# Vortex induced vibration

Vortex-induced vibrations (VIV) are motions induced on bodies facing an external flow by periodical irregularities on this flow. The classical example is the VIV of an underwater cylinder. You can see how this happens by putting a cylinder into the water (a swimming-pool or even a bucket) and moving through the direction perpendicular to its axis. Since real fluids always present some viscosity, the flow around the cylinder will be slowed down while in contact with its surface, forming the so called boundary layer. At some point, however, this boundary layer can separate from the body because of its excessive curvature. Vortices are then formed changing the pressure distribution along the surface. When the vortices are not formed symmetrically around the body (with respect to its midplane), different lift forces develop on each side of the body, thus leading to motion transverse to the flow. This motion changes the nature of the vortex formation in such a way as to lead to a limited motion amplitude (differently, then, from what would be expected in a typical case of resonance).

VIV manifests itself on many different branches of engineering, from cables to heat exchanger tube arrays. The rest of this article, however, will focus mainly on the problem of VIV around ocean structures such as production and drilling risers and umbilicals.

VIV of ocean structures is a major factor affecting all stages of development of offshore structures (conceptualization, design, analysis, construction and monitoring) and governs the arrangement of risers, details during fabrication, method of installation and instrumentation. Advances to deeper waters in search for crude oil has resulted in multi-billion dollar offshore projects off the Gulf of Mexico, for example: Independence Hub (\$2450m), Atlantis (\$2100m), Na Kika (\$2000m), Thunder Horse (\$1900m), Hoover/Diana (\$1400m) to name a few. Under such water depths, long flexible cylinders are increasingly required (umbilicals, risers, conductor tubes, pipeline spans), and prediction of VIV response increasingly important. A recent estimate by British Petroleum puts the estimated cost of countering VIV to approximately 10% of the project cost itself.

Thus study of VIV is a part of a number of disciplines, incorporating fluid mechanics, structural mechanics, vibrations, computational fluid dynamics (CFD), acoustics, wavelet transforms, complex demodulation analysis, statistics, and smart materials.

Motivation

They occur in many engineering situations, such as bridges, stacks, transmission lines, aircraft control surfaces, offshore structures, thermowells, engines, heat exchangers, marine cables, towed cables, drilling and production risers in petroleum production, mooring cables, moored structures, tethered structures, buoyancy and spar hulls, pipelines, cable-laying, members of jacketed structures, and other hydrodynamic and hydroacoustic applications. The most recent interest in long cylindrical members in water ensues from the development of hydrocarbon resources in depths of 1000 m or more.

Vortex-induced vibration (VIV) is an important source of fatigue damage of offshore oil exploration and production risers. These slender structures experience both current flow and top-end vessel motions, which give rise to the flow-structure relative motion and cause VIV. The top-end vessel motion causes the riser to oscillate and the corresponding flow profile appears unsteady.

One of the classical open-flow problems in fluid mechanics concerns the flow around a circular cylinder, or more generally, a bluff body. At very low Reynolds numbers (based on the diameter of the circular member) the streamlines of the resulting flow is perfectly symmetric as expected from potential theory. However as the Reynolds number is increased the flow becomes asymmetric and the so called Von Karman vortex street occurs.

The Strouhal number relates the frequency of shedding to the velocity of the flow and a characteristic dimension of the body (diameter in the case of a cylinder). It is defined as $St=f_\left\{st\right\}D/U$ and is named after Ce´nek (Vincent) Strouhal (a Czech scientist). In the equation fst is the vortex shedding frequency (or the Strouhal frequency) of a body at rest, D is the diameter of the circular cylinder, and U is the velocity of the ambient flow. The Strouhal number for a cylinder is 0.2 over a wide range of flow velocities. The phenomenon of lock-in happens when the vortex shedding frequency becomes close to a natural frequency of vibration of the structure. When this happens large and damaging vibrations can result.

Current state of art

Much progress has been made during the past decade, both numerically and experimentally, toward the understanding of the kinematics (vice dynamics) of VIV, albeit in the low-Reynolds number regime. The fundamental reason for this is that VIV is not a small perturbation superimposed on a mean steady motion. It is an inherently nonlinear, self-governed or self-regulated, multi-degree-of-freedom phenomenon. It presents unsteady flow characteristics manifested by the existence of two unsteady shear layers and large-scale structures.

There is much that is known and understood and much that remains in the empirical/descriptive realm of knowledge: what is the dominant response frequency, the range of normalized velocity, the variation of the phase angle (by which the force leads the displacement), and the response amplitude in the synchronization range as a function of the controlling and influencing parameters? Industrial applications highlight our inability to predict the dynamic response of fluid–structure interactions. They continue to require the input of the in-phase and out-of-phase components of the lift coefficients (or the transverse force), in-line drag coefficients, correlation lengths, damping coefficients, relative roughness, shear, waves, and currents, among other governing and influencing parameters, and thus also require the input of relatively large safety factors. Fundamental studies as well as large-scale experiments (when these results are disseminated in the open literature) will provide the necessary understanding for the quantification of the relationships between the response of a structure and the governing and influencing parameters.

It cannot be emphasized strongly enough that the current state of the laboratory art concerns the interaction of a rigid body (mostly and most importantly for a circular cylinder) whose degrees of freedom have been reduced from six to often one (i.e., transverse motion) with a three-dimensional separated flow, dominated by large-scale vortical structures.

Major Researchers in VIV

* Peter W. Bearman (Imperial College London, UK)
* C. H. K. Williamson (Cornell University, USA)
* M. M. Zdravkovich
* Robert D. Blevins
* T. Sarpkaya (Naval Postgraduate School, USA)
* J. Michael R. Graham (Imperial College London, UK)
* Michael Triantafyllou (MIT, USA)
* J. Kim Vandiver (MIT, USA)
* Don W. Allen (Shell Global Solutions, USA)
* Raghu Govardhan (Indian Institute of Science, India)
* Li Lee (Shell Global Solutions, USA)
* Franz Hover (MIT, USA)
* Alexandra H. Techet (MIT, USA)
* Jason Dahl (MIT, USA)
* Gary Flandro (University of Tennessee, UTSI, USA)
* Ricardo Galvao (MIT, USA)
* Harish Mukundan (MIT, USA)
* Evan Lee (MIT, USA)
* David E. Farrell (MIT, USA)
* Dean Henning (Shell Global Solutions, USA)
* G. E Karniadakis (Brown University, USA)
* Ram Gopalkrishnan (Shell)
* Michael S. Pantazopoulos (Exxon)
* Charles Dalton (University of Houston, USA)
* A. Bahtui (Brunel University, UK)
* H. Bahai (Brunel University, UK)

* Vortex
* Vortex shedding

* [http://oe.mit.edu/VIV Vortex induced vibration data repository]
* [http://web.mit.edu/13.42/www/ Design Principles for Ocean Vehicles Course Homepage at MIT]
* [http://www.efunda.com/DesignStandards/sensors/flowmeters/flowmeter_vtx.cfm eFunda: Introduction to Vortex Flowmeters]

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