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FLOW
A
b)
CROSS
SECTION
A-A
VORTEX
FREE FLOW
SYMMETRJC
VORTEX FLOW
STEADY
ASYMMETRIC
VORTEX FLOW
WAKE.LIKE
FLOW
NORMAL   SIDE
FORCE   FORCE
L
L
L/_
LJ~_
ANGLE OF ATTACK
Fig. 8.21   Schematic sketches of flow pattern and side force over slender bodies at
high angles of attack/
~
~
@1
~
L
~-
~-
[2~
%)
%
%
~
692             PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
    With angle of attack increasing further and approaching 90 deg, the organized
pair ofasymmetric vortex patterns disappears and the fiow assumes a pattern typical
of classical time-dependeFr:t K~trman vortex shedding from a circular-cylinder in
crossflow.
   The side force on the forebody arises in that angle of attack range when the
vortices are asymmetric and the wake flow is steady. The side force vanishes as the
angle of attack increases towards 90 deg because of the establishment of classical
unsteady, Karman vortex shedding.
8.6.1   Influence of Reynolds Number
   The forebody side force is found to decrease drastically in the transitional
Reynolds number range. A typical result for an ogive-cylinder of fineness ratio
of 2 at a - 55 deg is shown in Fig. 8.22. It is interesting to observe that, in the
transitional Reynolds number range, the side force decreases and, at high Reynolds
numbers when the flow is turbulent, the magnitude of side force increases back to
its value at low Reynolds numbers.
8.6.2  Effectof Forebody Geometry
   A properly designed forebody can significantly reduce the magnitude of the
side force and the associated yawing moment. Sometimes, a proper design of the
forebody can even enhance the directional stability at high angles of attack. One
of the primary geometric parameters that infiuences the forebody aerodynamics
is the forebody fineness ratio, which is defined as the forebody length I divided
r:i
o
Cy 2
[
E
       FULLY
 LAMINAR                      TUR8ULENT
SEPARATION    TRANSITION REGION    SEPARATION
0.1      0.2
0.4     OB,1.0     2.0  3.0 4.0
ReD/106
Fig. 8.22     Effect of Reynolds number on maidmum side force of an ogive-cylinder at
a = 55 deg.18
STABILIT.Y AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   693
Nose
Pineness
     Ra tio
a, dirjrees
                                                                                                      J" ,'
Fig. 8.23    Onset ofasymmetric flow separation on slender bodies of revolution.19
by its maximum diameter D. The angle of attack at which the separated vort,ex
 fiow becomes asymmetric is shown in Fig. 8.23. We observe that, as the forebody
fineness ratio increases, the angle of attack for the vortex asymmetry decreases
rapidly.
    Another geometrical parameter that has a strong influence on the vortex flow
field is the forebody cross-sectional shape. A forebody with circular cross section
 loses directional stability beyond 20 deg of angle of attack as shown in Fig. 8.24.
However, as the cross section becomes flatter, the directional stability level im-
proves significantly as shown in Fig. 8.25.
    The nose bluntness has a similar effect in reducing the adverse effect of aero-
dynamic asymmetr:ies at high angles of attack. As the bluntness is increased, the
 onset ofaerodynamic asymmetries is postponed to higher angles of attack. Another
geometric modification that can improve the directional stability at high angles of
attack is the addition of nose strakres.3 However, it is possible that the effect of
nose strakes may not always be beneficial.
　
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