Vibration Of Riser Research Articles

A time domain prediction method for the vortex-induced vibrations of a flexible riser

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.

Experimental study of the vortex-induced vibration of marine risers under middle flow

A considerable number of studies for vortex induced vibration (VIV) under uniform flow have been performed. However, investigation of VIV under middle flow is scarce. An experiment for VIV under middle flow was conducted in a deep-water offshore basin. Various measurements were obtained by the fiber Bragg grating strain sensors placed on the riser, and VIV under the effect of middle flow with was investigated. Results show that the riser vibrates at different order natural frequencies along the water depth in the CF and IL directions appearing as the multi-frequencies under middle flow. The variation vortex shedding frequencies along the riser under middle flow may generate different wake modes and vibration modals as the corresponding vortex shedding frequencies approach the riser natural frequencies. The dominant vibration frequency of the entire riser is consistent, and determined by high order natural frequency and the corresponding closing vortex shedding frequencies under the middle flow. Meanwhile, the vibration modal under middle flow appears multi-modals and other lower modal have effect on riser vibration. The VIV mechanism under middle flow possesses some aspects similar to those of uniform flow and several unique features.

Wake and structure model for simulation of cross-flow/in-line vortex induced vibration of marine risers

Three dimensional responses of riser subjected to Vortex Induced Vibration (VIV) are investigated. Proportionality relations of stress and fatigue damage are mentioned. A computer code has been developed for time domain modeling of VIV of riser accounting for both Cross-Flow (CF) and In-Line (IL) vibration. The wake oscillator model is used to calculate the VIV of each strip. The wake oscillators are coupled to the dynamics of the long riser, while the Newmark-beta method is used for evaluating the structural dynamics of riser. The wake dynamics, including IL and CF vibrations, is represented using a pair of non-linear Van der Pol equations that solved using modified Euler method. The existing experimental and numerical results for stepped and sheared current are used to validate the proposed model and the results show reasonable agreement. The proposed model was implemented on Amir-Kabir semi-submersible riser deployed at the water depth of 713 meters of Caspian Sea. CF/IL VIV of this riser is simulated for various current velocities. The results show that although displacement amplitude of IL direction is lower than CF direction but because of higher curvature, stress values of IL direction for some cases can be higher than CF direction. Also because of higher frequency of IL direction, fatigue damage of this direction can be higher than CF one in some cases. It is shown that with increasing of current velocity; however, variation of displacement amplitude of two directions is low but stress increased and fatigue damage also increased with higher rate. For lower velocities which the modes are controlled with tension, stress and fatigue damage of IL direction is higher than CF direction.

Analysis on multi-frequency vortex-induced vibration and mode competition of flexible deep-ocean riser in sheared fluid fields

Multi-frequency vortex-induced vibration of flexible riser in lineally sheared fluid fields with different shearing parameters is explored by using the numerical approach. By combining the finite element method with a hydrodynamic model, the approach can consider mode competition based on modal energy and can carry out nonlinearly simultaneously dynamic response in time domain. Our analysis shows that multi-frequency VIV may occur both in non-uniform and uniform fluid fields. And, the behaviors of multi-frequency VIV are different from single-frequency VIV. Because several modes are involved and compete with each other, and consequently the determination of modal excitation region become more complicated. As the towing speed (or the shearing parameter) increases in sheared flow, the average RMS displacement does not regularly rise (or drop), but slightly fluctuates owing to changes of the participating mode and its excitation region. On the other hand, the average RMS stress gradually rises owing to higher-order modes being included. Moreover, it is found that the dominant frequency distributing along structural span significantly changes with the towing speed, and the length of the first dominant frequency gets smaller due to larger shearing parameter along with more intense competition between the participating modes.

Numerical analysis of Vortex-Induced Vibration for flexible risers under steady and oscillatory flows

Vortex-Induced Vibration (VIV) of flexible risers under unsteady flows is receiving increasing attention over the recent years. In this paper, an alternative time domain force-decomposition model for flexible risers is proposed to predict VIV response under both steady and oscillatory flows. Non-dimensional frequency range of [0.125, 0.25] is deemed as lock-in region. When lock-in occurs, the riser will be synchronized onto its own natural frequency closest to the non-dimensional frequency of 0.17. The hydrodynamic forces are time-varying and will be updated at each time step according to the riser's response amplitude and frequency. Firstly, the adopted lock-in region is verified well for uniform and sheared flow cases. Next, the same numerical model is also validated against experimental measurements when expanding to oscillatory flow conditions. VIV response with different KC numbers and maximum reduced velocities presents quite individual features, which can be reasonably explained from the VIV mechanism level. Then, the comparisons of VIV response between uniform and oscillatory flows are discussed and analyzed in essence. Finally, another large-scale riser is simulated under the designed oscillatory flows, and some new conclusions different from the small-scale risers are obtained.

Improving time-domain prediction of vortex-induced vibration of marine risers

The prediction of the vortex-induced vibration (VIV) of marine risers becomes a critical issue as the offshore exploration and production moving into deepwater and ultra-deepwater regions. In this paper, a time-domain model, based on a forcing algorithm and on high Reynolds number experimental data, was further developed to predict the VIV of rigid and flexible risers. The forcing algorithm was integrated into a global-coordinate-based finite-element program. At each time step, the hydrodynamic forces on a riser, including added mass, lift and drag forces, were calculated for each element based on two non-dimensional state variables—the amplitude ratio and the reduced velocity. The state variables were determined from a zero up-crossing analysis of the time history of the cross-flow displacement. Validation studies were carried out for a full-scale rigid riser segment in a uniform flow and a flexible riser in a stepped current. The predicted motions of the risers were compared with experimental data and the motions predicted by other numerical models.

Effect of drilling pipe rotation on vortex induced vibration response of drilling riser

An experiment was carried out in a basin to investigate rotation of drilling pipe on vortex induced vibration response of drilling riser. Vibration displacement time-history and frequency are obtained. Results show that dominant vibration frequency in the in-line direction is almost twice as high as that in the cross-flow direction. The vibration amplitudes in both the cross-flow and in-line direction increase with an increase in rotation speed of drilling pipe under the experimental conditions. However, the influence of rotation speed drilling pipe on drilling riser vibration amplitude is insignificant. Dominant frequencies are invariant with variation of drilling pipe rotation under experimental conditions.

Drilling-Induced Riser Vibration

Drilling-Induced Riser Vibration

A variationally bounded scheme for delayed detached eddy simulation: Application to vortex-induced vibration of offshore riser

We present a bounded and positivity preserving variational (PPV) method for the turbulence transport equation of Spalart–Allmaras based delayed detached eddy simulation (DDES). We employ the developed solver to simulate the vortex-induced vibration of a slender flexible riser immersed in a turbulent flow. The fluid-structure interface problem is solved by recently proposed partitioned iterative scheme [1], which consists of nonlinear force correction for a stable coupling of the Navier–Stokes equations with the low-mass structure subjected to strong inertial effects from the surrounding incompressible flow. In our fluid-structure model, we consider the flexible cylindrical riser as a long tensioned beam via linear modal analysis. In the present contribution, we first validate the PPV-based DDES solver for the flow past a three-dimensional stationary cylinder at two subcritical Reynolds numbers of Re=3900 and Re=140,000 based on the diameter of the cylinder. We next simulate a three-dimensional flexible riser model under a pinned-pinned condition at Re=4000 and compare our results with that of the experimental measurements. We assess the response characteristics at various locations along the span of the riser and discuss the orbital trajectories at those locations. In particular, the numerical study emphasizes on (i) The effectiveness of the modal analysis in modeling the riser dynamics and a positivity-preserving variational method in DDES for turbulence modeling, (ii) validation of response amplitudes and motion trajectories, and (iii) new insights on the trajectories and vortical structures of the flexible riser undergoing vortex-induced vibrations (VIV). We confirm a standing wave response and complex chaotic response of riser VIV observed in the recent experiments.

Stress wave propagation analysis on vortex-induced vibration of marine risers

To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony’s method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the “global” dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.

Modelling and Control of Flow Induced Vibration of Top–Tensioned Marine Risers Using Analytical Methods

For a riser array in deep waters, interference between individual risers in strong ocean current is of operational concern and thereby a key design issue. The lateral deflection is likely to be large, and the risers may experience collision with fatigue or coating damage as a consequence. In this paper, active control of flexible marine riser angle and the reduction of flow induced (forced) vibration under a time varying distributed load were considered using boundary control approach. A torque actuator was introduced in the upper riser package and a boundary control was designed to generate the required signal for riser angle control and vibration reduction with guaranteed closed-loop stability. The design is based on the partial differential equations of the system, which are developed using energy principle. Analytical method of solution was deployed with the aid of a program, developed within the framework of MATLAB, to predict the riser's behaviour by top tensioning. A sensitivity analysis for different values of the control variables was carried out. The results of this work showed that active control of flexible marine riser by top-tensioning reduced flow induced vibration.

Nonlinear vibration of marine riser with large displacement

This paper investigates the nonlinear free vibration of a marine riser with large displacement. The nonlinear equation of motion is derived using a variational approach based on Hamilton’s principle. The strain energy functional is composed of the strain energies due to axial deformation and bending. The strain energy associated with the rotational restraint at the bottom end of riser is also considered. The kinetic energy is derived by considering the riser and transporting fluid motions. The finite element method is applied to develop the nonlinear stiffness matrix, mass matrix, and gyroscopic matrix of the riser system. Consequently, the nonlinear natural frequencies and their corresponding mode shapes are determined by solving the eigenvalue problem incorporating the direct iteration technique. Various numerical examples are investigated to evaluate the linear and nonlinear dynamic characteristics of the riser. The parametric investigations of the horizontal top end offset, top tension, and rotational spring constant at bottom support are provided to show the modal transition phenomenon of the riser system. The nonlinear natural frequencies and their corresponding mode shapes are also presented to identify the softening and hardening behaviors of the riser.

Experimental study on vortex induced vibration of risers with fairing considering wake interference

Vortex Induced Vibration (VIV) is a typical flow-structure interference phenomenon which causes an unsteady flow pattern due to vortex shedding at or near the structure's natural frequency leading to resonant vibrations. VIV may cause premature fatigue failure of marine risers and pipelines. A test model was carried out to investigate the role of a stationary fairing by varying the caudal horn angle to suppress riser VIV taking into account the effect of wake interference. The test results show significant reduction of VIV for risers disposed in tandem and side-by-side. In general, fairing with a caudal horn of 45° and 60° are efficient in quelling VIV in risers. The results also reveal fairing can reduce the drag load of risers arranged side-by-side. For the tandem configuration, a fairing can reduce the drag load of an upstream riser, but will enlarge the drag force of the downstream riser.

Using strip theory to model vibrations in offshore risers

This paper presents an algorithm for the coupled time-domain solution of flow and structure equations using strip theory. The approach is then adopted for numerical simulation of the multi-mode response of flexible long risers used in the offshore energy industry for vortex-induced vibrations. The various models currently used to solve the problem of vortex-induced vibrations in marine risers are briefly studied and compared. The work reported here initially includes calculation of eigenvalues and eigenmodes of risers, the results of which are subsequently used to predict the response of risers based on a modal analysis. The two-dimensional flow simulations used in the strip theory are validated using experimental and numerical results presented in the literature. The root mean square of the amplitude of the riser movement in the cross-flow direction for various top tensions are studied and compared with similar cases reported in the literature.

Parametrically excited vibrations of marine riser under random wave forces and earthquake

This article presents theoretical studies for parametrically excited vibrations of marine riser of the floating production, drilling, storage, and offloading system under random wave forces and earthquake excitation. The equation of motion of the riser is obtained by a mathematical method utilizing Euler beam theory and Galerkin method. The trigonometric series method is used to formulate random wave force and earthquake excitation in time domain. The dynamic analysis, spectral response analysis, and key parameters’ sensitivity analysis are conducted for the riser system. Parameter studies are conducted for the effects of wave and earthquake parameters and structural parameters on dynamics response of the riser system. The results from this study can provide valuable recommendations for the design and construction of the parametrically excited marine riser system under random wave forces and earthquake excitation and can promote widely practical application of the deep water riser in complicated environmental conditions.

Coupled dynamic analysis of deepwater drilling riser under combined forcing and parametric excitation

This paper presents a coupled dynamic analysis of a marine riser under combined forcing excitation and parametric excitation. The forcing and parametric excitation are induced by lateral sea wave and current, and time-varying heave motion of a floating vessel respectively. Firstly, the mechanical model and control equations, which can be solved by Runge-Kutta method, have been established. Then, the Mathieu instability region has been figured out by perturbation method through transforming the control equation into Mathieu equation. On this basis, riser vibration response, bending moment and shear force under the two kinds of actions, sea current (Case I) and combination action of sea current and sea wave (Case II), have been discussed respectively. Results show that, under these two cases, riser vibration responses are both given priority to the first order of vibration mode. The vibration amplitude of riser bending moment under Case II is bigger than that under Case I. Moreover, riser total shear force is mainly determined by the first order mode under Case I, while under Case II, the influences of the first several order vibration modes on the total shear force are non-ignorable.

Study on Multimode Vortex-Induced Vibration of Deepwater Riser in Different Flow Fields by Finite Element Simulations

Multimode vortex-induced vibration (VIV) of slender risers, respectively, in stepped and shear flows is explored by finite element simulations. Taking account of the interaction between fluid and structure, a hydrodynamic model is proposed and embedded into the finite element simulation so as to carry out dynamic response of multimode VIV in time-domain. Multimode VIV in both stepped and shear flow fields is examined. In the case of stepped flow, a semi-empirical formula of modal weight is given. In the case of shear flow, modal excitation region can be determined based on modal energy, and participating modes approximately distribute in scattering groups.

Top Tension Control of a Flexible Marine Riser by Using Integral-Barrier Lyapunov Function

This paper presents a boundary controller for a flexible marine riser to suppress the riser's vibration with a top tension constraint. The flexible marine riser is described by a distributed parameter system with a partial differential equation and four ordinary differential equations. The boundary controller is designed at the top boundary of the riser based on an integral-barrier Lyapunov function to suppress the riser's tension at top. Adaptive control is designed when the system parametric uncertainty exists. With the proposed robust adaptive boundary control, uniformed boundedness under the ocean disturbance can be achieved. Stability analysis of the closed-loop system is given using the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller with top tension constraint.

Axial and Transverse Coupled Vibration Characteristics of Deep-water Riser with Internal Flow

The present paper investigates the axial and transverse coupled vibration law of deep-water top-tensioned riser (TTR) under the combined effects of the internal fluid flow and external wave and current loads. The paper aims to derive nonlinear vibration equations of deep-water riser, which account for the coupling of axial and transverse vibration including vortex-induced vibration, the internal fluid flow and the changes of the riser cross-sectional area caused by internal and external pressure alteration. With all factors above involved, a coupling vibration model is developed for deep-water riser. Based on the numerical model established, the influences of internal flow and the changes of internal flow velocity on the coupled vibration of deep-water riser are analyzed. In addition, parameter excited dynamic response of the riser under complex environment is also studied. The comprehensive analysis demonstrates that the internal flow can greatly change the vibration characteristics of the riser, comparing with a hollow one. The results lend support to the conclusion that the vibration of riser is not sensitive to changes of the internal flow velocity.

Study on lateral vibration analysis of marine riser in installation-via variational approach

In this paper, a dynamic analysis model has been established to analyze lateral vibration of marine riser in installation. The governing differential equation has been deduced by variation method. The general formula of riser lateral dynamical response has also been obtained through analyzing the analysis model and the boundary conditions. In this model, the riser is regarded as a beam suspended in the floating drilling platform (ship) and subjected to the axial force and the lateral forces changes with time and water depth (WD). Finally, the expression of the lateral vibration has been obtained and the maximum lateral vibration displacement variations with WD, riser size, weight of Blow out preventers and Lower Marine Risers Package (BOPS/LMRP), wave height and wave period have also been discussed.