Vortex Induced Vibration
Encyclopedia
In fluid dynamics
, vortex
-induced vibrations (VIV) are motions induced on bodies
interacting with an external fluid flow, produced by – or the motion producing – periodical irregularities
on this flow.
A 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 it through the water in 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. It is also a major consideration in the design of ocean structures. Thus study of VIV is a part of a number of disciplines, incorporating fluid mechanics
, structural mechanics
, vibrations, computational fluid dynamics
(CFD), acoustics
, statistics
, and smart material
s.
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 Kármán 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
and is named after Čeněk (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.
(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.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
, vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
-induced vibrations (VIV) are motions induced on bodies
Physical body
In physics, a physical body or physical object is a collection of masses, taken to be one...
interacting with an external fluid flow, produced by – or the motion producing – periodical irregularities
Quasiperiodic motion
In mathematics and theoretical physics, quasiperiodic motion is in rough terms the type of motion executed by a dynamical system containing a finite number of incommensurable frequencies....
on this flow.
A 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 it through the water in the direction perpendicular to its axis. Since real fluids always present some viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
, the flow around the cylinder will be slowed down while in contact with its surface, forming the so called boundary layer
Boundary layer
In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...
. At some point, however, this boundary layer can separate
Flow separation
All solid objects travelling through a fluid acquire a boundary layer of fluid around them where viscous forces occur in the layer of fluid close to the solid surface. Boundary layers can be either laminar or turbulent...
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
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...
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
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
).
VIV manifests itself on many different branches of engineering, from cables to heat exchanger tube arrays. It is also a major consideration in the design of ocean structures. Thus study of VIV is a part of a number of disciplines, incorporating fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, structural mechanics
Structural mechanics
Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis...
, vibrations, computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
(CFD), acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
, statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, and smart material
Smart material
Smart materials or designed materials are materials that have one or more properties that can be significantly changed in a controlled fashion by external stimuli, such as stress, temperature, moisture, pH, electric or magnetic fields....
s.
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
Oil exploration
Hydrocarbon exploration is the search by petroleum geologists and geophysicists for hydrocarbon deposits beneath the Earth's surface, such as oil and natural gas...
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 Kármán vortex street occurs.
The Strouhal number
Strouhal number
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind...
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
and is named after Čeněk (Vincent) StrouhalVincenc Strouhal
Vincenc Strouhal was a Austrian physicist specializing in experimental physics. He was one of the founders of the Physics department at Charles University.-Further reading:* *...
(a Czech scientist). In the equation fst is the vortex shedding
Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
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
Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...
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 kinematicsKinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
(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
Shearing (physics)
Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material...
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
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
, the range of normalized velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
, the variation of the phase angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
(by which the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
leads the displacement
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...
), and the response amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
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.
See also
- Aeroelastic flutter
- Kármán vortex street
- Vortex powerVortex powerVortex power is a form of hydro power which generates energy by placing obstacles in rivers/oceans in order to cause the formation of vortices which can then be tapped to a usable form of energy such as electricity...
- Vortex sheddingVortex sheddingVortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...