Elsevier

Applied Ocean Research

Volume 59, September 2016, Pages 265-273
Applied Ocean Research

Parametric instability of a submerged floating pipeline between two floating structures under combined vortex excitations

https://doi.org/10.1016/j.apor.2016.06.009Get rights and content

Highlights

  • To investigate parametric instability of a submerged floating pipeline combined parametric and vortex excitations.

  • Wake oscillator model is coupled to simulate the lock-in phenomenon considering parametric excitation.

  • Motion of the floating structures is combined to calculate the parametric excitation.

  • The vibration mode jump phenomenon is found during parametric instability analysis.

Abstract

This study investigates a parametric instability prediction of a submerged floating pipeline connected between two floating structures under combined vortex excitations. The submerged floating pipeline is considered as a potential solution for fluid transportation between floaters in deepwater. However, the parametric instability combined with vortex-induced vibration is a major concern for its safety. The instability can lead to huge displacement and fatigue damage. Thus, it is essential to propose a methodology for analyzing nonlinear dynamic properties of the pipeline with combined parametric and vortex excitations. Here, coupled vibration equations of the pipeline are established, including hydrodynamic force model which contains vortex-induced load and structural model which contains parametric excitation due to motion of the two floating structures. Then Mathieu equation is derived from the homogeneous structural equation. Differences between the dynamic responses subjected to only vortex excitation and combined excitations are compared. The pipeline engineering cases and the effects of two important design factors are analyzed. The results show that the parametric instability may occur in cross-line vibration of the submerged floating pipeline between the two floaters. Even the maximum vibration amplitude of the pipeline under combined excitations is still larger than that under only vortex excitation, when the parametric instability does not take place. There is a vibration mode jump phenomenon while the parametric instability occurs. In addition, two design factors, transfer coefficient and phase angle of the floaters’ motion, can make a great impact on the parametric stability of the submerged floating pipeline.

Introduction

Offshore risers and pipelines are becoming more and more important while the exploration of marine oil and gas is moving in deep and ultra-deep water. There are several new concepts for the design of offshore risers and pipelines in recent years. The submerged floating pipeline is one of these new concepts to transfer fluid and gas in ocean engineering [1].

Generally speaking, the submerged floating pipeline is floating at a certain depth of ocean with some mooring chains or tethers anchoring it to the seabed [2], [3]. On the other hand, it can also be used to connect two floating structures, shown in Fig. 1, for example, the gravity actuated pipe which connects the FPSO and Spar platform at Kikeh outside Malaysia installed in 2008 [4]. Compared with the traditional pipelines that are put on or buried in the seabed, the submerged floating pipeline is considered as a more useful solution for offshore engineering with some challenging seabed condition. First of all, there is no need to do any intervention work for the seabed because the pipeline is floating at the mid-deep water without the direct interaction with the seabed soil. Besides the submerged floating pipeline is located at a certain depth under the sea surface, so wave forces can also be ignored. Finally, high hydrostatic pressure and temperature difference in the deep and ultra-deep ocean are avoided as well. Therefore, the submerged floating pipeline could prove to be a part of the future solutions for deep water gas and fluid transportation.

Although many complex environmental effects such as the wave forces and soil-pipeline interaction forces do not need to be considered for the submerged floating pipeline’s design, current forces and vortices which are also produced by the current are the major concerns. Nonlinear dynamic response for the submerged floating pipeline is a vital analysis task for its safety. And, it is necessary to study vortex-induced vibration which is thought to be the important cause of fatigue damage of the offshore risers and pipelines [5]. There are a lot of researches done by both experimental tests and numerical predictions on the vortex-induced vibration of such a circular cylinder structure. Govardhan and Williamson [6] applied several experiment tests for the vortex-induced vibration of the cylinder structure at low mass ratio value, and found the response could be divided into the initial, upper and lower branches. Srinil et al. [7] used a classical van der Pol wake oscillator model to simulate the fluid-structure interaction at both in-line and cross-line direction, and compared the numerical results with his experiments.

Because the submerged floating pipeline can be connected with the floating structures, the motion of these floaters will also influence the dynamic response of the pipelines, which may lead to parametric instability problem of the pipeline. The parametric instability, also called parametric resonance, is another major concern for offshore structures’ design, because it can excite the very large motion [8]. In the past decade, there are several studies on analyzing the parametric instability of tethers and risers of top tensioned platforms. Park and Jung [9] implemented a finite element method to study the lateral responses of a top tensioned platform tether under combined parametric and forcing excitations. Franzini et al. [10] analyzed the parametric instability of a flexible tensioned cylinder under harmonic excitation through experiment tests.

For the recent researches of the submerged floating pipeline, most of them concentrated on its static design analysis [2] and vortex-induced vibration. For example, Sergent et al. [11] applied CFD, experiments and software to analyze the fatigue life of the submerged floating pipeline because of vortex-induced vibration. Thus it is still necessary and urgent to propose a methodology to predict the parametric instability of such a pipeline between the floating structures and learn how the motion of the floaters can influence its dynamic stability. Besides, it is also important to combine the vortex-induced forces with the parametric excitation, and study the dynamic response of the pipeline under such combined excitations, because in the real sea condition, these two excitations must be interacted together on the pipeline. But few analysis methods consider both parametric and vortex-induced vibration excitations in the past few years [12].

The present study is meant to establish a suitable mathematic model to explore the stability of the submerged floating pipeline between two floating structures under vortex and parametric excitations. In Section 2, the governing motion equations of the pipeline subjected to combined excitations are derived, including structural model and wake oscillator hydrodynamic force model. Mathieu equation is also derived from the homogeneous structural equation. In Section 3, validation of the hydrodynamic force model is made, and the Mathieu equation is solved. The stability diagram is made for the submerged floating pipeline design. Then engineering cases and effects of two important design factors on the stability of the pipeline are discussed, and finally some suggestions to avoid the parametric instability are given.

Section snippets

Theory

The nonlinear dynamic motion of the submerged floating pipeline is complicated, because it involves the fluid-structure interaction which means that the motion of the structure and fluid dynamic forces affects each other. Therefore to simulate this interaction, the system model could be divided into two sub-models. The first one is called the structural model reflecting the transverse and axial vibration of the submerged floating pipeline under the hydrodynamic forces, while the second one is

Validation of the wake oscillator model

To take an advantage of the wake oscillator model for computing the dynamic response of the submerged floating pipeline, we should make the validation of this hydrodynamic force model at first. It is necessary to make sure how the wake oscillator model could simulate the lock-in phenomenon during the vortex-induced vibration of the cylinder structure, like the pipeline. Here the numerical simulation by the wake oscillator model is compared with the experiment data from Khalak and Williamson [19]

Conclusions

The parametric instability of a submerged floating pipeline between two floating structures has been studied according to the derived equations which are coupled with the structural model and hydrodynamic force model. The validation of the wake oscillator model is carried out, and the stability diagram of the Mathieu equation is used to explain the stability of the solution of the motion equation. Engineering cases are applied for this work by the finite difference method, and the effects of

Acknowledgment

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51379005 and 51009093).

References (28)

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