV) exhibited by four flexible cylinders positioned within a square geometric arrangement. The uniform flows were produced by a carriage on the top of a towing tank. Considering flow velocities and structural parameters, Reynolds number could reach 16000. The spacing between the cylindrical centres was selected as 6.0 D (D denotes the outer diameter of cylinders), and two typical incidence angles 0° and 45° were examined. For each flexible cylinder model, strain gages at seven distinct measuring positions were utilized to collect the oscillation data in cross-flow (CF) and in-line (IL) directions. Principal vibration modes, response frequencies, response amplitudes and motion trajectories were presented to understand the FIV features. For incidence angles 0°, considering the four flexible cylinders as two sets of tandem cylinders arranged in parallel is not appropriate due to the proximate effect. The behaviours of the two upstream cylinders resembles those of the pair of cylinders positioned in a side-by-side configuration, whereas behaviours for the downstream cylinders are influenced by wake interference generated from leading cylinders. IL response frequencies decrease to the values close to the CF response frequencies, resulting in the elliptical-shaped motion trajectories with large IL displacements. For incidence angles 45°, the upstream cylinder displays characteristics akin to those of a solitary cylinder experiencing vortex-induced vibration (VIV). Reactions for the central pair of cylinders result from the amalgamation of VIV and wake-induced flutter. While, reactions observed for downstream cylinder are characterized by low frequencies, significant IL displacements and more chaotic trajectories.

Predictions of multi-scale vortex-induced vibrations based on a multi-fidelity data assimilation method

This paper presents a data assimilation method based on the POD-DeepONet structure to fuse two types of fidelity data from vortex-induced vibration (VIV) problems. The data is mainly focused on amplitude response in different oncoming flow cases from cross-flow (CF) and inline (IL) directions for new flow speed predictions. The low-fidelity data in this paper is calculated from a semi-empirical code called DAVIV, while the high-fidelity data is measured from laboratory experiments. For a complex nonlinear correlation in amplitude and phase error between low and high-fidelity data, the POD-DeepONet structure receives better accuracy and more stable predictions than Neural Network with few training cases. It can successfully reconstruct the amplitude response along the marine riser and capture the changing trend with the oncoming flow speed. The POD-DeepONet is then applied to predict the VIV cross-flow and inline responses with different datasets. The prediction of mean square error (MSE) shows an exponential decline trend with the increasing case number for training. With the exponentially fitted MSE formula, the required case number under the expected error can be quickly obtained, which may provide a reference for efficient and high-fidelity VIV response prediction in engineering.

Fatigue damage characteristics of a flexible cylinder under concomitant excitation of time-varying axial tension and VIV

Flexible cylindrical structures are susceptible to the concomitant excitation of vortex-induced vibration (VIV) and time-varying axial tension in offshore engineering. The structural instability caused by the simultaneous excitation can lead to severe fatigue damage, threatening the safe application of cylindrical structures. In this paper, experimental research was conducted on a long flexible cylinder with an aspect ratio of L/D = 350 to investigate its fatigue characteristics under the concomitant excitation. The reduced velocity Vr ranged from 1.34 to 26.71. The axial tension excitation was characterized by three axial tension amplitude ratios Tv/Tc = 0.1–0.3 (where Tv is the tension amplitude and Tc is the constant tension) and six axial tension frequency ratios fv/f1 = 0.5–4.0 (where fv is the tension frequency and f1 is the fundamental frequency of the cylinder). The S–N curve method and the linear accumulative damage theory were employed to estimate the fatigue damage. The effects of reduced velocity, excitation amplitude and excitation frequency on the fatigue damage characteristics were discussed in terms of the fatigue damage distribution and maximum fatigue damage. The effect of the tension excitation on the fatigue damage is more pronounced at low reduced velocities (Vr ≤ 5.34) when the VIV is not excited, since the axial tension can excite the mode vibration. The fatigue damage area and maximum fatigue damage are significantly enhanced with the increase of the tension amplitude ratio and frequency ratio due to the occurrence of higher-order mode vibrations. The effect of axial tension excitation on the fatigue damage of the cylinder is more pronounced in the in-line (IL) direction than in the cross-flow (CF) direction. However, for a small amplitude ratio (Tv/Tc = 0.1), the tension excitation is only noticeable with a large frequency ratio (fv/f1 = 4.0). On the other hand, as the reduced velocity increases, the VIV of the cylinder is excited and dominates the fatigue characteristics. The accumulative fatigue damage distribution is aggravated with the increase of reduced velocity. The time-varying axial tension has a negligible effect on the fatigue damage distribution features and the maximum fatigue damage values of the cylinder. Nevertheless, under certain circumstances, the axial tension excitation can slightly alleviate the fatigue damage in some regions along the cylinder.

Investigation on the flow-induced vibration of tandem cylinders with varying diameters at subcritical Reynolds numbers

The flow interference among multiple cylinders is highly complex, and investigating it holds substantial engineering relevance. This paper considering three different arrangements at subcritical Reynolds numbers, a series of experiments were conducted to study the flow-induced vibrations (FIV) of rigid cylinders in tandem with variable diameters. Both cylinders are free to respond in both in-line (IL) and cross-flow (CF) directions. Utilizing a dynamic data acquisition system to obtain micro-strain time history information. The reference cylinder diameter (D) of 30 mm was employed as the standard for the spacing ratio (S/D). Both cylinders were exposed to uniform water flow at varying S/D: 3.0, 4.0, 6.0, and 8.0. A parametric investigation was conducted to analyze the effects of the relative spacing of the cylinders on the vibration response of the system. The results indicate that vibration intensity escalates as flow velocity increases. For the same cylinders, unsteady wave-induced vibrations (WIV) behind the upstream cylinder hinder the appearance of the lower branch of the amplitude response. Furthermore, the S/D substantially influences the cylinder vibration response. In the arrangement where the small cylinder is located upstream, the downstream cylinder undergoes WIV under smaller S/D, and the shielding effect is inconspicuous. In contrast, when the larger cylinder is located upstream, the shielding effect intensifies, leading to synchronous vibrations of the upstream and downstream cylinders. The S/D appears to exert minimal influence on the vibration under these conditions. In summary, the interference between cylinders in tandem configurations significantly impacts the vibration characteristics of the cylinders.

Experimental investigation of the effect of rotation rate and current speed on the dynamic response of riserless rotating drill string

Dynamic responses of rotating riserless drill string were investigated by varying rotation rate and current speed. Rotation rate ranged from 20 to 180 r/min, current speed ranged from 0.1 to 0.8 m/s, corresponding to Reynolds number of 1600–12,800 and rotation Reynolds number of 134–1206. Results show that the vibration energy of the rotating drill string is concentrated in rotation frequency, and its frequency doublings are stable in time series; equilibrium deflections are consistent in cross-flow (CF) and in-line (IL) directions and trajectory shows an oval-shape in still water. IL dominant frequency of rotating drilling string coupling VIV decreases, while CF dominant frequency and overall section dominant frequency increase with rotation rate. Vibration frequency transitions from high to low and its bandwidth increases in high shear-rate flow. Equilibrium deflection and vibration amplitude are higher than those of non-rotating drill string when Re ≤ 2400 due to the strong coupling of rotation and current. Rotation reduces mode participation, vibration envelopes are deflected to one side with both traveling and standing waves coexisting. Vibration amplitude reaches a maximum due to multiple resonances. Therefore, rotation rate near natural frequency should be avoided, and the rotation interference effect at low reduced velocity should not be overlooked.

Axial-transverse coupled vortex-induced vibration characteristics of composite riser under gas-liquid two-phase internal flow

In this paper, the dynamic behavior of axial (AX) and transverse coupled vortex-induced vibration (VIV) of composite riser under gas-liquid two-phase internal flow is studied. Firstly, based on Hamilton's principle, considering the structural characteristics of composite materials, gas-liquid two-phase internal flow, AX and transverse nonlinear coupling vibration and nonlinear external excitation, a more realistic VIV prediction model of composite riser is proposed. Compared with the existing experimental results, the validity of the model in this paper is verified, and it is found that the VIV prediction of the riser is more accurate when considering the AX and transverse coupling effects. Then, the effects of current velocity, liquid phase velocity, gas volume fraction and fiber orientation angle on the coupled VIV characteristics of gas-liquid mixed transport composite riser are studied. The results show that with the increase of current velocity, gas volume fraction and liquid phase velocity, the in-line (IL) vibration of the riser changes modally before the cross-flow (CF), but the fiber orientation angle has the opposite effect on this phenomenon. At the same time, when the two directions are in two different vibration modes, the vibration frequency in IL direction is obviously larger than that in CF direction. In addition, the riser AX vibration is almost unaffected by the parameters, but its vibration frequency is much larger than the other two directions, and the vibration center has shifted. We also find that the specific liquid phase velocity value will cause the chaotic vibration of the riser in the CF and IL directions, and the vibration displacements of the composite riser are almost equal in both directions.

Experimental Study on Vortex-Induced Vibration of Steel Tubes in Transmission Towers at Various Inflow Conditions

With the extensive construction of ultra-high voltage (UHV) transmission lines, the fatigue damage of steel tube members caused by vortex-induced vibration (VIV) in tubular towers has received growing attention. Although some progress has been made in the research of the VIV of steel tubes in uniform flow, there is still relatively scarce research on the VIV of steel tubes at various inflow conditions. In this paper, a series of wind tunnel tests are conducted to investigate the VIV of the steel tube subjected to uniform, turbulent, and oblique flows. Three turbulence intensities (Iu = 5.9%, 9.7%, and 12.6%), and four yaw angles (α = 10°, 20°, 30°, and 40°) are considered. The results show that the VIV response of the steel tube in the in-line (IL) direction is negligible compared to that in the cross-flow (CF) direction. The displacement amplitude gradually decreases as the turbulence intensity increases, accompanied by a more unstable response. For the inclined steel tube, the VIV maximum amplitude almost remains constant when α ≤ 20°, while it sharply decreased in the case of α = 30° and α = 40°. Furthermore, it was found that the so-called independent principle is applicable for α ≤ 10°.

Effects of surface roughness on two-degree-of-freedom vortex-induced vibration of a circular cylinder in oscillatory flow

The vortex-induced vibration (VIV) response performances of a two-degree-of-freedom circular cylinder with different surface roughnesses were numerically investigated in this work. Four typical roughnesses values of 1 × 10−4, 5 × 10−3, 1 × 10−2, and 2 × 10−2 were examined for the range of the reduced velocity (Vr = 1–20). The VIV response characteristics including the vibration amplitude, vibration frequency, VIV trajectory, vortex shedding flowing pattern, and hydrodynamic force for different rough cylinders were systematically compared. The numerical results showed that the VIV response of roughness cylinder experiences five evolutions as Vr increases, including five typical X–Y trajectories: centrosymmetry, “M” or “W,” “dough twists” or “candy,” “∞,” and asymmetrical ∞, exhibiting three vortex shedding flow pattern: S mode, C + S mode, and SS mode (a pair of symmetric vortices along the x-axis) under certain conditions. The VIV response was sensitive to the roughness in regime IV and regime V. Furthermore, the normalized vibration frequency of the rough cylinder was an integer multiple of the oscillatory flow frequency, except for the Vr ranged from 6 to 7. The vibration frequency in in-line (IL) direction was consistent with the frequency of the oscillatory flow, which was immune to the change of roughness. Additionally, when roughness was equal to 2 × 10−2, the reduction of maximum vibration amplitude in the cross-flow direction reached 31.2%, comparing with smooth cylinder, whereas the maximum vibration amplitude in the IL direction increased only by 6.2%.

Effect of internal solitary wave on the dynamic response of a flexible riser

Dynamic responses can arise when a flexible riser encounters the internal solitary wave (ISW) in the ocean. It is, thus, necessary to explore its dynamical behaviors induced by ISW. First, the governing equations of the flexible riser, ISW, and hydrodynamic force are introduced and interpreted. The accordant validations are performed so as to examine the accuracy of the applied models. Then, the dynamic response of the flexible riser is studied with the increase of the nondimensional ISW amplitude. Representative characteristics, such as vortex-induced vibration (VIV), top tension, and stress along the flexible riser, are mainly analyzed and discussed. The results prove that with the propagation of ISW, VIV in both inline (IL) and crossflow (CF) directions can be incurred. The maximum values of IL and CF oscillation frequencies, top tension, inline deflection, as well as riser stress can be detected while the ISW trough reaches to the flexible riser. Furthermore, all these four dynamic characteristics show an increasing trend with the increase of the nondimensional ISW amplitude. Note that the maximum values of oscillation frequencies, inline deflection, and stress on the upper section of the flexible riser tend to be larger compared with those on the lower section. In addition, the maximum inline deflection, top tension, and stress along the flexible riser can be affected by VIV responses.

Hydrodynamic coefficients of a forced oscillating flexible pipe with energy competition model

The objective of this study is to reveal the characteristics of hydrodynamic force and coefficients undergoing vortex-induced vibration (VIV) of a flexible pipe in an oscillatory flow. The flexible pipe is forced to oscillate with different amplitudes and periods in the still water to simulate the equivalent oscillatory flow. Different from the traditional model, the hydrodynamic forces for the flexible pipe under the new energy competition force model in both in-line (IL) and cross-flow (CF) directions are divided into drag, excitation and added mass force. The identification methods of the hydrodynamic coefficients for the energy competition force model are then established. The detailed features of the hydrodynamic coefficients under the new force model in an oscillatory are illustrated. The distribution comparison of the two forces, i.e., drag force plays a role in energy dissipation and excitation force acts as energy input, explains the differences of the VIV response in magnitudes under different oscillatory flows. By summarizing the hydrodynamic coefficients, the drag and excitation coefficients are found to be inverse proportion to the Keulegan-Carpenter (KC) number. The independence of the added mass coefficients and KC number is revealed. On the basis of the observation, the empirical models for hydrodynamic coefficients are preliminarily proposed. The effects of the oscillatory flow on the hydrodynamics are established to be determined by the KC numbers under the same reduced velocity. The present investigations will provide a better guideline for developing flow-induced vibration prediction methods in future work.

Experimental investigation on nonlinear dynamic response of towing cable under vessel motion

Marine towing cable is a crucial equipment of the underwater towing system which can acquire the marine resources distribution in the sea. The marine towing cable will experience nonlinear dynamic problems due to the vortex shedding and vessel motion during the towing movement. In order to investigate the dynamic response characteristics of the towing cable during the working process, a set of experimental devices for towing cable is designed and a PPR (Polypropylene-Random) pipe with the aspect ratio of 150 is tested with coupled uniform towing and vessel motion. The characteristics of response amplitude and frequency under uniform towing are compared and analyzed comprehensively with different towing speeds and towing depths. The key characteristics of nonlinear dynamic response under vessel motion are then discussed. Some phenomena involving multi-modal participation, frequency transition and amplitude modulation are captured. The vessel motion will excite ωCT - ωT, ωCT + ωT, ωT frequency components in the CF (cross-flow) direction which may be caused by the parametric excitation, and wave frequency ωT dominates the IL (in-line) direction response. Some extreme motion conditions may enlarge the response displacement in the IL and CF direction. It is suggested that the vessel motion should be taken into account in the evaluation of the nonlinear dynamic analysis of marine towing cable.

Experimental study on dynamic responses of a tensioned flexible vertical cylinder under waves and combined current and waves

The two degree-of-freedom (2DOF) dynamic responses of a flexible vertical cylinder under waves only and combined current and waves in a finite water depth were experimentally studied. The cylinder has multi-frequency response in both in-line (IL) and crossflow (CF) directions under waves. The response frequencies in the IL direction are multiples of wave frequency. The CF response frequencies include the multiples of wave frequency and the natural frequency of the cylinder, indicating that the CF response is controlled by both the wave actions and the vortex shedding. When the natural frequency of the cylinder is a multiple of the wave frequency, the CF vibration has the largest amplitude. A top tension can suppress the CF response more than the IL response amplitude, and the suppression effect increases with the increase of the top tension. With the decrease of the water depth, the response amplitudes in both directions decrease. Under combined current and waves, the IL response amplitude increases with the increase of KC number and the primary frequency of IL response is still the wave frequency. For a current velocity where VIV occurs, the superimposition of waves on current reduces the CF response amplitude because the vortex shedding frequency moves away from the natural frequency. The multi-frequencies of CF response are related to both the natural frequency of the cylinder and the wave frequency. The trajectories of the cylinder are mainly dependent on the ratio of the natural frequency to the wave frequency under waves or combined current and waves. There can be 2–6 cycles in the CF direction for each IL cycle with different wave frequencies and the top tension.

Coupled cross-flow and in-line vibration characteristics of frequency-locking of marine composite riser subjected to gas-liquid multiphase internal flow

In this paper, the frequency locking characteristics of marine composite riser coupled with cross-flow (CF) and in-line (IL) under the combined action of internal and external ocean currents in gas-liquid multiphase transportation are studied. Based on Hamilton's variational principle, the coupled vibration control equations of composite marine riser in CF and IL directions were established considering the combined action of internal and external ocean currents in gas-liquid multiphase transport. The Van der Pol wake oscillator model was used to simulate the flow force of the ocean current on the CF and IL directions of the slender riser. Newmark-β and fourth-order Runge-Kutta coupling iterative method were used to solve the coupled dynamics equation. The effectiveness and accuracy of the proposed method were verified by comparing with the results in literature. Subsequently, the effects of liquid phase velocity, fiber orientation angle and top axial tension on the frequency-locking characteristics of marine riser were given. The research results show that the internal flow velocity, external ocean current velocity, fiber orientation angle and top axial tension have a great influence on the coupled vibration stability and frequency locking characteristics of the riser. In addition, compared with the uniform single internal flow, the critical value of the velocity of the gas-liquid multiphase mixed internal flow is larger; The frequency-locking interval of the riser “shifts to the right” with the increase of liquid flow velocity and fiber orientation angle, and “shifts to the left” with the increase of top axial tension. It is also found that the frequency locking range of the riser decreases with the increase of fiber orientation angle and top axial tension, and expands with the increase of liquid flow velocity.

Vortex-induced forces of crossflow and inline oscillating bluff bodies at moderate Reynolds numbers

The Reynolds number (Re) is found to play an important role in the vibration response of a cross-flow (CF) only oscillating cylinder in the uniform flow that the maximum CF displacement (Ayd) increases with the increase of Re in the sub-critical regime, from 0.6 diameter (d) at Re = 1, 000 to 1.1d at Re = 20, 000. However, no existing research comprehensively studied the Re effect on the rigid cylinder vibrating in both the In-line (IL) and the CF directions. In this paper, with the help of the intelligent towing tank using an adaptive GPR sampling strategy for automatic sequential experimentation, we studied the vortex forces on a rigid cylinder forced to vibrate in the CF-only direction and the combined-IL-and-CF direction. We constructed a functional representation of the hydrodynamic coefficient database for the cylinder forced CF-only vibration (Re from 1200 to 19,000) and the cylinder combined-IL-and-CF vibration (Re from 1200 to 14,000). The results reveal that the maximum Ayd associated with the zero value of the lift coefficient in phase with velocity Clv = 0 increases significantly with Re for the CF-only vibrating cylinder, which compares well with and explains the trend observed in the free vibration experiment. In the meantime, Re is shown to have a less stronger effect on Ayd when the cylinder is allowed to move in both the IL and the CF directions in the sub-critical Re regime.

Spacing effect on the vortex-induced vibrations of near-wall flexible cylinders in the tandem arrangement

The vibration responses and flow dynamics in the vortex-induced vibrations of two near-wall flexible cylinders in the tandem arrangement are investigated through three-dimensional direct numerical simulations with the spacing ratio s/D =1.5–6 (D = diameter of the cylinder), gap ratio G/D = 0.8, cylinder length of 25D, and Reynolds number of 500. The in-line (IL) and crossflow (CF) vibrations are predominated by the first-order mode along the span. The upstream cylinder oscillates at a higher CF amplitude than the downstream one, and the maximum IL and CF vibration amplitudes of the tandem cylinders are both smaller than those of the single cylinder. The dominant frequencies of IL and CF oscillation are identical for the tandem cylinders, and they are larger than that of the single cylinder. The smaller mean drag and larger rms drag occur on the downstream cylinder than in the upstream counterpart. The difference between the spanwise rms lift of the two cylinders reduces as the s/D increases. Different flow types are observed along the flexible cylinders: at s/D = 1.5–2, an “extended-body regime” and a “reattachment regime” are excited near the two-ends and the middle regions along the span, respectively; at s/D = 3, a reattachment regime and a “co-shedding regime” appear; at s/D = 4–6, the co-shedding regime is observed but with different vorticities related to the vibration amplitudes. At s/D = 3, the wall proximity induces multi-frequencies in both the IL and CF oscillations, compared to single-frequency oscillations in wall-free conditions. The lower IL and higher CF vibration amplitudes are excited in the near-wall conditions. Weak “2S” and the typical 2S vortex shedding patterns are observed in the near-wall and wall-free conditions, respectively.

Three-dimensional nonlinear vortex-induced vibrations of top-tension risers considering platform motion

A novel three-dimensional (3-D) dynamic model considering nonlinearity of tension is proposed to explore in-line (IL), cross-flow (CF) and axial (AX) vortex-induced vibration (VIV) responses of riser under platform motion. The interaction between riser and external flow is simulated by the van der Pol equation, and the nonlinear equations of motion are established by Hamilton's principle and the Galerkin method, and solved by Runge-Kutta method. The influences of heave and swing motions of platform on VIV responses of the riser are investigated. It is found that for large velocity of external flow, the axial displacement of riser results in an increase in IL excitation mode and also an increase in IL oscillating displacement. When the riser is excited by swing motion of platform, with the increase of excitation amplitude, the maximum response amplitudes will also increase in all the three directions, and the amplitudes in high frequency domain increase more obviously. Combined effect of heave and swing motions of the platform results in the increase of VIV amplitudes in IL and AX directions, and combined action of forced and parametric excitations has little effect on response amplitude of riser in CF direction.

Galloping of two-dimensional section of a marine riser attached with fairing under different inflow angles

Fairing is one of the most effective and popular devices for suppressing vortex-induced vibration (VIV) of marine risers. However, when the fairing is stuck and cannot rotate due to biological contamination and other reasons, it may cause serious galloping oscillation and endanger the safety of the riser. In this paper, a reliable two-dimensional fluid-structure interaction (FSI) model with two degrees of freedom (DOF) was established based on computational fluid dynamics (CFD) and finite element method (FEM). The steady flow fields and galloping characteristics of a faired riser under different inflow attack angles were studied by numerical method. The results showed that when the structure is stationary, there is a critical attack angle αc ∈ (25°, 30°), which divides the vortex shedding state and the variation law of the hydrodynamic coefficient. This is because when the inflow attack angle α > αc, a reattachment of the shear layer occurs on one side of the fairing. In the 2 DOF FSI analysis, typical cross-flow (CF) direction galloping was observed in the region of α < αc. When α > αc, the oscillation was relatively weak, and the amplitudes in the in-line (IL) and CF directions were similar. When the α was near αc, the vibration was smallest. According to the structure of the wake vortex, the stable reattachment of the separated shear layer generated on one side of the fairing affected by the inflow attack angle is not easy to cause galloping. Only when the periodic reattachment occurs, it will trigger a strong galloping.

Comparative studies of hydrodynamic force models for flexible pipe in an oscillatory flow

The objective of this comparison study is to verify and clarify whether the energy competitive force model has significant benefits in eliminating the influence of certain factors on the hydrodynamic coefficient. The typical cases with the smaller Keulegan–Carpenter (KC) number (KC = 31) and larger KC number (KC = 178) under the maximum reduced velocity of 6.5 with the prominent VIV responses are selected for analysis. The characteristics of the ortex-induced vibration (VIV) response, the hydrodynamic force, and the corresponding spatiotemporal coefficients in typical cases are revealed, compared, and discussed. The results suggest that the energy competition force model cannot avoid spatial-temporal distribution characteristics of the hydrodynamic coefficients. Drag and excitation coefficients with energy roles under Sarpkaya's and energy competitive force models are affected by the VIV response and wake effects in an oscillatory flow. The larger coefficients are witnessed under the smaller KC number. When the KC number increases from 31 to 178, the mean drag coefficients decrease from 2.25 to 1.73, and the mean excitation coefficients in in-line (IL) and cross-flow (CF) directions decrease from 1.42 and 1.44 to 0.60 and 0.81, respectively, under the energy competition force model. Changes in wake effects under a larger KC number lead to distinctive differences in drag and excitation coefficients during the acceleration and deceleration phases. Through a quantitative comparative analysis, the current identified drag and excitation coefficients under the energy competition force model can obtain a more accurate prediction result. The present work shows that there exists the blindness in the selection of coefficients within the framework of the energy competition force model.