Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s.Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.

Experimental Study on Coupled Cross-Flow and in-Line Vortex-Induced Vibration of Flexible Risers

In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flow where the mass and natural frequencies are precisely the same in both X- and Y-direction. The fluid speed varies from low to high with the corresponding vortex shedding frequency varying from below the first natural frequency to above the second natural frequency of the flexible pipe. Particular emphasis was placed on the investigation of the relationship between in-line and cross-flow vibration. The experimental results analyzed by using these measurements exhibits several valuable features.

Global Analysis of a Flexible Riser

The mechanical performance of a flexible riser is more outstanding than other risers in violent environmental conditions. Based on the lumped mass method, a steep wave flexible riser configuration attached to a Floating Production Storage and Offioading （FPSO） has been applied to a global analysis in order to acquire the static and dynamic behavior of the flexible riser. The riser was divided into a series of straight massless line segments with a node at each end. Only the axial and torsional properties of the line were modeled, while the mass, weight, and buoyancy were all lumped to the nodes. Four different buoyancy module lengths have been made to demonstrate the importance of mode selection, so as to confirm the optimum buoyancy module length. The results in the sensitivity study show that the flexible riser is not very sensitive to the ocean current, and the buoyancy module can reduce the Von Mises stress and improve the mechanical performance of the flexible riser. Shorter buoyancy module length can reduce the riser effective tension in a specific range of the buoyancy module length when other parameters are constant, but it can also increase the maximum curvature of the riser. As a result, all kinds of the riser performances should be taken into account in order to select the most appropriate buoyancy module length.

Analytical and Numerical Models to Predict the Behavior of Unbonded Flexible Risers Under Torsion

This paper presents analytical and numerical models to predict the behavior of unbonded flexible risers under torsion.The analytical model takes local bending and torsion of tensile armor wires into consideration,and equilibrium equations of forces and displacements of layers are deduced.The numerical model includes lay angle,cross-sectional profiles of carcass,pressure armor layer and contact between layers.Abaqus/Explicit quasi-static simulation and mass scaling are adopted to avoid convergence problem and excessive computation time caused by geometric and contact nonlinearities.Results show that local bending and torsion of helical strips may have great influence on torsional stiffness,but stress related to bending and torsion is negligible;the presentation of anti-friction tapes may have great influence both on torsional stiffness and stress;hysteresis of torsion-twist relationship under cyclic loading is obtained by numerical model,which cannot be predicted by analytical model because of the ignorance of friction between layers.

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.

Enhanced Multi-Layer Fatigue-Analysis Approach for Unbonded Flexible Risers

This paper proposes an enhanced approach for evaluating the fatigue life of each metallic layer of unbonded flexible risers. Owing to the complex structure of unbonded flexible risers and the nonlinearity of the system, particularly in the critical touchdown zone, the traditional method is insufficient for accurately evaluating the fatigue life of these risers. The main challenge lies in the transposition from global to local analyses, which is a key stage for the fatigue analysis of flexible pipes owing to their complex structure. The new enhanced approach derives a multi-layer stress-decomposition method to meet this challenge. In this study, a numerical model validated experimentally is used to demonstrate the accuracy of the stress-decomposition method. And a numerical case is studied to validate the proposed approach. The results demonstrate that the multi-layer stress-decomposition method is accurate, and the fatigue lives of the metallic layers predicted by the enhanced multi-layer analysis approach are rational. The proposed fatigue-analysis approach provides a practical and reasonable method for predicting fatigue life in the design of unbonded flexible risers.

Behavior of Unbonded Flexible Risers Subject to Axial Tension

Owing to nonlinear contact problems with slip and friction, a lot of limiting assumptions are made when developing analytical models to simulate the behavior of an unbonded flexible riser. Meanwhile, in order to avoid convergence problems and excessive calculating time associated with running the detailed finite element （FE） model of an unbonded flexible riser, interlocked carcass and zeta layers with complicated cross section shapes are replaced by simple geometrical shapes （e.g. hollow cylindrical shell） with equivalent orthotropic materials. But the simplified model does not imply the stresses equivalence of these two layers. To solve these problems, based on ABAQUS/Explicit, a numerical method that is suitable for the detailed FE model is proposed. In consideration of interaction among all component layers, the axial stiffness of an eight-layer unbonded flexible riser subjected to axial tension is predicted. Compared with analytical and experimental results, it is shown that the proposed numerical method not only has high accuracy but also can substantially reduce the calculating time. In addition, the impact of the lay angle of helical tendons on axial stiffness is discussed.

Experimental study and numerical simulation on vortex-induced vibration of flexible riser

In order to study the effect of internal flow on vortex-induced vibration of flexible riser, the experiment on the vortex - induced vibration of flexible riser transporting fluid in the current was conducted in the physical oceanography laboratory of Ocean University of China. Considering the internal flowing fluid and external marine environment, the dynamic response of the flexible riser was measured. The corresponding numerical simulation was performed using the wake oscillatory model considering the extensibility of the riser system. Both the experiment and the numerical simulation indicated that with the increase of internal flow speed, the response amplitude increases, while the response frequency decreases.

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

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.

Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number

This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration(VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34 E5 to 2.35 E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow(CF) and inline(IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under"lock-in" condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.

Development of a Robot for In-service Radiography Inspection of Subsea Flexible Risers

The extreme operational environmental conditions and aging conditions of subsea structures pose a risk to their structural integrity and is critical to their safety.Nondestructive testing is essential to identify defects developing within the structure,allowing repair in a timely manner to mitigate against failures that cause damage to the environment and pose a hazard to human operators.However,to be cost effective,inspections must be carried out without taking the risers out of service.This poses significant safety risks if undertaken manually.This paper presents the development of an automated inspection system for flexible risers that are used to connect wellheads on the seafloor to the offshore production and storage facility.Due to the complex structure of risers,radiography is considered as the best technique to inspect multiple layers of the risers.However,radiography inspection,in turn,requires a robotic system for in-situ inspection with higher payload capacity,precise movement of source and detector which is able to withstand an extreme operational environment.The deployment of a radiography inspection system hasbeen achieved bydeveloping acustomized subsearobotic system called RiserSure that can provide precise scanning motion of a gamma ray source and digital detector moving in alignment.The prototype has been tested on a flexible riser during shallow water sea trials with the system placed around a riser by a remotely operated vehicle.The results from the trials show that the internal inner and outer tensile armor layer and defects in the riser can be successfully imaged in real operational conditions.

Vibration Control of A Flexible Marine Riser System Subject to Input Dead Zone and Extraneous Disturbances

An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control algorithm can update the control law online through real-time data to make the controller adapt to the environment and improve the control precision.Specifically,based on the adaptive backstepping framework,virtual control laws and Lyapunov functions are designed for each subsystem.Three direction interference observers are designed to track the timevarying boundary disturbance.On this basis,the inverse of the dead zone and linear state transformation are used to compensate for the original system and eliminate the adverse effects of the dead zone.In addition,the stability of the closed-loop system is proven by Lyapunov stability theory.All the system states are bounded,and the vibration offset of the riser converges to a small area of the initial position.Finally,four examples of flexible marine risers are simulated in MATLAB to verify the effectiveness of the proposed controller.

Numerical simulations of vortex-induced vibrations of a flexible riser with different aspect ratiosin uniform and shear currents

This paper aimed at describing numerical simulations of vortex-induced vibrations（VIVs） of a long flexible riser with different length-to-diameter ratio（aspect ratio） in uniform and shear currents. Three aspect ratios were simulated： L/D= 500, 750 and 1 000. The simulation was carried out by the in-house computational fluid dynamics（CFD） solver viv-FOAM-SJTU developed by the authors, which was coupled with the strip method and developed on the OpenFOAM platform. Moreover, the radial basis function（RBF） dynamic grid technique is applied to the viv-FOAM-SJTU solver to simulate the VIV in both in-line（IL） and cross-flow（CF） directions of flexible riser with high aspect ratio. The validation of the benchmark case has been completed. With the same parameters, the aspect ratio shows a significant influence on VIV of a long flexible riser. The increase of aspect ratio exerted a strong effect on the IL equilibrium position of the riser while producing little effect on the curvature of riser. With the aspect ratio rose from 500 to 1 000, the maximum IL mean displacement increased from 3 times the diameter to 8 times the diameter. On the other hand, the vibration mode of the riser would increase with the increase of aspect ratio. When the aspect ratio was 500, the CF vibration was shown as a standing wave with a 3-（rd） order single mode. When the aspect ratio was 1 000, the modal weights of the 5-（th） and 6-（th） modes are high, serving as the dominant modes. The effect of the flow profile on the oscillating mode becomes more and more apparent when the aspect ratio is high, and the dominant mode of riser in shear flow is usually higher than that in uniform flow. When the aspect ratio was 750, the CF oscillations in both uniform flow and shear flow showed multi-mode vibration of the 4-（th） and 5-（th） mode. While, the dominant mode in uniform flow is the 4-（th） order, and the dominant mode in shear flow is the 5-（th） order.

Nonlinear Analysis of Flexible and Steel Catenary Risers with Internal Flow and Seabed Interaction Effects

Flexible risers and steel catenary risers often provide unique riser solutions for today’s deepwater field development. Accurate analysis of these slender structures, in which there are high-speed HP/HT internal flows, is critical to ensure personnel and asset safety. In this study, a special global coordinate-based FEM rod model was adopted to identify and quantify the effects of internal flow and hydrostatic pressure on both flexible and deepwater steel catenary risers, with emphasis on the latter. By incorporating internal flow induced forces into the model, it was found that the internal flow contributes a new term to the effective tension expression. For flexible risers in shallow water, internal flow and hydrostatic pressure made virtually no change to effective tension by merely altering the riser wall tension. In deep water the internal pressure wielded a dominant role in governing the riser effective tension and furthering the static configuration, while the effect of inflow velocity was negligible. With respect to the riser seabed interaction, both the seabed support and friction effect were considered, with the former modeled by a nonlinear quadratic spring, allowing for a consistent derivation of the tangent stiffness matrix. The presented application examples show that the nonlinear quadratic spring is, when using the catenary solution as an initial static profile, an efficient way to model the quasi-Winkler-type elastic seabed foundation in this finite element scheme.

Nonlinear Dynamic Analysis of Flexible Marine-Risers

A nonlinear dynamic analysis model is estabilished on the basis of 'lumped mass' approach, which takes the influence of the fluid flow within the pipe into consideration. Numerical results are compared with the published works, and the effects of internal fluid flow, internal pressure, dyanmics as well as the nonlinear characteristics on the behavior of flexible risers are discussed. From this work, some useful conclusions are drawn.

Coupled Element Modeling Scheme for the Global Dynamic Analysis of Unbonded Flexible Risers

A coupled element modeling method is proposed for global dynamic analyses of unbonded flexible risers.Owing to the multi-layer structure of unbonded flexible risers, the global-dynamic-analysis method applied to the steel rigid risers is insufficient for flexible risers. The main challenges lie in the enormous difference between the anti-tension and anti-binding capacity of unbonded flexible risers which results in serious ill-conditional calculation in global dynamic analysis. In order to solve this problem, the coupled element modeling approach was proposed in this study. A time domain fatigue analysis was applied to illustrate the necessity of the proposed approach.A dynamic benchmark case is used to demonstrate the accuracy of the coupled element method respectively.Subsequently the validated coupling element method is employed to conduct the global dynamic analyses for a free hanging flexible riser. The results demonstrate that the proposed approach can give the accurate global dynamic response under the guidance of the fatigue failure mode for unbonded flexible riser. The parametric influence analyses also provide a practical and effective way for predicting the global dynamic response.

Hydrodynamic performance of flexible risers subject to vortex-induced vibrations

The Vortex-Induced Vibration （VIV） displacements are determined from both the measured accelerations and strains in a series of VIV experiments. Based on the results, the forces in the longitudinal, transversal and tangential directions are estimated by using the finite element method with and without considering the interactions between adjacent elements. The numerical simulation indicates that the method considering the interactions performs better in the estimation of the forces. The component of the transversal force in phase with the acceleration is associated with the added mass coefficient. The estimated added mass coefficients take abnormally high values at the locations where the displacements are small. An improved formula based on the L＇Hospital＇s rule is pro- posed to deal with this problem. The results show the advantage of this formula in estimating the added mass coefficients at the loca- tions with small VIV displacements.

Stress Analysis of the Subsea Dynamic Riser BaseProcess Piping

Thesubsea dynamic riser base （SDRB） is an important piece of equipment for the floating production platform mooring system.One end is connected to the rigid pipeline, carrying a rigid pipeline thermal expansion load and the other end is connected to a flexible riser, carrying the dynamic load of the flexible riser, so its function is a transition connection between the flexible riser and the rigid pipeline which fixes the flexible riser on the seabed. On the other hand. as a typical subsea product, the design will satisfythe requirements of the standards for subsea products. By studying the stress analysisphilosophy of the topside piping and subsea pipeline, a physical model and procedure for piping stress analysis of the SDRB have been established.The conditions of the adverse design load have been considered, and a combination of the static load from the rigid pipeline and the dynamic load flexibility has also been optimized. And a comparative analysis between the AMSE, DNV and API standards for piping stress with the checking rules has been done.Because theSDRB belongs to the subsea pipeline terminal product, the use of DNV standards to check its process piping stress is recommended. Finally, the process piping stress of the SDRB has been calculated, and the results show that the jacket pipe and the carrier pipe stress of the SDRB process piping satisfy the DNV standards as a whole.The bulkhead cannot be accurately simulated by the AutoPIPE software which uses the FEA software ANSYS inthe detailed analysis, but the checking results will still meet the requirements of the DNV standards.

Nonlinear Behaviour of Coflexip Risers

A modified Newton-Raphson iterative technique is formulated for obtaining the static configuration of the Lazy 'S' flexible marine riser between the floater and mid-arch buoy under its submerged self weight and the applied top tension. The geometrically non-linear problem is solved by finite difference with the above technique. The problem is formulated as a regular boundary value problem with specified moments and deflections at both ends. Usually the bending stiffness of the flexible riser made of Coflexip pipe is very low. By use of the above analysis, several flexible riser configurations are analyzed and their characteristic behaviors are investigated. Also, changes in the riser characteristics due to quasi-static motion of the floater end are estimated for the safety of the riser layout.