Advertisement

Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 829–844 | Cite as

Nonlinear Dynamics of Three-Dimensional Prediction Model for a Flexible Riser Under Linearly Sheared Currents

  • Ruyi Gou
  • Xiaodong Zhang
  • Wenwu YangEmail author
  • Xueping Chang
  • Shaojie Lu
Research Article - Mechanical Engineering
  • 69 Downloads

Abstract

This paper presents a three-dimensional vortex-induced vibration prediction model for a long flexible riser under linearly sheared currents. Two distributed and coupled van der Pol wake oscillators are utilized to characterize the fluctuating lift and drag coefficients, respectively. It should be noted that geometric and hydrodynamic nonlinearities are also considered in our model. Numerical simulations by finite element method are carried out to solve the highly coupled nonlinear fluid–structure interaction equations. Firstly, modal analysis is performed to obtain the foremost ten natural frequencies of the flexible riser under top-end tension by theoretical and numerical methods, and the results agree very well. Then, nonlinear dynamic analyses are carried out to investigate the effects of linear shear flow on displacements, stresses, modal variations and phase portraits. The results obtained in uniform and linear shear currents are compared in detail. The results indicate that the asymmetric phenomenon along the riser span is more obvious with increasing linear shear velocity and the lock-in phenomenon of IL (in-line) response frequencies with multi-frequency is also observed along riser span. Moreover, it is also revealed that the dynamic responses simultaneously exhibit the standing and travelling wave patterns under linearly sheared currents, and the dynamic responses become more irregular than uniform flow.

Keywords

Flexible riser Linearly sheared current Wake oscillator Vortex-induced vibration Fluid–structure interaction 

List of Symbols

L

Length of pipe (m)

D

Outer diameter (m)

d

Inner diameter (m)

\(\rho _\mathrm{o}\)

Outer fluid density (kg/m\(^{3}\))

m

Pipe mass per unit length (kg/m)

\(m_\mathrm{a} \)

Additional fluid mass per unit length (kg/m)

U

Cross-flow velocity (m/s)

E

Elasticity modulus (Pa)

c

Damping coefficient (N/s)

I

Moment of inertia (m\(^{4}\))

\(A_\mathrm{r} \)

Section area of pipe (m\(^{2}\))

\(T_\mathrm{t} \)

Top pre-tension (N)

T

Static effective tension (N)

\(F_x \)

x direction hydrodynamic force (N)

\(F_y \)

y direction hydrodynamic force (N)

\(F_z \)

z direction hydrodynamic force (N)

uvw

Displacements components (m)

\({\dot{\square }}\)

Differentiation about time (t)

\({\square }'\)

Differentiation about axial coordinate (z)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Montoya-Hernandez, D.J.; Vazquez-Hernandez, A.O.; Cuamatzi, R.; Hernandez, M.A.: Natural frequency analysis of a marine riser considering multiphase internal flow behavior. Ocean Eng. 92, 103–113 (2014).  https://doi.org/10.1016/j.oceaneng.2014.09.039 CrossRefGoogle Scholar
  2. 2.
    Srinil, N.; Wiercigroch, M.; O’Brien, P.: Reduced-order modelling of vortex-induced vibration of catenary riser. Ocean Eng. 36(17–18), 1404–1414 (2009).  https://doi.org/10.1016/j.oceaneng.2009.08.010 CrossRefGoogle Scholar
  3. 3.
    Wang, J.; Fu, S.; Baarholm, R.; Wu, J.; Larsen, C.M.: Fatigue damage of a steel catenary riser from vortex-induced vibration caused by vessel motions. Mar. Struct. 39(39), 131–156 (2014)CrossRefGoogle Scholar
  4. 4.
    Wang, J.G.; Fu, S.X.; Baarholm, R.; Wu, J.; Larsen, C.M.: Out-of-plane vortex-induced vibration of a steel catenary riser caused by vessel motions. Ocean Eng. 109, 389–400 (2015).  https://doi.org/10.1016/j.oceaneng.2015.09.004 CrossRefGoogle Scholar
  5. 5.
    Wang, J.L.; Duan, M.L.: A nonlinear model for deepwater steel lazy-wave riser configuration with ocean current and internal flow. Ocean Eng. 94, 155–162 (2015).  https://doi.org/10.1016/j.oceaneng.2014.11.025 CrossRefGoogle Scholar
  6. 6.
    Abdel Raheem, S.E.: Study on nonlinear response of steel fixed offshore platform under environmental loads. Arab. J. Sci. Eng. 39(8), 6017–6030 (2014).  https://doi.org/10.1007/s13369-014-1148-x CrossRefGoogle Scholar
  7. 7.
    Doan, V.P.; Nishi, Y.: Modeling of fluid-structure interaction for simulating vortex-induced vibration of flexible riser: finite difference method combined with wake oscillator model. J. Mar. Sci. Technol. 20(2), 309–321 (2015)CrossRefGoogle Scholar
  8. 8.
    Luo, D.D.; Zhu, R.Q.: Three dimensional numerical simulation of VIV on marine riser in linearly sheared flow. Ship Sci. Technol. 37(2), 82–86 (2015)Google Scholar
  9. 9.
    Wang, K.P.; Xue, H.X.; Tang, W.Y.: In-Line VIV response and fatigue damage of a deepwater riser in linearly sheared flow. J. Vib. Shock 32(19), 1–6+27 (2013)Google Scholar
  10. 10.
    Brika, D.; Laneville, A.: Vortex-induced vibrations of a long flexible circular cylinder. J. Fluid Mech. 250(250), 481–508 (2006)Google Scholar
  11. 11.
    Huera-Huarte, F.J.; Bearman, P.W.: Wake structures and vortex-induced vibrations of a long flexible cylinder–Part 1: Dynamic response. J. Fluids Struct. 25(6), 969–990 (2009)CrossRefGoogle Scholar
  12. 12.
    Srinil, N.: Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities. J. Fluids Struct. 26(7–8), 1098–1122 (2010).  https://doi.org/10.1016/j.jfluidstructs.2010.08.005 CrossRefGoogle Scholar
  13. 13.
    Srinil, N.: Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents. Appl. Ocean Res. 33(1), 41–53 (2011).  https://doi.org/10.1016/j.apor.2010.11.004 CrossRefGoogle Scholar
  14. 14.
    Bearman, P.W.: Circular cylinder wakes and vortex-induced vibrations. J. Fluids Struct. 27(5–6), 648–658 (2011)CrossRefGoogle Scholar
  15. 15.
    Gabbai, R.D.; Benaroya, H.: An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 282(3–5), 575–616 (2005)CrossRefGoogle Scholar
  16. 16.
    Sarpkaya, T.: A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19(4), 389–447 (2004)CrossRefGoogle Scholar
  17. 17.
    Williamson, C.H.K.; Govardhan, R.: Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36(1), 413–455 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Wu, X.; Ge, F.; Hong, Y.: A review of recent studies on vortex-induced vibrations of long slender cylinders. J. Fluids Struct. 28(1), 292–308 (2012)CrossRefGoogle Scholar
  19. 19.
    Dai, H.L.; Abdelkefi, A.; Wang, L.: Modeling and nonlinear dynamics of fluid-conveying risers under hybrid excitations. Int. J. Eng. Sci. 81, 1–14 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Dai, H.L.; Wang, L.; Qian, Q.; Ni, Q.: Vortex-induced vibrations of pipes conveying fluid in the subcritical and supercritical regimes. J. Fluids Struct. 39, 322–334 (2013).  https://doi.org/10.1016/j.jfluidstructs.2013.02.015 CrossRefGoogle Scholar
  21. 21.
    Dai, H.L.; Wang, L.; Qian, Q.; Ni, Q.: Vortex-induced vibrations of pipes conveying pulsating fluid. Ocean Eng. 77, 12–22 (2014).  https://doi.org/10.1016/j.oceaneng.2013.12.006 CrossRefGoogle Scholar
  22. 22.
    Wang, L.; Dai, H.L.; Qian, Q.: Dynamics of simply supported fluid-conveying pipes with geometric imperfections. J. Fluids Struct. 29, 97–106 (2012).  https://doi.org/10.1016/j.jfluidstructs.2011.12.013 CrossRefGoogle Scholar
  23. 23.
    Liu, J.; Zhao, H.; Liu, Q.; He, Y.; Wang, G.; Wang, C.: Dynamic behavior of a deepwater hard suspension riser under emergency evacuation conditions. Ocean Eng. 150, 138–151 (2018).  https://doi.org/10.1016/j.oceaneng.2017.12.050 CrossRefGoogle Scholar
  24. 24.
    Zanganeh, H.; Srinil, N.: Three-dimensional VIV prediction model for a long flexible cylinder with axial dynamics and mean drag magnifications. J. Fluids Struct. 66, 127–146 (2016).  https://doi.org/10.1016/j.jfluidstructs.2016.07.004 CrossRefGoogle Scholar
  25. 25.
    Song, J.-N.; Lu, L.; Teng, B.; Park, H.-I.; Tang, G.-Q.; Wu, H.: Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow. Ocean Eng. 38(11–12), 1308–1322 (2011).  https://doi.org/10.1016/j.oceaneng.2011.05.020 CrossRefGoogle Scholar
  26. 26.
    Yang, W.; Ai, Z.; Zhang, X.; Gou, R.; Chang, X.: Nonlinear three-dimensional dynamics of a marine viscoelastic riser subjected to uniform flow. Ocean Eng. 149, 38–52 (2018).  https://doi.org/10.1016/j.oceaneng.2017.12.004 CrossRefGoogle Scholar
  27. 27.
    Yang, W.; Ai, Z.; Zhang, X.; Chang, X.; Gou, R.: Nonlinear dynamics of three-dimensional vortex-induced vibration prediction model for a flexible fluid-conveying pipe. Int. J. Mech. Sci. 138–139, 99–109 (2018).  https://doi.org/10.1016/j.ijmecsci.2018.02.005 CrossRefGoogle Scholar
  28. 28.
    Chaplin, J.R.; Bearman, P.W.; Huarte, F.J.H.; Pattenden, R.J.: Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current. J. Fluids Struct. 21(1), 3–24 (2005)CrossRefGoogle Scholar
  29. 29.
    Lie, H.; Kaasen, K.E.: Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow. J. Fluids Struct. 22(4), 557–575 (2006)CrossRefGoogle Scholar
  30. 30.
    Bourguet, R.; Karniadakis, G.E.; Triantafyllou, M.S.: Vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 677(677), 342–382 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Bourguet, R.; Karniadakis, G.E.; Triantafyllou, M.S.: Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows. J. Fluids Struct. 41(8), 33–42 (2013)CrossRefGoogle Scholar
  32. 32.
    Holmes, S.; Oakley, O.H.; Constantinides, Y.: Simulation of riser VIV using fully three dimensional CFD simulations. In: 25th International Conference on Offshore Mechanics and Arctic Engineering, pp 563–570 (2006)Google Scholar
  33. 33.
    Bourguet, R.; Karniadakis, G.E.; Triantafyllou, M.S.: Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow. J. Fluid Mech. 717(1), 361–375 (2013)CrossRefzbMATHGoogle Scholar
  34. 34.
    Wang, E.; Xiao, Q.: Numerical simulation of vortex-induced vibration of a vertical riser in uniform and linearly sheared currents. Ocean Eng. 121, 492–515 (2016)CrossRefGoogle Scholar
  35. 35.
    Facchinetti, M.L.; de Langre, E.; Biolley, F.: Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19(2), 123–140 (2004).  https://doi.org/10.1016/j.jfluidstructs.2003.12.004 CrossRefGoogle Scholar
  36. 36.
    Srinil, N.; Zanganeh, H.: Modelling of coupled cross-flow/in-line vortex-induced vibrations using double Duffing and van der Pol oscillators. Ocean Eng. 53, 83–97 (2012).  https://doi.org/10.1016/j.oceaneng.2012.06.025 CrossRefGoogle Scholar
  37. 37.
    Dahl, J.M.F.S.; Triantafyllou, M.S.; Oakley, O.H.: Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers. J. Fluid Mech. 643(3), 395–424 (2010)CrossRefzbMATHGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Ruyi Gou
    • 1
  • Xiaodong Zhang
    • 1
  • Wenwu Yang
    • 1
    Email author
  • Xueping Chang
    • 1
  • Shaojie Lu
    • 2
  1. 1.School of Mechatronic EngineeringSouthwest Petroleum UniversityChengduChina
  2. 2.CNOOC Shanghai Branch West Lake Operating CompanyShanghaiChina

Personalised recommendations