VIV-Induced Axial Vibrations in Deep Sea Risers
Authors: Huse E. , Kleiven G. , Nielsen F.G. 
Published: October 2008

Abstract
Recent investigations have shown that transverse vortex-induced vibrations (VIV) in risers may lead to tension fluctuations at twice the VIV frequency. For deep sea risers the corresponding stresses represent a significant fatigue loading. A theory covering the case where the tension fluctuation excites axial non-resonant vibration in the riser was described together with experimental verification in a paper at OTC 1998. The present paper describes a complete numerical procedure for estimating the VIV-induced tension fluctuations, including also the case where the first axial resonant mode is excited. The theory, as well as recent experiments, show that in such a case of axial resonance, there exists a "feedback effect" that tends to reduce the transverse VIV response. The calculation procedure also includes the necessary formulations to specify additional damping of the axial vibration, in case it is considered necessary to reduce the resonant amplification of the tension fluctuation.

Introduction
The riser system represents one of the main challenges in the design of safe and cost-effective concepts for production of oil and gas at sites with ocean depth of one to two thousand meters or more. The risers become very heavy, and may require buoyancy elements to be fitted. Furthermore, the loads due to current become much more important for such deep sea risers, compared with installations in more shallow water. Important aspects are the large lateral deflections, large inclination angles at top and bottom, possible clashing between individual risers, and fatigue stresses due to vortex induced vibrations (VIV). In an OTC paper in 1998 (Ref.1) the authors described tests and theoretical developments which indicated that VIV might give rise to considerable tension fluctuations in deep sea risers. Such tension fluctuations could cause compression in the risers during part of the vibration cycle, and could lead to significantly increased fatigue stresses. Speculation about hitting the first mode of axial resonant vibration indicated a possibly very serious situation.

Objective
The objective of the present paper is to provide more detailed information and numerical methods to predict VIV-induced axial vibrations in deep sea risers, in particular to determine what happens in case one hits the axial resonance.

State-of-the-art survey of VIV-induced axial vibrations
In Ref.1 is reported observations of significant tension fluctuations in a test program with deep sea rigid risers. The phenomenon is explained as a consequence of the transverse VIV response of the risers. Let us for simplicity assume the riser to oscillate in the form of a standing wave, at a high mode of transverse vibration as indicated by Fig.1. The riser is assumed to be pinned at the lower end and free to move axially at the top end, where the tensioning system provides more or less constant pretension. The distance along the arc measured from the pinned lower end to a certain level z will vary during the oscillation cycle, being maximum at the instant of extreme transverse excursion and minimum at the instant when the riser passes the neutral position, forming a straight line. This means that a certain mass element at this level of the riser is moving up and down at twice the frequency of the transverse vibration. This up-and-down motion of the mass element represents a certain acceleration and corresponding inertia force. If we sum up the inertia orces on all mass elements that constitute the riser, we end up with a total inertia force which has to be balanced by a corresponding reaction force at the pinned end of the riser.