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number.
separated boundary layer reattaches to the surface of the circular cylinder, forming
a bubble as shown in Fig. 1.8b. Because the reattached turbulent boundary layer is
more resistant to the adverse pressure gradient, it sticks to the surface to a greater
extent before eventually separating again. As a result, the drag coefficient drops
from its subcritical value to a minimum value Cd.rmn in the critical Reynolds-num-
ber range as shown in Fig. 1.9. For a smooth circular cylinder, the subcritical value
of drag coe:fficient is approximately 1.18 and Cd. n - 0.3 (Ref. 1)- In the critical
range of Reynolds number, the organized Karman vortex pattern is suppressed and
the wake fiow consists of random,large eddy fiuid motion.
As the freestream Reynolds number increases further and exceeds the critical
Reynolds number (supercritical flow), the transition pointin the bubble moves for-
ward and eventually moves ahead of the separation point, wiping out the bubble.
This process leads to the supercritical flow pattern as shown in Fig. 1.8c* However,
the fiow eventually separates, and the separation point is usually located upstream
of that in the critical Reynolds number r~nge. Because of this, the drag coefficient
starts rising slowly in the supercritical Reynolds number range as indicated in
Fig. 1.9.
A schematic variation of the pressure distribution over a circular cylinder in
crossflow is shown in Fig. 1.10.' Y"
The above phenomenon oflaminar and turbulent flow separations can be used to
explain the swing of a cricket ball.lt is common knowledge that the swing occurs
when the ballis smooth (new) and is thrown by a fast bowler. As shown in Fig. 1.11,
10 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Cp
+
1.0
0
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ┃
┣━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃~ 0 180o I ┃
┃ al ┃
┃ \ ┃
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