Figure 11-3 Boundary layer over a flat plate.

Figure 11-3 Boundary layer over a flat plate.

the body and remains laminar until NRe,x « .2 x 105, where x is the distance traveled along the boundary, at which point it becomes turbulent. If the boundary layer is laminar at the point where streamline separation occurs, the separation point can lie ahead of the equator of the sphere, resulting in a wake diameter that is larger than that of the sphere. However, if the boundary layer becomes turbulent before separation occurs, the three-dimensional eddy structure in the turbulent boundary layer carries momentum components inward toward the surface, which delays the separation of the streamline and tends to stabilize the wake. This delayed separation results in a smaller wake and a corresponding reduction in form drag, which is the cause of the sudden drop in CD at NRe « 2 x 105.

This shift in the size of the wake can be rather dramatic, as illustrated in Fig. 11-4, which shows two pictures of a bowling ball falling in water, with the wake clearly visible. The ball on the left shows a large wake because the boundary layer at the separation point is laminar and the separation is ahead of the equator. The ball on the right has a rougher surface, which promotes turbulence, and the boundary layer has become turbulent before separation occurs, resulting in a much smaller wake due to the delayed separation. The primary effect of surface roughness on the flow around immersed objects is to promote transition to the turbulent boundary layer and delay separation of the streamlines and thus to slightly lower the value

Figure 11-4 Two bowling balls falling in still water at 25 ft/s. The ball on the left is smooth, and the one on the right has a patch of sand on the nose. (From Coulson et al., 1991.)

of NRe at which the sudden drop (or "kink") in the CDNRe curve occurs. This apparent paradox, wherein the promotion of turbulence actually results in lower drag, has been exploited in various ways, such as the dimples on golf balls and the boundary layer "spoilers" on airplane wings and automobiles.

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