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The fluid fiow past a circular cylinder in crossfiow has attracted the attention of
several researchers, including Theodore 'von Karman. According to the ideal fiuid
theory, the maximum velocity is equal to twice the freestream velocity and occurs
at the maximum thickness point as shown in Fig. 1.3.
The fiow pattern over a circular cylinder in a real fiuid flow depends on the
Reynolds number. At a low Reynolds number, i.e., when the Reynolds number is
below the critical value (subcritical), the fiow within the boundary layer is laminar
and the separation pointis located ahead of the maximum thickness point as shown
schematically in Fig. 1.8a. rfhis separation is of laminar type and is of permanent
nature. The separated flow rolls into a pair of alternating vortices, which are known
as Karman vortices. The pattern of alternating vortices is also known as Karman
vortex street. The wake flow is oscillatory and the drag coefficient is a function of
time. The frequency of the Karman vortex shedding is usually given in terms of a
8 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Karman Vortex
a) Flow at subcritical Reynolds numbers
b) Flow at criticaIReynolds numbers
c) Flow at supercritical Reynolds numbers
Fig.1.8 Flow over circular cylinder.
-,
)
nondimensional number known as Strouhal number St, which is defined as
St = (/d (1.11)
where f is the frequency of the vortex shedding, d is the diameter of the circular
cylinder, and Voo is the freestream velocity. For a circular cylinder, the Strouhal
number is approximately 0.21 for a Reynolds number range of l03 to l04 (Ref. 1).
As the freestream Reynolds number increases towards the critical value, there
is an increasing tenden/:y for the transition to occur in the separated boundary
layer. For a smooth circular cylinder, the critical Reynolds number, based on the
diameter, is in the range of4 x l05 to 8 x l05. As a result of flow transition, the
REVIEW OF BASIC AERODYNAMIC PRiNCIPLES 9
Fig. 1.9 Schematic variation of drag coefficient of circular cylinder with Reynolds
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,
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