<DOC>
<DOCNO>
1202
</DOCNO>
<TITLE>
uniformly valid second-order solution for supersonic
flow over cruciform surfaces .
</TITLE>
<AUTHOR>
wallace,j. and clarke,j.h.
</AUTHOR>
<BIBLIO>
aiaa jnl. 1, 1963, 179.
</BIBLIO>
<TEXT>
  considered is the second-order supersonic flow over a cruciform
configuration consisting of two intersecting rectangular
wings of high aspect ratio .  the practical interest is in application
to supersonic inlets, wing-body junctions and vehicle fins .
the fundamental interest centers about identification and adjustment
of the severe local failures of the ordinary second-order
theory .  for wings with discontinuous slopes, discontinuous
potentials occur across the planar shock and square-root singularities
in the velocities occur at the intersection of these shocks
with the cruciform surfaces .  the problem is simple enough so
that these interesting features stand out clearly .
  a second-order solution uniformly valid to first order is constructed
by adjustment of the ordinary second-order solution obtained
first .  the uniformly valid solution has two different
series representations in the thickness parameter .  one is the
ordinary second-order series in ascending integral powers of the
thickness parameter which is valid in the interior of the vertexcentered
undisturbed mach cone, and the other is a series containing
fractional powers which is valid adjacent to and upstream
of this mach cone .  the uniformly valid solution gives the detailed
wave structure and shows a flow regime upstream of the
vertex-centered undisturbed mach cone not predicted by the
ordinary theory .  the two solutions are otherwise identical .
the wave structure consists of a pyramidal arrangement of planar
shocks adjacent to and upstream of the above cone, followed by
weaker oblique expansion fans and finally by two extremely
weak shocks coincident with the vertex-centered undisturbed
mach cone .  as an example of the above, detailed results are
presented for the case of two intersecting wedges .  application
of the techniques to other quasi-cylindrical problems is discussed .
</TEXT>
</DOC>
