Search

A coupled flow-induced vibration response prediction method in the frequency domain for double flexible risers in tandem arrangements with wake interference is developed. The non-iterative vortex-induced vibration (VIV) prediction method for a single riser is applied to the upstream riser. Based on the VIV prediction results of the upstream riser, a wake-induced vibration (WIV) prediction method of the downstream riser is established by iterating the clearance between adjacent risers, the wake velocity, the WIV amplitude and the drag displacement to consider the wake interference. To predict the WIV frequency and amplitude of the downstream riser, the flow velocity input is the wake velocity of the upstream riser. In addition, if frequency capture occurs, the added mass coefficient of the downstream riser will be adjusted to obtain a natural frequency identical to the upstream dominant frequency. Otherwise, the added mass coefficient is still 1. The other procedures of WIV prediction are identical to the VIV prediction steps. Finally, compared to the experimental results, the coupled VIV-WIV prediction results can reach satisfactory precision in far-field wake interference, which is conducive to the practical engineering design for multiple-riser systems. • A frequency-domain prediction method for VIV-WIV of double flexible risers in tandem arrangements is developed. • The method can predict frequency capture of the upstream larger riser and the downstream smaller riser. • The method can obtain satisfactory prediction precision for multiple-riser design in practical engineering. [ABSTRACT FROM AUTHOR]

Featured Application: The present work highlights a novel empirical formula to estimate both mean and fluctuating lift force on a semi-submerged cylinder under oscillatory flow. It greatly avoids the complicated and time-consuming hydrodynamic calculation problem and will be helpful to calculate the hydrodynamic force in the design of relevant marine structures, such as floating collar of fish farming. This work experimentally investigated the performance of hydrodynamic forces on a semi-submerged cylinder under an oscillatory flow. To generate the equivalent oscillatory flow, the semi-submerged cylinder is forced to oscillate in several combinations of different periods and amplitudes. The mean downward lift force was observed to be significant and the fluctuating lift forces show dominant frequency is twice that of oscillatory flow and amplitude that is the same as the mean lift force. Based on this main hydrodynamic feature, a novel empirical prediction formula for the lift forces on semi-submerged cylinder under oscillatory flow is proposed where the lift forces expression is proportional to the square of oscillatory flow velocity. This novel empirical formula directly assigns the fluctuating lift force with frequency twice of oscillatory flow and the amplitude that is the same as the mean lift force. This assignment of empirical lift force formula reduces parameters required to determine a dynamic lift force but is demonstrated to well predict the fluctuating lift force. The lift coefficient can reach 1.5, which is larger than the typical value 1.2 of the drag coefficient for a fully submerged cylinder with infinite depth. Moreover, relationships among hydrodynamic coefficients, Keulegan-Carpenter (KC) number, Stokes number and Froude number are studied. With the increase of KC number, the Froude number has a more significant influence on the distribution of hydrodynamic coefficients. As Froude number is increasing, the drag coefficient shows a nonlinear decay (KC < 20) but a linear increase (KC > 20), while the added mass coefficients show a nonlinear (KC < 20) and a linear (KC > 20) increase trend. The present work can provide useful references for design of the relevant marine structures and serve as the useful guideline for future research. [ABSTRACT FROM AUTHOR]

The drag force coefficients of a flexible riser undergoing vortex-induced vibration (VIV) in sheared flow are investigated for Reynolds numbers (Re) up to 1.2×10 5 . 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 1.0×10 4 –1.2×10 5 , 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 1.2×10 5 . [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, vortex-induced force (VIF) characteristics of a flexible pipe under oscillatory flow are experimentally investigated with different KC numbers ranging from 10 to 178, and reduced velocities from 4 to 7.9. The strain information caused by vortex-induced vibration (VIV) at different cross-sections on the flexible cylinder is measured in the model test. Combined with the modal superposition method and inverse analysis method for hydrodynamic force, the hydrodynamic forces on the flexible cylinder are inverted, including the excitation force in phase with velocity and added mass force in phase with acceleration. Then, through a least square method with forgetting factors, the excitation coefficients and added mass coefficients at each time step are identified. The results show that the VIV excitation coefficient of a flexible pipe under oscillatory flow has a significant "acceleration and deceleration" effect, that is, the excitation coefficients are mostly positive at the acceleration section of the oscillatory flow and negative at the deceleration section. This "acceleration and deceleration" effect also explains the response amplitude modulation feature of VIV under oscillatory flow. And this effect can be represented by the dimensionless acceleration parameter γ of the flow field, and the range of γ corresponding to the positive excitation coefficient is affected by the KC number and the maximum reduced velocity. In addition, the added mass coefficients present different time-varying features under oscillatory flow with different maximum reduced velocity. When the maximum reduced velocity is larger than 6.5, the time-varying trend of the added mass coefficient is opposite to that of the flow velocity. While when the maximum reduced velocity is smaller than 6.5, the added mass coefficient is maintained around 2.0 in VIV excitation region; and it is around 1.0 in the non-excited region which is close to the added mass coefficient of a cylinder in still water. [ABSTRACT FROM AUTHOR]

A modified wake oscillator model for modelling vortex-induced vibrations (VIVs) of a free-hanging riser subjected to vessel motion is presented. Different from the conventional wake oscillators which have typically utilized in the prediction of steady flow VIVs , the new model can be applied to simulate VIVs introduced by the vessel motion where the flows around the riser are not known in advance. This has been achieved by introducing an equivalent flow based on the relative flow velocity and coupling the wake oscillator with the acceleration of the riser in the lift direction. The modified wake oscillator model is tuned against the experiments of riser VIVs subjected to steady flows and a set of empirical parameters is obtained. The model is then applied to simulate the VIVs of a large-scale free-hanging water intake riser (WIR) subjected to different vessel motions and the simulated results are compared to those of experiments. The comparison shows that the proposed model is able to predict response frequency in good agreement with the experiment, and generates satisfactory prediction with respect to the response amplitude for three test cases out of five that have been studied in the present paper. • A modified wake oscillator model is proposed for vessel-motion induced VIV. • An equivalent flow and acceleration coupling in the lift direction are introduced. • The proposed model is able to predict response in good agreement with the experiment. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid FEM-DNN-based vortex-induced vibration (VIV) prediction method for flexible pipes under an oscillatory flow in the time domain is proposed. In this method, a vortex-induced force coefficient model is regressed by a deep neural network (DNN) from experimental data. The model takes into account the effects of flow velocity variation, VIV responses and their coupling features on vortex-induced forces. Then, it is combined with finite element method (FEM) to predict the VIV responses of flexible pipes in time domain. In addition, a phase modulation model is developed to ensure that synchronization between forces and responses can be achieved. The proposed prediction method is used to predict the VIV responses of the flexible pipe used in DNN regression training under oscillatory flows. Comparisons between the predicted results and the experimental results are conducted to verify the feasibility and accuracy of the proposed method. Then, the generalizability of the proposed method is further verified via comparisons between the predicted VIV results and the experimental results of another flexible pipe whose structural parameters are different from the DNN training pipe. • A hybrid FEM-DNN-based VIV prediction method for flexible pipes under an oscillatory flow is proposed. • The effects of flow velocity variation, KC number, β number and other flow field features are considered in the DNN-based VIF model. • A phase modulation model is developed to ensure the synchronization between VIF and VIV velocities. • The feasibility and accuracy of the proposed method are statistically verified by experimental results. [ABSTRACT FROM AUTHOR]

With the development of ocean engineering, freely hanging water intake riser (WIR) has aroused widespread interests. The WIR with one free end would be easier to deflect remarkably, along with more complex vortex-induced vibration (VIV) responses and hydrodynamic forces. To elucidate the VIV characteristics of WIR under uniform flow, a series of VIV experiments for a scaled WIR model are carried out. Then a hydrodynamic identification method for VIV along with large offset is developed. The response and hydrodynamic characteristics of the WIR in cross-flow (CF) and in-line (IL) directions are further analyzed. Results indicate that VIV displacements with higher exciting modes are unstable when uniform flow velocity gets large. The IL-to-CF dominant frequency ratio of VIV is found to be 1.0, not 2.0 in conventional VIV knowledge and the IL harmonic at nearly twice the dominant CF frequency is observed more complex for flow velocity greater than 0.3 m/s. The vortex-induced force coefficients are found to be time-varying. Moreover, it is found that within the spectrum of Reynolds number from 2 × 103 to 1.1 × 104, the drag coefficient distribution changes along the WIR model, and the average drag coefficient is in range of 1.0–1.5, which is slightly smaller than the results predicted by the other published empirical formulae. • A series of VIV experiments for a scaled water intake riser model were carried out. • A hydrodynamic identification method for VIV of water intake riser was developed. • The vortex-induced force coefficients of WIR under uniform flow were time-varying. • The drag coefficient is slightly smaller than the results of empirical formulae. [ABSTRACT FROM AUTHOR]

For a fluid-discharging cantilevered pipe attached with an end-mass, there are two methods to account for the end-mass effect. The first is that the end-mass is considered in the boundary conditions. The second is that the end-mass is included in the equation of motion via a Dirac delta function. As the analytical solution of the linear free vibration model is not available due to the presence of Coriolis force, the eigenfunctions of a beam, which satisfy the same boundary conditions, are commonly employed in the Galerkin method. It has been found the first method is incorrect for natural frequency calculation when the internal flow velocity is nonzero. However, the intrinsic mechanism remains to be clarified. This study has demonstrated the eigenfunctions in the first method depend on the end-mass and the orthogonality relations are quite different from that of typical simple beams, based on which a new model is proposed and the prediction compares well with that in the second method. For further validation, the critical internal flow velocity, the onset flutter frequency, and the dynamic responses of suspended pipes under gravity are computed, which compare well with experimental observations. This study can provide a workbench for fluid-conveying pipes with various boundary conditions. [ABSTRACT FROM AUTHOR]

Vortex-induced vibrations (VIVs) of a top tensioned riser (TTR) subjected to flows with spanwise varying directions have been simulated and studied in this paper. The riser is simplified as an Euler–Bernoulli beam and its dynamics is described using the finite element method with the Absolute Nodal Coordinate Formulation (ANCF). The hydrodynamic forces due to vortex shedding are modelled with wake oscillators attached to nodes along the riser. The model has been firstly used to simulate an experiment and acceptable model results have been obtained in comparison with the measurements. Then, the VIVs of the TTR under two flow conditions, one with uniform and the other with linearly sheared velocity, have been simulated. In both cases, the direction of the flow varies linearly along the riser. Simulation results have shown different response characteristics at small and high flow velocities with respect to the frequency, amplitude and vibrating direction of the riser. In general, at a small flow velocity where the response of the riser is dominated by the standing wave, the variation in the flow direction has a major influence on the VIV of the riser. However, when the travelling wave is predominant at a high flow velocity, the effect of the spanwise varying flow direction is insignificant. The energy transfer between the structure and flow has been studied to reveal the possible mechanism that leads to these differences in the responses of the riser at small and high flow velocities. The results of the present paper suggest that the engineering simplification of ignoring the influence of flow direction variation on VIV may only be applicable at high flow velocities when the response of the riser is dominated by the travelling wave. [Display omitted] • VIVs of a top tensioned riser subjected to flows with spanwise varying directions are studied. • Preliminary validation of the numerical model is made against the only publicly available experiment. • The influence of the spanwise varying flow direction is only significant for the standing wave dominant VIV. • The energy transfer exhibits different patterns between cells separated by nodes of the standing wave. [ABSTRACT FROM AUTHOR]

This study tries to examine the IFE (Internal Flow Effect) on the coupled CF (Cross-Flow) and IL (In-Line) VIVs (Vortex-Induced Vibration) of flexible marine risers in the subcritical region of internal flow. The dynamic equations of a flexible riser subjected to a uniform current are established based on Hamilton Principle employing a semi-empirical hydrodynamic force model. The governing equations can be discretized and solved by finite element method. The VIV responses of a flexible riser at different internal flow velocities, internal flow densities and current velocities are examined. With the increase of internal flow velocity and density, it has demonstrated that (1) whether the CF RMS (Root Mean Square) displacement is increased or decreased depends on whether the CF VIV dominant frequency approaches or departs from the vortex shedding frequency; (2) The CF/IL dominant mode can transfer to a higher order, accompanied by a jump increase of the CF/IL dominant frequency. (3) The CF VIV can significantly influence the IL drag force coefficient and thus affect the IL mean deformation. (4) The IFE has a non-negligible effect on the IL dynamic response. (5) The travelling wave characteristics can be enhanced. One interesting finding is that the transmission direction of the travelling wave is the same as the direction of internal flow velocity. • IFE on the 2DOF VIVs of a flexible riser subjected to a uniform current is examined. • It has demonstrated that with the increase of internal flow velocity and density, (1) the CF root mean square amplitude is affected by the varying CF dominant frequency; (2) the CF/IL dominant mode is switched with a jump increase of CF/IL dominant frequency; (3) the CF VIV influences the drag coefficient and thus affects the IL mean deformation; (4) The travelling wave characteristics can be enhanced. • The transmission direction of travelling wave is the same as that of internal flow. [ABSTRACT FROM AUTHOR]