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for p < Pcr, decreases further as p increases and assumes a minimum value in
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK 723
the neighborhood of p " pcr = 0.2, and starts nsing for higher values of p. For
p > 0.55,it becomes positive.
For p < pcr, the upstream moving wall effect on the bottom side causes a
forward movement in the transition point in the lifted shear layer. On the top side,
the downstream moving wall effect causes a delay in the transition to such an
extent that the boundary layer may not reattach to the cylinder surface. In other
words, the flow separation essentially is of subcritical type on the top side. As a
result, the Magnus lift is negative. For p > pcr, the transition takes place in the
separated shear layer, and the fiow reattaches to the top surface, forming a bubble.
On the bottom side, the upstream moving wall effect establishes a subcritical flow
pattern. As a result, the Magnus lift assumes positive values.
Ericson's conceptua/ f/ow mechanism for forebody-induced wing rock.
One of the main assumptions in Ericson's hypothesis for the forebody-induced
wing rock is that the freestream Reynolds number is in the critical range.3 ? Thus,
according to Ericson, the forebody-induced wing rock is not likely to occur if
the Reynolds number is in the subcritical or supercritical range. Furthermore, he
assumes that the wing and tail surfaces provide the downstream surfaces needed to
generate the necessary rolling moments. With these assumptions, an explanation
to the development of a vortex-asymmetry-switching mechanism that is necessary
for the occurrence of forebody-induced wing rock is offered as follows.37
When disturbed at high angles of attack, the free-to-roll wing-body model starts
oscillating because of a loss of damping in roll. Let this happen at t = ti and let
us assume that the model starts rolling in the clockwise direction as shown in
Fig. 8.53a. Once the model starts rolling, the moving waLl effect comes into exis-
tence. As shown in Fig. 8.53a, the adverse moving wall effect promotes transition
and a turbulent reattachment on the right side. On the left side, the proverse mov-
ing wall effect does not do much to alter the subcritical-type flow separation. As
a result, an asymmetric vortex pattern is formed as shown. However, it takes a
certain time 8t for this vortex pattern to reach the wing. During this interval of
time, the model continues to rollin the clockwise direction. At t - t2 - 11 +8t, the
asymmetric vortex pattern reaches the wing and establishes a type of pressure dis-
tribution that begins to generate a rolling motion in the counterclockwfse direction.
With this, the moving wall effect switches sides, The adverse moving wall effect
on the left side causes a transition and turbulent reattachment with the result that
the vort.ex on this side is closer to the body. On the right side, the proverse moving
wall effect leads to laminar type (subcritical) fiow separation and leads to a vortex
located further away from the body as shown in Fig:v8.53c. As before, because of
the time delay of 8t, the model will continue to roll in the counterclockwise direc-
tion until this new asymmetric vortex reaches the wing at t = t3 + At. At this point,
the rolling motion reverses, starting a new wing rock cycle. Thus, the moving wall
effect generates an alternating asymmetric vortex pattern, which produces t.he nec-
essary aerodynamic spring or the statically stabilizing effect. Because of the time
delay effect, tlus statically stabilizing effect becomes dynamically destabilizing.
For additional information, the reader may refer elsewhere.36,37
The fiow over the slender forebody of a fighter aircraft at high angles of attack is
much more complex than the classical crossfiow over a two-dimensional circular
cylinder, which forms the basis of Ericson's moving wall hypothesis. In view of
this, it is quite possible that the actual mechanism causing the forebody-induced
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724 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
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