Von Kármán vortex street
Encyclopedia
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...
for a repeating pattern of swirling vortices
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...
caused by the unsteady separation of flow
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...
of a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
over bluff bodies. It is named after the engineer and fluid dynamicist, Theodore von Kármán
Theodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
and is responsible for such phenomena as the "singing" of suspended telephone or power lines, and the vibration of a car antenna at certain speeds.
Analysis
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
l to viscous forces
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...
in the flow of a fluid and may be defined as:
where:
= the diameter of the cylinder (or some other suitable measure of width of non-circular bodies) about which the fluid is flowing
= the steady velocityVelocityIn 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 ...
of the flow upstream of the cylinder
= the kinematic viscosity of the fluid.
The range of Re values will vary with the size and shape of the body from which the eddies
Eddy (fluid dynamics)
In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object...
are being shed
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...
, as well as with the kinematic viscosity of the fluid. Over a large Re range (47
Wake
A wake is the region of recirculating flow immediately behind a moving or stationary solid body, caused by the flow of surrounding fluid around the body.-Fluid dynamics:...
. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears.
When a single vortex is shed, an asymmetrical
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
flow pattern forms around the body and changes the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
distribution. This means that the alternate shedding of vortices can create periodic
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...
lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding 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...
is similar to the natural frequency of a body or structure, it causes 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...
. It is this forced vibration which, at the correct frequency, causes suspended telephone
Telephone line
A telephone line or telephone circuit is a single-user circuit on a telephone communication system...
or power line
Power Line
Power Line is an American political blog, providing news and commentary from a conservative point-of-view. It was originally written by three lawyers who attended Dartmouth College together: John H. Hinderaker, Scott W. Johnson, and Paul Mirengoff...
s to "sing" and the antenna
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
on a car to vibrate more strongly at certain speeds.
Engineering problems
In low turbulence, tall buildings can produce a Kármán street so long as the structure is uniform along its height. In urban areas where there are many other tall nearby structures the turbulence produced by these prevents the formation of coherent vortices. Periodic crosswind forces set up by vortices along object's sides can be highly undesirable, and hence it is important for engineers to account for the possible effects of vortex shedding when designing a wide range of structures, from submarineSubmarine
A submarine is a watercraft capable of independent operation below the surface of the water. It differs from a submersible, which has more limited underwater capability...
periscope
Periscope
A periscope is an instrument for observation from a concealed position. In its simplest form it consists of a tube with mirrors at each end set parallel to each other at a 45-degree angle....
s to industrial chimney
Chimney
A chimney is a structure for venting hot flue gases or smoke from a boiler, stove, furnace or fireplace to the outside atmosphere. Chimneys are typically vertical, or as near as possible to vertical, to ensure that the gases flow smoothly, drawing air into the combustion in what is known as the...
s and skyscraper
Skyscraper
A skyscraper is a tall, continuously habitable building of many stories, often designed for office and commercial use. There is no official definition or height above which a building may be classified as a skyscraper...
s.
In order to prevent the unwanted vibration of such cylindrical bodies, a longitudinal fin can be fitted on the downstream side, which, providing it is longer than the diameter of the cylinder, will prevent the eddies from interacting, and consequently they remain attached. Obviously, for a tall building or mast, the relative wind could come from any direction. For this reason, helical
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
projections which look like large screw threads are sometimes placed at the top, which effectively create asymmetric three-dimensional flow, thereby discouraging the alternate shedding of vortices; this is also found in some car antennas, such as late 1990s/early 2000s Fuba (Fuba Communications Systems) amplified antenna masts, used on the Volkswagen Golf Mk4
Volkswagen Golf Mk4
Launched in 1999, the Volkswagen Golf Mk4 was the best selling car in Europe in 2001 . The Mk4 was a deliberate attempt to take the Volkswagen Golf series further upmarket, with a high-quality interior and higher equipment levels...
, Jetta
Volkswagen Jetta
Although the Golf had reached considerable success, in the North American markets, Volkswagen observed that the hatchback body style lacked some of the appeal to those who preferred the traditional three-box configuration...
Mk4 and New Beetle
Volkswagen New Beetle
-Specifications:*Dimension:**Length: **Width: **Height: **Wheelbase: **Curb weight: *Max speed: 177–210 km/h *Acceleration : 6.5-13.2 sec-Body styles:-Engine choices:-Safety:...
. Another countermeasure with tall buildings is using variation in the diameter with height, such as tapering - that prevents the entire building being driven at the same frequency.
Even more serious instability
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...
can be created in concrete cooling tower
Cooling tower
Cooling towers are heat removal devices used to transfer process waste heat to the atmosphere. Cooling towers may either use the evaporation of water to remove process heat and cool the working fluid to near the wet-bulb air temperature or in the case of closed circuit dry cooling towers rely...
s, for example, especially when built together in clusters. Vortex shedding caused the collapse of three towers at Ferrybridge power station
Ferrybridge power station
The Ferrybridge power stations refers to a series of three coal-fired power stations situated on the River Aire in West Yorkshire, England. The first station on the site, Ferrybridge A power station, was constructed in the mid-1920s, and was closed as the second station, Ferrybridge B power...
in 1965 during high winds.
The failure of the Tacoma Narrows Bridge (1940)
Tacoma Narrows Bridge (1940)
The 1940 Tacoma Narrows Bridge was the first incarnation of the Tacoma Narrows Bridge, a suspension bridge in the U.S. state of Washington that spanned the Tacoma Narrows strait of Puget Sound between Tacoma and the Kitsap Peninsula. It opened to traffic on July 1, 1940, and dramatically collapsed...
was originally attributed to excessive vibration due to vortex shedding, but was actually caused by aeroelastic flutter.
Formula
where:
- f = vortex shedding frequency.
- d = diameter of the cylinder
- V = flow velocity.
This formula will generally hold true for the range 250 < Re < 2 × 105. The dimensionless parameter fd/V is known as 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...
and is named after the Czech physicist, Vincenc Strouhal
Vincenc 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:* *...
(1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.
Insect flight
Recent studies have shown that insects such as beeBee
Bees are flying insects closely related to wasps and ants, and are known for their role in pollination and for producing honey and beeswax. Bees are a monophyletic lineage within the superfamily Apoidea, presently classified by the unranked taxon name Anthophila...
s borrow energy from the vortices
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
that form around their wings during flight. Vortices inherently create drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
. Insects can recapture some of this energy and use it to improve speed and maneuverability: They rotate their wings before starting the return stroke, and the wings are lifted by the eddies
Eddy (fluid dynamics)
In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object...
of air created on the downstroke. The high frequency oscillation of insect wings means that many hundreds of vortices are shed every second. However, this leads to a symmetric vortex street pattern, unlike the ones shown above.
See also
- 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...
- Vortex-induced vibration
- Strouhal numberStrouhal numberIn 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...
- Aeroelastic flutter - where the self-resonance of the solid object dominates, e.g. flapping to give +/- Lift (force)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...
resulting from angle of attackAngle of attackAngle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...
External links
- 3D animation of the Vortex Flow Measuring Principle
- Vortex streets and Strouhal instability
- How Insects Fly
- YouTube — Flow visualisation of the vortex shedding mechanism on circular cylinder using hydrogen bubbles illuminated by a laser sheet in a water channel
- Various Views of von Karman Vortices, NASA page