Wake shedding frequency

The validity of the various simplifications has been the subject of considerable discussion [e.g. (A3, B2, H3, T4)]. Schoneborn (S4) showed that in the range where periodic wake shedding normally occurs (Re > 200 see Chapter 5), the effect of fluid oscillations depends on the relationship between the forced fluid frequency and the natural wake frequency ... 

For plastic beads with pp = 500 kg/m3 falling in air at ambient conditions, estimate the range of variation of the shedding frequency of the particle wake when the particle Reynolds number, based on the particle terminal velocity, varies from 500 to 1,000. For this particle Reynolds number range, what is the corresponding range of variation for the particle sizes ... 

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... 

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 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. 

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 ... 

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. 

Few observations have been reported on wakes of ellipsoidal bubbles and drops at Re > 1000. Yeheskel and Kehat (Y4) characterized shedding in this case as random. However, Lindt (L7, L8) studied air bubbles in water and distinguished a regular periodic component of drag associated with an open helical vortex wake structure. Strouhal numbers (defined as 2af/Uj, where / is the frequency and 2a is the maximum horizontal dimension) increase with Re, to level off at about 0.3 as bubbles approach the transition between the ellipsoidal and spherical-cap regimes. 

Instead of using this equation, in the literature, there are few models proposed by which the frequency or Strouhal number of the shedding is fixed. Koch (1985) proposed a resonance model that fixes it for a particular location in the wake by a local linear stability analysis. Upstream of this location, flow is absolutely unstable and downstream, the flow displays convective instability. Nishioka Sato (1973) proposed that the frequency selection is based on maximum spatial growth rate in the wake. The vortex shedding phenomenon starts via a linear instability and the limit cycle-like oscillations result from nonlinear super critical stability of the flow, describ-able by Eqn. (5.3.1). 

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. 

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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