Wake shedding cylinders

Experimental data are available for large particles at Re greater than that required for wake shedding. Turbulence increases the rate of transfer at all Reynolds numbers. Early experimental work on cylinders (VI) disclosed an effect of turbulence scale with a particular scale being optimal, i.e., for a given turbulence intensity the Nusselt number achieved a maximum value for a certain ratio of scale to diameter. This led to speculation on the existence of a similar effect for spheres. However, more recent work (Rl, R2) has failed to support the existence of an optimal scale for either cylinders or spheres. A weak scale effect has been found for spheres (R2) amounting to less than a 2% increase in Nusselt number as the ratio of sphere diameter to turbulence macroscale increased from zero to five. There has also been some indication (M15, S21) that the spectral distribution of the turbulence affects the transfer rate, but additional data are required to confirm this. The major variable is the intensity of turbulence. Early experimental work has been reviewed by several authors (G3, G4, K3). 

The marked influence of the polymer solution at 100 ppm concentration, as compared to the less-concentrated solutions, was accompanied by two other phenomena. The first of these was an earlier appearance of vortices in the wake. For cylinders of 0.17 and 0.25 mm diameter, the vortices appeared at Re=13 (as compared with first appearance at Re=40 for the Newtonian case) The second was the disappearance of the velocity fluctuation signals (Fig.6) indicating vortex shedding from the cylinder. The disappearance occurred at Re=150 for the 0.25 mm cylinder and at Re=100 for the 0.17 mm cylinder, although the shedding frequency before the signal disappearance was the same for both cases. 

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. 

The flow in the wake of the cylinder will, in general, be unsteady due to the shedding of vortices from the rear portion of the cylinder as shown schematically in Fig. 3.30. This shedding causes the wake flow to be asymmetric about an axis that is parallel to the upstream flow and drawn through the center of the cylinder as shown in Fig. 3.30. 

Williamson, C.H.K. (1989). Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynold numbers. J. Flmd Mech. 206, 579-627. 

As Re increases, the adjacent vortices are elongated and shedding of vortices occurs (Karman s vortices are formed). Finally, for Re > 1000, the remote wake becomes completely turbulent [117]. At the same time, the separation point moves toward the midsection and even a bit farther upstream. For such values of Re, we can speak about a pronounced boundary layer. In a large part of the boundary layer, the flow remains laminar [486], Strong turbulence within the boundary layer occurs for considerably higher Reynolds numbers (Re 2x 105), at which the cylinder drag drops rapidly [117], This phenomenon is called the drag crisis. 

On the other hand, the flow in the region downstream of the cylinder and in the wake, where vortex formation occurs has only been scetchily investigated. Measurement of the detailed flow structure for this region is extremely difficult since the diameter of the cylinder should be very small (0.1-0.5 mm). Even measurements of Strouhal number, St=fd/V were accomplished in a small number of works [4,8,9], and in very limited range of Reynolds numbers, Re=dV/v, where f is the vortex shedding frequency, d-cylinder, diameter, V-velocity of the undisturbed flow, v-kinematic viscosity. The... 

For the cylinder of 0.7 mm in diameter only small departures from the Newtonian vortex shedding frequency was observed. No early appearance of vortices in the wake of their disappearance was detected in this case. 

Flow across a tube produces a series of vortices in the downstream wake formed as the flow separates alternately from the opposite sides of the tube. This alternate shedding of vortices produces alternating forces which occur more frequently as the velocity of flow increases. For a single cylinder the tube diameter, the flow velocity, and the frequency of vortex shedding can be described by the dimensionless Strouhal number ... 

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