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Analytical and numerical biaxial bending analysis of deepwater riser due to vortex-induced vibration

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Abstract

Previous studies of analysis and prediction of marine risers responses usually focus on vortex-induced vibration (VIV) of cross-flow (CF) direction rather than in-line (IL). Recent studies show that responses of IL direction tend to dominate in some cases. Responses of long riser due to biaxial bending of IL and CF VIV are investigated. Closed-form formulas are derived for estimating maximum normal stress due to the biaxial moment of CF/IL VIV and relations for estimating biaxial stress using CF values are presented. Analytical results are compared with numerical results of the time domain model and a good correlation is observed. It is shown that for tension and bending-controlled modes of vibration if the ratio of displacement amplitude of IL to CF direction is, respectively, higher than 0.22 and 0.35, normal stress due to biaxial bending is noticeably more than one directional (CF) bending stress. For a case study, the maximum biaxial stress along the riser is about 20 and 40% higher than the maximum CF stress along the length of the riser for bending and tension-controlled modes of vibration, respectively. Such results can be important not only directly in design issues, but also they may be noticeable in fatigue analysis.

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Abbreviations

D :

Cylinder outer diameter

EI :

Bending stiffness of riser

L and A :

Length and cross-sectional area of the riser

U :

Current velocity

\(F_{z}\) :

The axial force in the longitudinal direction

m :

Sum of structure mass and added fluid mass per unit length

ρ :

Fluid density

\(C_{{{\text{L}}0}}\) and \(C_{{{\text{D}}0}}\) :

Amplitude of fluctuating lift and drag coefficients for a fixed rigid cylinder subjected to vortex shedding

c and \(c^{\prime}\) :

Damping coefficients due to structure and hydrodynamic forces, respectively

St :

Strouhal number

γ :

Stall parameter determined through experiment

\(x_{0} , \, y_{0}\) :

Displacement amplitude of IL and CF direction, respectively

\(n_{{{\text{IL}}}} , \, n_{{{\text{CF}}}}\) :

Mode number IL and CF direction

\(\phi\) :

Phase between IL and CF motions

\(\sigma_{{{\text{CF}}}}\), \(\sigma_{{{\text{IL}}}}\) and \(\sigma_{\theta }\) :

Longitudinal stress due to CF and IL vibration and combination of these at a point with angle of \(\theta\)

\(\varepsilon_{{{\text{IL}}}} ,\varepsilon_{{{\text{CF}}}} ,A_{{{\text{IL}}}} ,A_{{{\text{CF}}}}\) :

Nondimensional parameters estimated through experiment

\(\omega\) :

CF vibration frequency

\(Y_{{{\text{rms}}}}\) :

Standard deviation of the anti-node displacement in diameters

\(q_{{{\text{IL}}}}\) and \(q_{{{\text{CF}}}}\) :

Wake parameters of IL and CF direction, respectively

\(\Omega_{{\text{f}}}\) :

Strouhal frequency

β and γ :

Integration parameters

\(M_{{{\text{CF}}}}\), \(M_{{{\text{IL}}}}\) :

Bending moments caused by IL and CF vibration, respectively

\(\sigma_{{\max ,{\text{O}},{\text{CF}}}}\), \(\sigma_{{\max ,{\text{O,IL}}}}\) and \(\sigma_{{\max ,{\text{O}}}}\) :

Overall maximum stress due to CF bending, IL bending and biaxial bending, respectively

\(\sigma_{\max ,N}\) :

Maximum stress at each node of riser

\(z_{\sigma \max ,O}\), \(\theta_{{\sigma \max ,{\text{O}}}}\) :

Height and angle of critical point along the overall length of riser

\(\theta_{\max }\) :

Angle of critical point at each node

DAR:

Displacement amplitude ratios (\({{x_{0} } \mathord{\left/ {\vphantom {{x_{0} } {y_{0} }}} \right. \kern-\nulldelimiterspace} {y_{0} }}\))

OSR:

Overall stress ratio (\({{\sigma_{{\max ,{\text{O}}}} } \mathord{\left/ {\vphantom {{\sigma_{{\max ,{\text{O}}}} } {\sigma_{{\max ,{\text{O}},{\text{CF}}}} }}} \right. \kern-\nulldelimiterspace} {\sigma_{{\max ,{\text{O}},{\text{CF}}}} }}\))

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Acknowledgements

We would like to pay special thankfulness, warmth, and appreciation to Dr. Payman Rahmatabadi (Maning Director of Fan Omran Pars Co.) for his valuable guidance and supporting us.

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Authors and Affiliations

  1. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Reza Tabeshpour

  2. Department of Civil Engineering, Pardis Branch, Islamic Azad University, Pardis, Iran

    Younes Komachi

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  1. Mohammad Reza Tabeshpour
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  2. Younes Komachi
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Correspondence to Mohammad Reza Tabeshpour.

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Tabeshpour, M.R., Komachi, Y. Analytical and numerical biaxial bending analysis of deepwater riser due to vortex-induced vibration. J Mar Sci Technol 27, 492–507 (2022). https://doi.org/10.1007/s00773-021-00846-6

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  • DOI: https://doi.org/10.1007/s00773-021-00846-6

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