Wake formation

Table 5.2 gives a new correlation, based on a critical examination of available data for spheres (N6). Results in which wall effects, compressibility effects, noncontinuum effects, support interference, etc. are significant have been excluded. The whole range of Re has been divided into 10 sub intervals, with a distinct correlation for each interval. Adjacent equations for match within 1% at the boundaries between sub intervals, but the piecewise fit shows slight gradient discontinuities there. The Re = 20 boundary corresponds to onset of wake formation as discussed above, the remaining boundaries being chosen for convenience. 

Johansson (Jl) reported numerical calculations of the flow around a sphere fixed on the axis of a Poiseuille flow (Fig. 9.1 with b = 0,U = 0). Only solutions for 2 = 0.1 were considered, and wake formation was predicted for Re = 20.4 based on the centerline velocity Uq. ... 

Air approaching the tower is displaced, resulting in flow separation and wake formation. A strong negative pressure and secondary flow patterns in the wake are created, the naturally buoyant exhaust plume is drawn down and ground fog forms. This is illustrated in Figure 6.13(A). 

Figure 6.13 Fog formation is assisted by wake formation and hourly variations in the ambient air humidity.

BOUNDARY-LAYER SEPARATION AND WAKE FORMATION. In the preceding paragraphs the growth of boundary layers has been discussed. Now consider what happens at the far side of a submerged object, where the fluid leaves the solid surface. 

Figure 10 shows representative streamline patterns for oblates, prolates, and spheres in Newtonian and shear-thinning fluids similar results (not shown here) are obtained for dilatant fluids. The streamline patterns for sphere match with the literature predictions for example see Clift et al. (1978) for Newtonian fluids and Adachi et al. (1973) for power-law fluids (n< 1). The effect of the flow behavior index on streamline patterns for a sphere is found to be negligible, except the fact that the wake formation is somewhat delayed. For prolate spheroids (E = 5), no wake formation occurs even at Re = 100, whereas for oblates, a visible wake is formed even at Re= 10 for = 0.2. To recap, the flow patterns appear to be much more sensitive to the... 

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