Karman vortex street

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]. 

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 ... 

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. 

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.]...

Separated flow past a cylinder at high Reynolds numbers. With further increase of Re, the rear vortices become longer and then alternative vortex separation occurs (the Karman vortex street is formed). Simultaneously, the separation point moves closer to the equatorial section. The frequency Uf of vortex shedding from the rear area is an important characteristic of the flow past a cylinder. It can be determined from the empirical formula [117]... 

A special case of chaotic advection occurs in open flows in which the time-dependence of the flow is restricted to a bounded region (Tel et al., 2005). This kind of flow structure with an unsteady mixing region and simple time-independent inflow and outflow regions is typical for example in stirred reactors or in a flow formed in the wake of an obstacle. A well known example is the von Karman vortex street behind a cylinder at moderate Reynolds numbers (Jung et al., 1993 Ziemniak et al., 1994), where around the cylinder the flow is time-periodic, but at some distance from it upstream or downstream the velocity field is time independent. 

When a fluid flows past a bluff body, the wake downstream will form rows of vortices that shed continuously from each side of the body as illustated in Figure 4.16. These repeating patterns of swirling vorticies are referred to as Karman vortex streets named after the fluid dynamicist Theodore von Karman. Vortex shedding is a common flow phenomenon that causes car antennas to vibrate at certain wind speeds and also lead to the collapse of the famous Tacoma Narrows Bridge in 1940. Each time a vortex is shed from the bluff body it creates a sideways force causing the body to vibrate. The frequency of vibration is linearly proportional to the velocity of the approching fluid stream and is independent of the fluid density. 

A closer analysis of this problem would reveal more complex situations, such as a fluid flowing around a solid body. In that case the streamlines may take off behind the body at the limit of zero viscosity of the fluid. However, all fluids exhibit some viscosity and no such phenomenon can be observed. Experiments show that vorticity is generally generated in a thin boundary layer, close to a solid surface. It is propagated from the wall by both viscous diffusion and convection. The vortices are transported with the fluid they are observable for some time after their appearance. If the experiment is made with a circular cylinder moving at a constant velocity, the eddies appear in the wake of the body and their regular distribution constitutes the famous, as well as beautiful, Karman vortex street . 

Strouhal foimd the Strouhal Niunber (Sj) to be about %. Actually the constant varies between 0.2 and 0.5 depending on the shape of the body, but has a constant value for a given shape. In 1911, von Karman showed anal5 ically lhat the only stable vortex configuration was that given by the Strouhal Niunber. These vortices are, therefore, sometimes called the Karman Vortex Street. 

The largest reported Karman Vortex Street was one observed by den Hartog. It was formed by clouds passing over a volcanic crater in the Hawaiian Islands that was five miles in diameter. This was photographed and the spacing of vortices found to be 24 miles on each side. 

In the previous chapter, a brief account of the Tacoma Narrows bridge disaster was considered. Tests on scale bridge models are being used today to be sure a proposed structure is not dynamically unstable to excitation due to a Karman Vortex Street that may develop in a high wind. 

Rotation is caused by the alternate peeling of vertices (Karman Vortex Street) from the edges of the paper when oriented perpendicular to linear velocity vector (F) as in Fig. 12.4 (a). As each vortex leaves, it subjects the edge of the paper to a force opposite to (V) due to a... 

Karman vortex street A phenomenon in which vortices of a moving fluid form as repeating patterns. They are caused by the unsteady separation of flow of a fluid as it passes around an object such as a wire and observed over Reynolds numbers of around 90. It is named after Hungarian-American mathematician and physicist Theodore von Karman (1881 -1963) and is also known as the von Kton n vortex street. 

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