Before this decrease happens, drag cefficient is almost constant - as expected for the pressure drag. As an example, in the case of a cylinder transverse to flow or sphere (Fig. J-16 below) there is = 0,47 (if we do not take into account the region of very low - which correspond to extremely slow, creeping motions or to extremely small, submillimetre sizes: note that = 1000 in air is achieved at velocity = 3 m/s which is the threshold of Pitot probe sensitivity, Fig. C-7, with diameter around 5 mm). Similar decrease was plotted already for the 25 % thickness profile in Fig. J-12. The effect is a result of the change of the separation point position (Fig.J-16) due to transition of laminar boundary layer to turbulence. Note that pressure increases along the surface and separation takes place if kinetic energy converted into pressure rise in slowed-down boundary layer does not suffice to overcome the pressure gradient. In a laminar boundary layer this happens already in front of the position of larges transversal dimension. On the other hand, vortex motions in a turbulent boundary layer transport into it the undecelerated outside fluid particles. The problem of insufficient pressure rise takes place there too, but further downstream - and this means the wake becomes smaller. The fact that drag depends upon extent of the wake was already apparent in Fig.J-14. We have already seen in Fig.J-8
Fig.J-16
that transition to turbulence is dependent upon the fluctuation level of the oncoming flow. It should not be surprising that in the flow past sphere or cylinder the transition to the transcritical regime is also influenced by . A controversy concerning the drag coefficient value od a sphere developed before WWI between the Eiffel's laboratory in Paris (at that time still located directly under the Eiffel tower) and the insitute directed by Prandtl (at that time the Kaiser-Wilhelm-Institut, later AVA) in Gottingen in Germany. Prandtl's value of was 5-2-times smaller - at the same Reynolds number . This was later explained by the higher level of turbulence in tunnels of Prandtl type (such as shown in Fig.J-17). In his closed-circuit arrangement, recirculating air is turbulised both by passage through the blower and by passage through the system of turning vanes in corners (which are commonly used to decrease bend losses, cf. Fig.D-24).
Earlier transition may be also caused by small objects or roughess elements on the body surface.
Note: This is the reason why golf balls have dimples on their surface. Standard (British) golf ball has diameter = 41,1 mm. A good golf player accelerates it up to velocity = 100 m/s. A corresponding smooth-surface ball, cf. Fig.J-16, has critical Reynolds number = 385 . To achieve this, it would be necessary for the ball to move with velocity = 147 m/s .... this is outside the capabilities of even the best players. On the other hand, the critical Reynolds number of the ball with dimples is = 92 . The corresponding velocity is = 35 m/s .... well within usual range. The flow past the ball may be transcritical and its aerodynamic drag is about five times smaller.
Australian aborigines decorate the surface of their boomerangs (above) by ridges transverse to flow direction in flight.
No doubt experience has taught them this leads (due to earlier transition to turbulence) to better performance.


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This is page Nr. J07 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

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