Vortex street

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

The periodic shedding produces lateral forces of the same period on the cylinder. Should the cylinder be weakly supported and have a natural frequency close to the shedding frequency, it oscillates strongly in concert with the vortex street. Such behavior is responsible for the singing of power lines, the oscillation of tall smokestacks, and, most spectacularly, for the coUapse in 1940 of the newly built Tacoma Narrows suspension bridge, in Washington state, under the influence of a steady 65 km/h wind. 

Development of a vortex street, or von Kdrmdn vortex street is shown in Fig. 6-50. Discussions of the vortex street may be found in Panton (pp. 387—393). The Reynolds number is... 

For flow past a cyhnder, the vortex street forms at Reynolds numbers above about 40. The vortices initially form in the wake, the point of formation moving closer to the cylinder as Re is increased. At a Reynolds number of 60 to 100, the vortices are formed from eddies attached to the cylinder surface. The vortices move at a velocity slightly less than V. The frequency of vortex shedding/is given in terms of the Strouhal number, which is approximately constant over a wide range of Reynolds numbers. 

Above Re = 10 the vortex shedding is difficult to see in flow visualization experiments, but velocity measurements still show a strong spectral component at St = 0.2 (Panton, p. 392). Experimental data suggest that the vortex street disappears over the range 5 X 10 < Re < 3.5 X 10 , but is reestablished at above 3.5 X 10 (Schhchting). 

In order to achieve a high level of product safety it is well known that good work practices in the bench are necessary, and having a clean environment and proper work clothing are of vital importance. Knowledge about the interaction between air movements and the dispersion of contaminants plays an important role. Wake regions and vortex streets can easily be formed behind obstacles. 

In the unidirectional air flow of an open bench, a vortex street is easily created behind small obstacles. Such an obstacle can be as insignificant as a small lamp or a fixture connecting HEPA filters. Ljungqvist, et al. have, with the help of isothermal smoke, visually depicted the air movements behind such a horizontal 30 mm wide fixture at an air velocity of 0.45 m s The observed flow pattern is schematically shown in Fig. 10.55. 

The flow pattern in Fig. 10.55 has a violent turbulent region, characterized by a vortex street and two free vortices rotating in opposite directions... 

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. 

However, one should be cautious when comparing the Reynolds number from regular Karman vortex streets with the Reynolds number calculated from factual situations in clean benches as the airflow from behind an obstacle is usually not the typically formed Karman vortex street predicted for an indefinitely long circular cylinder. The wake situations during actual conditions often seem to have a three-dimensional stmcnire. 

Meanwhile, the flow near the cylinder curls towards the cylinder and forms a new vortex that takes the place of the original. As time goes on, the vortices on either side of the cylinder take turns breaking off and traveling down stream. A snapshot of this behavior is shown schematically in figure 9.3. This stream of successively broken-off vortices is known as a von Karman vortex street [trittSS]. 

A little bit of physical intuition as to how the vortices form in the first place may help in explaining the behavior as TZ is increased still further. We know that u = 0 at the cylinder s surface. We also know that the velocity increases rapidly as we get further from that surface. Therefore vortices are due to this rapid local velocity variation. If the variation is small enough, there is enough time for the vorticity to diffuse out of the region just outside the cylinder s surface and create a large von Karman vortex street of vorticity down stream [feyn64]. 

A so-callod von Kannaii Vortex Street form.s behind a cylinder for TZ 100. 

When a bluff body is interspersed in a fluid stream, the flow is split into two parts. The boundary layer (see Chapter 11) which forms over the surface of the obstruction develops instabilities and vortices are formed and then shed successively from alternate sides of the body, giving rise to what is known as a von Karman vortex street. This process sets up regular pressure variations downstream from the obstruction whose frequency is proportional to the fluid velocity, as shown by Strouai. 9. Vortex flowmeters are very versatile and can be used with almost any fluid — gases, liquids and multi-phase fluids. The operation of the vortex meter, illustrated in Figure 6.27, is described in more detail in Volume 3, by Gjnesi(8) and in a publication by a commercial manufacturer, Endress and Hauser.10 ... 

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Eddies are turbulent instabilities within a flow region (Fig. 2). These vortices might already be present in a turbulent stream or can be generated downstream by an object presenting an obstacle to the flow. The latter turbulence is known as Karman vortex streets. Eddies can contribute a considerable increase of mass transfer in the dissolution process under turbulent conditions and may occur in the GI tract as a result of short bursts of intense propagated motor activity and flow gushes. ... 

In Fig. 3.5, visualization sequences are shown for the Case 3. In this case of non-rotating translating cylinder, no violent instability was seen to occur for two reasons. Firstly the imposed disturbance field, as given by Eqn. (3.3.1) has no captive vortex i.e.F = 0) as the cylinder does not rotate while translating. Secondly, if there are shed vortices present, they will be very weak and Benard- Karman vortex street is seen to affect the flow weakly far downstream of the translating cylinder - only at earlier times. 

Tritton, D.J. (1970). A note on vortex streets behind circular cylinders at low Reynolds numbers. J. Fluid Mech. 45(1), 203-208. 

Fig. 9. Karman vortex street formed behind a cylinder (diameter d) positioned in a channel (width 2h) at a Reynolds number of 106, [From Anagnostopoulos, R, and Iliadis, G. Numerical study of the blockage effect on viscous flow past a circular cylinder. Int. J. Num. Methods Fluids 22, 1061 (1996). Copyright John Wiley Sons Limited. Reproduced with permission.]...

Zhang, H.J., and Zhou, Y. (2001) Effect of unequal cylinder spacing on vortex streets behind three side-by-side cylinders, Physics of Fluids, 13(12), 3675-3686. 

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