Vortex shedding

If the bluff structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. This vibration is the cause for overhead power line wires humming in the wind, and for the fluttering of automobile whip radio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

Vortex shedding was one of the causes proposed for the failure of the original Tacoma Narrows Bridge (Galloping Gertie) in 1940, but was rejected because the frequency of the vortex shedding did not match that of the bridge. The bridge actually failed by aeroelastic flutter.

A thrill ride, "VertiGo" at Cedar Point in Sandusky, Ohio suffered vortex shedding during the winter of 2001, causing one of the three towers to collapse. The ride was closed for the winter at the time. In northeastern Iran, the Hashemi-Nejad natural gas refinery's flare stacks suffered vortex shedding seven times from 1975 to 2003. Some simulation and analyses were done, which revealed that the main cause was the interaction of the pilot flame and flare stack. The problem was solved by removing the pilot.

Governing equation

The frequency at which vortex shedding takes place for a cylinder is related to the Strouhal number by the following equation:

${\displaystyle \mathrm{S}\mathrm{t}=\frac{f\cdot D}{V}}$

Where ${\displaystyle \mathrm{S}\mathrm{t}}$ is the dimensionless Strouhal number, ${\displaystyle f}$ is the vortex shedding frequency (Hz), ${\displaystyle D}$ is the diameter of the cylinder (m), and ${\displaystyle V}$ is the flow velocity (m/s).

The Strouhal number depends on the Reynolds number ${\displaystyle \mathrm{R}\mathrm{e}}$, but a value of 0.22 is commonly used. As the unit is dimensionless, any set of units can be used for the variables. Over four orders of magnitude in Reynolds number, from 10² to 10⁵, the Strouhal number varies only between 0.18 and 0.22.