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Spiral~type breakdown,
Fig. 8.7    Conceptual sketches of vortex breakdown.8
flow region, a decrease in. the circumferential velocity, and an increase in the size
of the vortex.
       As shown in Fig. 8.7, two types of vortex breakdown are commonly observed on
delta wings at high angles of attack, bubble type and spiral type. The bubble type or
"axisymmetric" mode of vortex breakdown is characterized by a stagnation point
on the swirl axis, followed by an oval-shaped recirculation bubble. The spiral mode
of breakdown is characterized by a rapid deceleration of the core flow, followed by
an abrupt kink. At the kink, the core flow takes the form of a spiral, which persists
for one or two turns before breaking up into a large-scale turbulence. While the
bubble-type breakdown has been observed on delta wings in low Reynolds number
water-tunnel tests,it is the spiral type that is more routinely observed in wind-tunnel
experiments.8
    The stall of a thin, highly swept, sharp-edged, delta wing (such a wing is also
called slender delta wing) is different from the stall ofaconventionalround leading-
edge airfoil or a finite wing, which is largely influenced by the boundary-layer and
fiow separation characteristics (see Chapter 1). The stall of a slender delta wing
essentially depends on the Iocation of the vortex breakdown point on the wing. The
variation ofthe vortex breakdown point on the wing with angle ofattackis sho6wnin
Fig. 8.8. The effect oflocation ofthe vortex breakdown point on the variation oflift
coefficient with angle of attack is shown in Fig. 8.9. WePobserve that a slender delta
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF All-ACK   681
z
co
Fig. 8.8  Locahon of vortex breakdown point for slender delta wings.9 (Courtesy
AGARD.)
wing of high Ieading-edge sweep, 75 deg or higher, attains its maximum lift and
stalls at the angle of attack when the vortex breakdown point reaches the trailing
edge. For delta wings of lower leading-edge sweeps, the stall occurs when the
vortex breakdown point has moved ahead of the wing trailing edge and towards
the wing apex. Also, there will be a break in the Iift-curve slope at the angle of
attack when the vortex breakdown point reaches the trailing edge as can oe observed
in Fig. 8.9. With further increase in angle of attack, the vortex breakdown point
moves towards the wing apex and, at some point, the wing stalls. For example,
the 70-deg delta wing stalls at or = 33 deg when the vortex breakdown point is
located approximately 35qo chord upstream of the trailing edge. In general, as
CL
              a (dq0
a) A < 70o
CL
             a (de0
b) A > 70o
Fig. 8.9     Effect of vortex breakdown locatlion on'the lift coefficient of delta wings.lO,Jl
682            PERFORMANGE, STABILITY, DYNAMICS, AND CONTROL
Cm
             
             
┏━━┳━━┓
┃//  ┃\\  ┃
┣━━╋━━┫
┃    ┃    ┃
┗━━┻━━┛
         
         
┏━┳━┓
┃/ ┃) ┃
┣━╋━┫
┃  ┃  ┃
┗━┻━┛
a) Inboard migration of vortex            b) Inboard m~ration with
+
E
cores with increasing a (no
vorfex breakdown)
┏━━━━━━━━━━━━━┓
┃ ct                       ┃
┣━━━━━━━━━━━━━┫
┃\               ~-4( -':  ┃
┗━━━━━━━━━━━━━┛
With Vortu
Breakdown
No Vorten
Breakdown
Fig. 8.10   Schematicillustration ofpitch-up ofslender delta wings.
the leading-edge sweep decreases, the stall occurs when the vortex breakdown is
located closer to the leading edge.
   The slender delta wing experiences the so-called pitch-up phenomenon (Fig.
8.10) at high angles of attack because of the progressive loss of vortex lift from
the wingtip regions as the leading-edge vortices migrate inboard. Tlus pitch-up
problem may be further accentuated by the vortex breakdown and movement of
　
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