Number Strouhal

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. 

For 40 < Re < 200 the vortices are laminar and the Strouhal number has a nearly constant value of 0.2 for flow past a cylinder. Between Re = 200 and 400 the Strouhal number is no longer constant and the wake becomes irregular. Above about Re = 400 the vortices become turbulent, the wake is once again stable, and the Strouhal number remains constant at about 0.2 up to a Reynolds number of about 10. ... 

Constant-volume J/(kg-K) Btii/(lb.°R) Ns Strouhal number Dimensionless Dimensionless... 

Strouhal number, 11 747, 756, 757 Structural adhesives, 1 534-545 Structural alloys, of titanium, 24 840 Structural analysis, in fine art... 

Figure 6.1 shows the apparatus diagram. The diffusion flame burner consisted of an air plenum with an exit diameter of 22 mm, forced at a Strouhal number of 0.73 (100 Hz) by a single acoustic driver, and a coaxial fuel injection ring of diameter 24 mm, fed by a plenum forced by two acoustic drivers at either 100 Hz (single-phase injection) or 200 Hz (dual-phase injection). The fuel was injected circumferentially directly into the shear layer and roll-up region for the air vortices. In addition, this fuel injection was sandwiched between the central air flow and the external air entrainment. Thus the fuel injection was a thin cylindrical flow acted upon from both sides by air flow. 

As Re increases beyond about 400, vortices are shed as a regular succession of loops from alternate sides of a plane which precesses slowly about the axis (A4, K6, MU). As shown in Fig. 5.9, the Strouhal number Sr for vortex shedding increases. At the same time, the point at which the detached shear layer... 

Fig. 6.7 Regimes of motion for disks in free fall or rise. Contours of constant Strouhal number Sr and constant Reynolds number are also shown.

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. 

Sherwood number for dilTusion into stagnant medium, based on Strouhal number, =fd/Ur,fb/U, or fy w/U j... 

A dimensional analysis of the problem of film flow (F7) has shown that in general the properties of a film flow may depend on the Reynolds, Weber, and Froude numbers of the flow, a dimensionless shear at the free surface of the film, and, for wavy flows, a Strouhal number formed from the frequency of the surface waves, and various geometrical ratios, e.g., the ratios of the wave amplitude and length to the mean film thickness. 

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

Time pulsing can be characterized by the Strouhal number (St), which is a dimensionless parameter describing the ratio of the flow characteristic time scale (L/V) to the pulse time period (1/j) [Eq. (1.8)] [26], where Lis the hydraulic diameter, V the average velocity in the outlet channel and/the pulsing frequency. For a pulsing frequency of 5 Hz, a Strouhal number of 0.375 derives. 

Stockholm convention 60 stoichiometric number 42 stokes 112 strain 12 bulk 12 linear 12 shear 12 volume 12 stress 12, 72 Strouhal number 65 structural formula 45 structure factor 36 sublimation 51 substance concentration 5 substitution structure distance 24 sum over states 39 surface amount 63 surface charge density 14, 59 surface chemistry 63 surface concentration 42 surface coverage 63 surface density 12 surface electric potential 59 surface excess 63 surface excess concentration 63 surface pressure 63 surface properties 64 surface tension 12, 48, 63 susceptance 15 svedberg 111 symbols 5... 

Similarly, one can also obtain the equilibrium Strouhal number after the nonlinear saturation from Eqn. (5.1.8). In the following, we discuss specifically about the flow past a circular cylinder. 

While lots of attention have been paid on the real part of Landau s equation, the imaginary part has not been analyzed in great detail. As A approaches its asymptotic value Ag, the circular frequency ( ) also reaches its as miptotic value, LOg. Thus, the Strouhal number is found to be amplitude dependent and is given by. 

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). 

Figure 5.4 Variation of Strouhal number with Reynolds number.

In Fig. 5.4, the computed Strouhal number is shown plotted against Re3molds number by discrete S3mibol and solid line. In the same figure, the dotted curve shows the correlation proposed by Norberg (2003) based on experimental data from his facility. The empirical correlations are given by, St = 0.2663 - for 47 < Re < 190 and St... 

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