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┃A-﹢p -. UW/Uoo
leyndh NOb
3.38 X I04
4.9
6. 0;
7.91
9.9
12.8
I S.2
Ia.IS
2 Z- t
26
29.3
32-3
36.J
47
.s
SO-1
Fig. 8.49 Magnus lif;t on a rotating arcular cylinder.35 (Courtesy ASME,JournaL of
Btrsic Engineering.)
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK 719
group 1 (laminar fiow), Pcr varies from 0.52 at a Reynolds number of3.58 x l04 to
0.3 at 12.8 x l06. For group 2 (transitional flow, Reynolds number from 15.2 x l04
to 36.5 x l04), Pcr is around 0.2 and for group 3 (turbulent flow, Reynolds number
from 42 x l04 to 50.1 x l04), and Pcr is in the range 0.1-0.2. Thus, the lower the
Reynolds number, the higher the critical rotation rate. In the following, we will
discuss the moving wall effect for vanious flow regimes.
Laminar f/ow. Here, we consider the effect of rotation rate when the flow
is laminar, corresponding to the data of group 1 of Fig. 8.49. For a stationar}
cylinder (p = 0, Fig. 8.50a), the flow separates ahead of the lateral meridian
point or the maximum thickness point, forming a large wake characterized by the
classical Karman vortex shedding. When the rotation rate p < Pcr, the Magnus
effect comes mainly from the downstream moving wall effect on the top side of
the rotating cylinder as shown in Fig, 8.50b. On the top side, the flow separation
point is moved in the downstream direction whereas, on the bottom surface, the
flow separation is still oflaminar type. Tlus movement of the separation point on
the top sLuface takes place because of the moving wall effect and not because of
fiow transition. On the bottom side, the moving wall effect does not do much to
alter the location of the flow separation point. As a result, the suction on the top
side increases relative to that on the bottom side, and a positive Magnus lift is
generated as shown in Fig. 8.49 for the data of group 1 (laminar fiow).
When p > pcr, the moving wall effectinfiuences the flow pattern on the bottom
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