Kármán vortex street

As a Karman vortex street is called a phenomenon in fluid mechanics, in which flow around the body behind a train opposing vertebrae. The vortex streets were detected and calculated by Theodore von Kármán for the first time in 1911.

Vortex formation

The character of the vortex formation is mainly determined by the Reynolds number Re. It represents the ratio of inertial to viscous forces and is calculated from the flow rate, the diameter of the body and viscosity. In the simplest case, that of a stationary cylinder in a steady flow, can be based on the Reynolds number different configurations of the vortex street is observed: At very low speeds, or very large viscosities ( Re < 4-5, eg honey) finds no flow separation instead. This case is a classic application of potential theory. With increasing speed form on the flow side facing away from two counter-rotating vortex bubbles that are increasingly unstable as Re = 30-48 and then starting to show the typical periodic oscillating motion. The frequency of vortex shedding is characterized by the Strouhal number. Up to Re = 180-200, the entire vortex street remains completely laminar. In the higher Reynolds numbers, it is discriminated which takes place in the flow field of the envelope from laminar to turbulent flow. This initially takes place in the distant follower instead of ( Re ≈ 200 ) and advances with increasing Reynolds number up in the boundary layer directly on the body approach. In this area of Recrit ≈ 10,000, the flow resistance of the body is minimal. Even in areas with very high Reynolds numbers ( Re> 5 million), as they occur in wind currents to TV towers or islands, Karman vortex streets are still watching. The Strouhal number is changing it only slightly and reaches values ​​up to 0.30.

Examples

Vortices and vortex streets are a common phenomenon. However, their observation is not easy. Air currents can not be readily apparent. Eddies are just as transparent as water itself Upon closer observation you will discover them in the bathtub, when you move your finger through the water. After treating a liquid of high viscosity, such as a water - Glyzeringemisch, some with food coloring, the color threads indicate the directions of rotation.

The video sequence ( GIF, 500 Kbyte ) shows how turbulence results in an obstacle, you flow with the flow and its rotation towards the obstacle.

Karman vortex streets can form, for example behind island groups that tower high above the sea. The turbulence is then visible on aerial photographs as a huge cloud structures, see the satellite image on the right.

Shedding frequency

The shedding frequency of the vortices can be determined by the Strouhal number. The following applies:

Where is the free stream velocity and a characteristic dimension of the flow around the body. The Strouhal number is dependent on the shape of the body and the Reynolds number. For cylindrical body it is for a wide range of Reynolds numbers 0.18-0.22. Here is chosen. As a characteristic dimension of the diameter is used here. Thus produced a 4 mm thick radio antenna on the roof of a 25 m / s (90 km / h) fast-moving vehicle a clearly audible tone with the frequency

Another example is the whistling overhead power lines in high winds.

Due to the linear relationship of shedding frequency and flow rate of the physical effect for flow measurement (" Vortex Flowmeter " ) in non- abrasive (see: wear) is low-viscous media used.

Resonance case

Does the shedding frequency of the vortices of the natural frequency of the body in flow, it is vibrated. A familiar example is an aeolian harp.