Journal of Marine Science and Engineering Article Effect of Top Tension on Vortex-Induced Vibration of Deep-Sea Risers Jie Zhang 1,2,* , He Guo 1, Yougang Tang 3 and Yulong Li 3 1 College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China; [email protected] 2 Department of Civil, Environmental and Geomatic Engineering, University College London, London WC1E 6BT, UK 3 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China; [email protected] (Y.T.); [email protected] (Y.L.) * Correspondence: [email protected] Received: 21 January 2020; Accepted: 12 February 2020; Published: 15 February 2020 Abstract: With the increase of water depth, the design and use of the top-tensioned risers (TTR) are facing more and more challenges. This research presents the effect of top tension on dynamic behavior of deep-sea risers by means of numerical simulations and experiments. First, the governing equation of vortex-induced vibration (VIV) of TTR based on Euler-Bernoulli theory and Van der Pol wake-oscillator model was established, and the effect of top tension on natural vibration of TTR was discussed. Then, the dynamic response of TTR in shear current was calculated numerically by finite difference method. The displacement, bending stress and vibration frequency of TTR with the variation of top tension were investigated. Finally, a VIV experiment of a 5 m long flexible top-tensioned model was carried out at the towing tank of Tianjin University. The results show that the vibration displacement of TTR increases and the bending stress decreases as the top tension increases. The dominant frequency of VIV of TTR is controlled by the current velocity and is barely influenced by the top tension. With the increase of top tension, the natural frequency of TTR increases, the lower order modes are excited in the same current. Keywords: deep-sea riser; top tension; vortex-induced vibration; numerical simulation; experiment 1. Introduction In recent years, owing to the large demand of crude oil, offshore oil and gas explorations have been shifted to deeper water regions. Risers are one of the basic elements of offshore installations that are usually used for drilling and production. The riser is installed between wellhead at the sea bed and floating platform. Actually, the riser has suffered the strong influences of environmental conditions in unshielded deep-water region, hence it has complicated dynamic behavior under the influence of platform’s motions, wind, waves and sea current, as shown in Figure1. One of the most famous phenomena is vortex-induced vibration (VIV). When the riser moves under the action of sea current, vortices are shed along its surface, resulting in the formation of an unstable wake region behind it. Vortex shedding normally takes place with different frequencies and amplitudes, thus induces a periodically varying transverse force on the riser (i.e., perpendicular to the direction of the current), resulting in a periodically transverse vibration known as the VIV [1–4]. J. Mar. Sci. Eng. 2020, 8, 121; doi:10.3390/jmse8020121 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 121 2 of 14 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 2 of 15 Figure 1. SchematicSchematic of a t top-tensionedop-tensioned riser in ocean environment. Drilling and production risers are are mostly affected affected by VIV, which leads to increases in their hydrodynamic loading and reduction in their service life due to fatigue. In In the past, to ensure the safety and to enhance the productivity of riser systems, many i investigationsnvestigations on VIV of marine risers have been reported. Srinil [[5]5] studiedstudied dynamicdynamic behaviorbehavior of of a a variable variable tension tension vertical vertical riser riser placed placed in in a alinearly linearly sheared sheared current current by usingby using numerical numerical methods methods and experiments.and experiments. He concluded He concluded that the that current the velocitycurrent velocity and the variableand the variable tension had tension great had influence great influence on VIV response on VIV ofresponse a deep-sea of a riser. deep The-seaprediction riser. The predictionof VIV of a of deep-sea VIV of risera deep was-sea a challengingriser was a challenging task since the task incident since currentthe incident was practicallycurrent was non-uniform practically nonand- theuniform associated and the fluid-structure associated interactionfluid-structure (FSI) interaction phenomena (FSI) was highlyphenom complex.ena was Wang highly and complex. 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[14] response studied ofthe the dynamic riser su responseffering both of the the riser floating suffering top-end both and the VIV. floating Anintegrated top-end and system VIV. withAn integrated both platform system and with riser both was establishedplatform and by meansriser was of finite established element by numerical means of simulations. finite element The numericalresult showed simulations. that the displacement The result showed of the riserthat the was displacement multiple times of largerthe riser than was that multiple of the casetimes without larger thanmoving that top-end. of the Wangcase etwithout al. and moving Yin et al. top [15-,end.16] performed Wang et experimentsal. and Yin inet towing al. [15,16] tank forperformed the riser experiments in towing tank for the riser which was excited at the top by platform surge motion, and the results showed that the platform surge had a great influence on VIV of the riser. J. Mar. Sci. Eng. 2020, 8, 121 3 of 14 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 3 of 15 which was excited at the top by platform surge motion, and the results showed that the platform surge The top-tensioned risers (TTR) are widely deployed by FPSOs, Semi-submersible platforms, had a great influence on VIV of the riser. Spar or Tensioned-leg platforms for drilling and production. The bottom end of TTR is connected The top-tensioned risers (TTR) are widely deployed by FPSOs, Semi-submersible platforms, Spar with the wellhead by ball joint, and the top end is connected with the platform by heave compensator or Tensioned-leg platforms for drilling and production. The bottom end of TTR is connected with (or tensioner, see Figure 1). The compensator provides a large static tensile tension at the top end of the wellhead by ball joint, and the top end is connected with the platform by heave compensator (or TTR (known as “top tension” for short in this paper), which can keep TTR vertical and avoid buckling tensioner, see Figure1). The compensator provides a large static tensile tension at the top end of TTR due to its large length. TTR is very sensitive to heave movements due to waves and to VIV caused by (known as “top tension” for short in this paper), which can keep TTR vertical and avoid buckling due sea current, since the rotation at the top and bottom connections is limited. The heave movement also to its large length. TTR is very sensitive to heave movements due to waves and to VIV caused by sea requires top tension equipment to compensate for the lack of tension.