Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019


MATHEMATICAL MODEL AND ANALYTICAL SOLUTION FOR THE VIBRATION OF INCLINED FLUID-TRANSPORTING SUBMARINE PIPELINES (DOI No: 10.3940/rina.ijme.2019.a4.524)


C An*, T T Li, W Liang and M L Duan, College of Safety and Ocean Engineering, China University of Petroleum- Beijing, China, H B Huang School of Geography, University College Cork, Ireland


SUMMARY


Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free- spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.


1. INTRODUCTION


As a transportation facility in offshore engineering, the submarine pipeline plays a crucial role in transporting oil and gas from deep down the bottom of the sea to the far away user terminal. Deep and even ultra-deep water create a wide range of challenges for pipeline design in oil and gas industry and the safety operation of pipelines must be prioritized considering their importance and coverage in any oil and gas projects, particularly the offshore projects.


In deepwater area, pipelines are laid on the seabed and due to scour of the current or seabed unevenness, some parts of submarine pipelines may have to cross a depression or a gully (Fyrileiv & Mørk, 2002), and the pipeline section between two touchdown points is called a free span (Vedeld, et al, 2013). If a free-span is exposed to currents, vortex shedding may occur and produce vibration of the pipeline structure. The vortex-induced vibration (VIV) of the suspended part of the pipeline may consequently induce accumulative fatigue damage of the pipelines. This consequence is one of the most concerned issues in the design of submarine pipelines.


Due to its simplicity and effectiveness, the wake oscillator model has been acknowledged as a feasible way to model the vortex shedding. Facchinetti et al. (2004) investigated three different coupling terms, i.e. acceleration, velocity and displacement to study the VIV of pipelines, and concluded that the acceleration coupling best coincide with the experimental results. Low and Srinil (2016) carried out a nonlinear fluid-structure interaction analysis of marine risers by identifying the uncertainties of a wake oscillator model which simulates the fluctuating


©2019: The Royal Institution of Naval Architects


hydrodynamic force. However, the above-mentioned literature neglect the fact that pipelines and risers in offshore engineering often transport fluid. For pipelines that transport internal fluid, the dynamic behaviors are affected by both the current and fluid running inside itself. The currents and the pipelines transporting internal fluid interact with each other and form a coupled nonlinear system. The pipelines exposed to currents are prone to VIV, while the internal fluid travels along the curved pipeline amplifies the vibration of the system to an extent that the effect cannot be neglected when predicting the fatigue life of submarine pipelines (Guo, et al, 2006).


Housner (1952) is one of the pioneers who studied the dynamic behaviors of pipelines considering the effect of internal fluid in pipelines and showed that at certain high velocity, the internal fluid will even cause dynamic instability of the pipeline. Based on Housner’s model, Shen and Zhao (1996) studied the impact of internal fluid on the fatigue life of the pipeline free span subject to VIV. Guo et al. (2004), Lou et al. (2005) and Guo and Lou (2008) investigated the coupled effect of internal and external fluid on the vibration behavior of free-spanning pipelines by using Finite Element Method (FEM). Kaewunruen et al. (2005) investigated nonlinear free vibrations of marine pipes transporting fluid, and determined the nonlinear fundamental frequencies and the mode shapes by the modified direct iteration technique. And lately, Dai et al. (2014) investigated the VIV of pipes conveying pulsating fluid through the direct perturbation method of multiple scales.


It should be noted that the majority of the previous literature on this topic consider the pipelines in the horizontal position and neglect the fact that in real circumstances, pipelines are most likely to be placed over


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