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tack at wluch the burst asymmetry as measur2d by Ax]c also reaches a maximum
value. With further increase in angle of attack, the burst asymmetry and the asso-
ciated destabilizing effect decrease, and the stability in roll improves as shown in
Fig. 8.13.
   Effects of downstream obstacle.   The vortex breakdown location over the
wing is also susceptible to downstream disturbances. An obstacle placed down-
stream of the wing trailing edge has a strong influence on the vortex breakdown
Iocation12 as shown schematically in Fig. 8.14. Such a sensitivity of the vortex
breakdown to downstream obstacles demands extreme care and caution in con-
ducting wind-tunnel tests on sting mounted slender delta wings at high angles of
attack.
      Several fighter aircraft like the F  15 and the F/A-18 feature twin vertical tail sur-
faces for enhancjng the directional stability at high angles of attack. The designer
has to carefully select the location of the twin vertical tails because an improper
placement can promote premature vortex bursting, limit the maximum lift coeffi-
cient, and influence the IongitudinaUlateral- directional stability parameters.3.12
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   685
IV
a) No obstacle
lv
b) With obstacle
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Fig. 8.14   Schematic illustration of effect of downstream obstacle on vortex break-
down.
   Effects of Reyno/ds number.   Generally, the separated vortex flows where
the primary separation line is fixed at the sharp leading edge are relatively insensi-
tive to the fiow Reynolds number. This is true in a broader sense because the main
structure of the vortex fiow field on the lee side of the delta wing is not infiuenced
by the flow Reynolds number. However, the Reynolds number can have some sec-
ondary effects, i.e., it can influence the flow transition in the boundary layer of
the reattached fiow on the lee side. Beneath the primarjr vortex, the upper surface
boundary-layer is moving outboard and aft. As noted earlier, this boundary-layer
flow encounters an adverse pressure gradient outboard and separates and rolls
up to form a secondary vortex of opposite sense (see Fig. 8.3). If the boundary
layer undergoes a transition before separation, the separation will be delayed, and
the secondary vortex will be much smaller in size compared to that formed with
laminar separation. Furthermore, the displacement effect of the secondary vortex
on the primary vortex will be reduced, allowing the latter to move outboard and
downward towards the wing surface.
    It is suggested13 that, to ignore the effects of Reynolds number on separated
vortex flows over delta wings, the relation L >> x/f~~- must be satisfied. Here,
L is the typical lateral dimension of the large-scale vortex at a distance x from
the origin of the vortex (wing apex), and Rx is the local Reynolds number based
on freestream velocity and distance x. This relation basically gives the condition
under which the structure ofthe vortexis determined mainly by vorticity convection
rather than by vorticity diffusion. Another way ofinterpreting this relation is that
the typical lateral dimension of the vortex should be much greater than the local
boundary-layer thickness. Recall that the local laminar boundary-layer thickness
is inversely proportional to the square root of the local Reynolds number.
   Effect of Mach number.   In general, the vortex lift decreases with increase
in Mach number. To illustrate this point, a typical spanwise pressure distribution
o'ver a delta wing is shown in Fig.  8.15. It may be observed that the footprint of the
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