Vortex Street

The term Kármán vortex street (or a von Kármán vortex street) is used in singing” of suspended telephone or power lines, and the vibration of a car antenna at certain speeds.

Contents 1 Analysis 2 In Meteorology 2.1 Mountains Known to create the Kármán vortex street 3 Engineering problems 4 Formula 5 Insect flight 6 History 7 See also 8 References 9 External links

[edit] Analysis

A vortex street will only be observed over a given range of viscous forces 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 velocity of the flow upstream of the cylinder.
• = the kinematic viscosity of the fluid.

or:

where:

• = the free stream fluid density.
• = the steady free stream velocity of the flow upstream of the cylinder.
• = the diameter of the cylinder (or some other suitable measure of width of non-circular bodies) about which the fluid is flowing.
• = the free stream dynamic viscosity of the fluid.

The range of Re values will vary with the size and shape of the body from which the energy 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 flow pattern forms around the body and changes the pressure distribution. This means that the alternate shedding of vortices can create periodic lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding frequency is similar to the natural frequency of a body or structure, it causes resonance. It is this forced vibration which, at the correct frequency, causes suspended telephone or power lines to “sing” and the antenna on a car to vibrate more strongly at certain speeds.

[edit] In Meteorology

This section requires expansion. (November 2012)

[edit] Mountains Known to create the Kármán vortex street

The following list all the islands, mountains in the world known to cause a Von Karman Vortex street.

• Guadalupe Island ^[2]
• Hallasan Volcano, Jeju Island, South Korea.^[3]
• New Mexico. The 37.4 km2 island often causes unusually long, vortex streets, with small vortices.

^[4]

• Juan Fernandez Islands^[5]
• All Canary Islands

^[6]

• Jan Mayen island.

^[7]

• fog.

^[8]

• Saint Helena Island^[9]
• Broutona Island, Japan.^[10]
• Japan

^[11]

• South Atlantic Ocean.
• Tristan da Cunha, South Atlantic ocean.

^[13]

• Alaska. About 70% of the group of islands have been known to create the Von Karman Vortices.

^[14]

• Indian Ocean

^[15]

• Galapagos Islands

^[16]

• Juan Fernández Islands, Chile

^[17]

[edit] 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.^[18] 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 submarine periscopes to industrial chimneys and skyscrapers.

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 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. 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 Ferrybridge power station in 1965 during high winds.

The failure of the aeroelastic flutter.

[edit] 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 Vincenc Strouhal (1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.

[edit] Insect flight

Recent studies have shown that eddies 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.

[edit] History

Although named after [23]

[edit] See also

• Kelvin–Helmholtz instability
• Vortex shedding
• Vortex-induced vibration
• Strouhal number
• Coandă effect
• Aeroelastic flutter – where the self-resonance of the solid object dominates, e.g. flapping to give +/- Lift (force) resulting from angle of attack

[edit] References

1. ^ Theodore von Kármán, Aerodynamics. McGraw-Hill (1963): ISBN 978-0-07-067602-2. Dover (1994): ISBN 978-0-486-43485-8.
2. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=987
3. http://www.hko.gov.hk/wxinfo/intersat/satellite_gallery/misc_e.htm#m6
4. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=1254
5. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=625
6. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=AtlanticOcean.A2010226.1455.1km.jpg
7. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=2270
8. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=9043
9. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=79720
10. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=2313
11. ^ http://earthobservatory.nasa.gov/IOTD/view.php?id=2313
12. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?
13. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=SouthSandwich.A2012118.1620.1km.jpg
14. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=AleutianIslands.A2012108.2240.500m.jpg
15. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=HeardIsland.A2011262.0430.1km.jpg
16. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=Galapagos.A2010251.1635.1km.jpg
17. ^ http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=JuanFernandezIslands.A2010020.1920.1km.jpg
18. 0031-9228.
19. ^ T. von Kármán: Nachr. Ges. Wissenschaft. Göttingen Math. Phys. Klasse pp. 509–517 (1911) and pp. 547–556 (1912).
20. ^ T. von Kármán: and H. Rubach, 1912: Phys. Z.”, vol. 13, pp. 49–59.
21. ^ T. Kármán, 1954. Aerodynamics: Selected Topics in the Light of Their Historical Development (Cornell University Press, Ithaca), pp. 68–69.
22. ^ A. Mallock, 1907: On the resistance of air. Proc. Royal Soc., A79, pp. 262–265.
23. ^ H. Bénard, 1908: Comptes rendus de l’Académie des Sciences (Paris), vol. 147, pp. 839–842, 970–972.

[edit] External links

Wikimedia Commons has media related to: Von Kármán vortex street

• Encyclopedia of Mathematics article on von Karman vortex shedding
• 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

Source: Wikipedia