Vortex Karman

Blade stall causes Karman vortices in the airfoil wake. Whenever the frequency of these vortices coincides with the natural frequency of the airfoil, flutter will occur. Stall flutter is a major cause of compressor blade failure. 

The distance between the Karman vortices (1) is only a function of the width of the obstruction (d), and therefore, the number of vortices per unit of time gives flow velocity. 

Kumar et al. (1995) used the CFDLIB code developed at Los Alamos Scientific Laboratory to simulate the gas-liquid flow in bubble columns. Their model, which is based on the Eulerian approach, could successfully predict the experimentally observed von Karman vortices (Chen et al., 1989) in a 2D bubble colunm with large aspect ratio (i.e., ratio of colunm height and colunm diameter). 

Kalashnikov, V.N. Kudin, A.M. Karman vortices in flow of solutions of friction-drag reducing polymers. DISA Information, No. 10 1979. 

Indeed, from the first set of experiments carried out with water, it can be concluded that the high level of the fluctuations power in condition B (Figure 4), is due to the Karman vortices which are known to appear for Re > Rec (with Rec 5). Since they arise in the wake, i.e. in a region... 

On the contrary, in polymer solutions, the fluctuations start at much smaller Re values than in water (about 30 times below between B and C Figure 5). However, the f values are equal ( C f 0.6 Hz) or higher ( D -> F, f 2 Hz) than that measured in water. A reasonable assumption which implies a smaller 6 value can then be put forward. Since the Karman vortices cannot be established in this creeping flow (Re 0.3), one must assume that the instabilities are not generated in the wake, but actually in the upstream region where the local 6 value is small. This hypothesis is consistent with the above interpretation based on the onset of a conformation change upstream. 

Kalashnikov, V. N. and A. M. Kudin, Karman vortices in the flows of drag reducing polymer solutions. Nature 225.AA5 (1970). 

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. ... 

Strouhal number St L vortex shedding frequency x characteristic flow Vortex shedding, von Karman vortex... 

In Cases 6 to 8, rotation and translation velocities of the cylinder are the same, but the cylinder is located at different distances above the boundary layer. The last column of the table shows the ratio of surface speed Ug = Qd/2) to the relative free stream speed, Uoo — c). Except for Case 3 where the cylinder is not rotating, the values given in the last column for all other cases are greater than 2. This parameter value is known to cause limited or no Karman vortex shedding, as noted experimentally in Tokumaru Dimotakis (1993) and Diaz et al. (1983). 

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. 

Another interesting effect of the particle inertia is that it can transform non-attracting chaotic sets into chaotic attractors. This has been shown by Benczik et al. (2002) who studied the motion of inertial particles in the time-periodic Karman vortex flow that produces transient chaotic advection of non-inertial particles, while inertial particles are trapped indefinitely in the wake indicating the presence of an attractor. 

Figure 6.7 Numerical simulation of a decaying tracer in the Karman vortex flow in the wake of a cylindrical obstacle. The flow is from left to right and a source with Gaussian distribution is located upstream on the left from the obstacle. The concentration field changes smoothly almost everywhere except for the filaments behind the cylinder that coincide with the unstable manifold of the chaotic saddle.

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. 

In determining the effect of the cross flow, the maximum possible velocity of 7 ft s was used to determine the maximum von Karman vortex frequency of 17.5 cps. The cross flow velocity distribution was taken as shown in Figure 12-2 which is, of course, an approximation of the actual case. 

A fatigue analysis was made to determine if the tie rods will fail due to fatigue in the unlikely event that the rod vibrates in resonance with the von Karman vortex frequency. The modified Goodman diagram was used in this analysis. This method is described in Reference 6. 

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. 

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