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at Iugh angles of attack. However, before we do so, let us develop some basic
understanding ofthe high-angle-of-attack aerodynamics of delta wings and slender
forebodies.
8.4   Delta Wings at High Angles of Attack
    For a highly swept, thin, sharp leading-edge delta wing held at high angles of
attack, the boundary layer cannot negotiate the large adverse pressure gradients
formed at the wing leading edge. As a result, the flow separates right at the leading
edge, forming a fixed line of flow separation all along the leading edge of the
wing. The separated fiow rolls up into a pair of spiral vortices with concentrated
cores on the lee- side as shown in Fig. 8.3.4 The leading-edge geometry has very
littie effect on such vortex fiow fields formed on the lee side as long as the leading
edges are sufficientjy thin and sharp. The external fiow reattaches to the surface
of the wing, forming a primar}r reattachment line as shown in Fig. 8.3b. As this
reattached flow moves in the spanwise direction,it encounters an adverse pressure
gradient and separates once again, forming another vortex called the secondary
vortex. The secondary vortex is much smaller in size and has a sense of rotation
 opposite that ofthe primary vortex.The fiow in the region between the two primary
 reattachmentlines on either side of the centerline is the attached flow, which moves
in the freestream direction. Evidently, this flow is not influenced by the primary
or secondary vortices as illustrated in Fig. 8.3b.
   The suction formed over the lee side of the wing under the influence of the
vortices enhances the lift and causes the lift coefficient to var}r nonlinearly with
angle of attack as shown in Fig. 8.4. This part of the total lift, which is in excess
over the potential or the attached fiow lift, is called vortex lift. The vortex lift
increases with increase in angle of attack until the vortex breakdown occurs on
the lee side of the wing. However, this beneficial vortex lift is accompanied by a
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   677
a) Schematic diagram
1)
2)
3)
4)
5)
6)
7)
 Primary or main vortex
  Secondarry vortac
Central  zone without yortex
Zone induced by ttn:main vortex
Zone uiduct:d by the secondar}r vortex
Accrrmulation zone (tur bubble or coating)
 Rcattachment line
z
                                                                 b) Details of flow pattern
F1g. 83   Vortex flow over sharp leading-edge delta wing at high angles of attack.4
(Courtesy AGARD.)
678           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
CL
Fig. 8.4    Schematic variation oflift coefficient with angle of attack for slender delta
wings.
   As the angle of attack increases, the amount of vorticity fed into the vortex
core increases. The vortices become stronger and physically lift themselves above
the wing surface. For highly swept'delta wings, the vortices assume asymmetric
configuration as depictedin Fig, 8.6lhe angle of attack for the onset ofasymmetry
depends on the leading-edge sweep]
   Another interesting phenomenon associated with the leading-edge vortices is
the vortex breakdown. The breakdown, or bursting as itis commonly called, refers
to a sudden and rather dramatic structural change, which usually results in the
turbulent dissipation of the vortex. Vortex bursting is characterized by a sudden
deceleration of the axial flow in the vortex core, formation of a small recirculator)r
Lift
~g.8.5a   Vortex flap concept.s
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   679
 ----- N
  V
AFTI/F-111
M=0.6
.5
cL
1. 0
Fig. 8.5b   Subsonic drag reduction using vortex flaps.6
Section A A
Fig.8.6    Schematic illustration of'vortex asymmetry over slender delta wings at high
angles of attack.
  .05
  .04
AC D .03
  .02
  .01
      o
680           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Stagn
AxiaJ
7
8ubbTe-type breakdown.
　
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