Abstract
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.
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Abbreviations
- A :
-
Amplitude of vibration
- \(A_z\) :
-
Cross-flow motion amplitude
- \(A^*\) :
-
Cross-flow amplitude ratio
- \(C_\mathrm{d}\) :
-
In-line drag coefficient
- \(C_{\mathrm{d}0}\) :
-
Mean in-line drag coefficient
- \(C_{\mathrm{lv}}\) :
-
Cross-flow lift coefficient
- \(C_{\mathrm{m}}\) :
-
Added mass coefficient
- D :
-
Diameter of the cylinder
- \(f_{\mathrm{nw}}\) :
-
Natural frequency in still water
- \(f_{\mathrm{osc}}\) :
-
Oscillation frequency
- \(F_{\mathrm{D}}\) :
-
In-line drag force amplitude
- \(F_{\mathrm{D}0}\) :
-
Mean in-line drag force
- \(F_{\mathrm{L}}\) :
-
Cross-flow lift force amplitude
- \(F_x\) :
-
Total in-line drag force
- \(F_z\) :
-
Total cross-flow lift force
- \(F_{\dot{z}}\) :
-
Cross-flow lift force in phase with velocity
- \(F_{\ddot{z}}\) :
-
Cross-flow lift force in phase with acceleration
- L :
-
Length of the cylinder
- m :
-
Mass of the cylinder
- \(m'\) :
-
Added mass of the cylinder
- k :
-
Spring stiffness
- \(k_x\) :
-
Structural stiffness in the in-line direction
- \(k_z\) :
-
Structural stiffness in the cross-flow direction
- t :
-
Time
- \(T_{\mathrm{app}}\) :
-
Apparent period of motion
- U :
-
Incoming flow velocity
- \(U^*\) :
-
Nominal reduced velocity
- V :
-
Relative normal velocity between the incoming flow and the structure
- \(V_\mathrm{r}\) :
-
Reduced velocity
- \(V_{\mathrm{tow}}\) :
-
Towing speed of carriage
- \(Z_{\mathrm{max}}\) :
-
Maximum transverse displacement in a motion cycle
- \(Z_{\mathrm{min}}\) :
-
Minimum transverse displacement in a motion cycle
- \(\rho\) :
-
Density of fluid
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Acknowledgements
This work was supported by the Natural Science and Engineering Research Council (NSERC) of Canada.
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Zhang, B., Qiu, W. Improving time-domain prediction of vortex-induced vibration of marine risers. Mar Syst Ocean Technol 13, 13–25 (2018). https://doi.org/10.1007/s40868-017-0041-3
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DOI: https://doi.org/10.1007/s40868-017-0041-3