<DOC>
<DOCNO>
160
</DOCNO>
<TITLE>
approximate analytical solutions for hypersonic flow
past slender power-law bodies .
</TITLE>
<AUTHOR>
mirels,h.
</AUTHOR>
<BIBLIO>
nasa r-15, 1959.
</BIBLIO>
<TEXT>
approximate analytical solutions are presented
for two-dimensional and axisymmetric
hypersonic flow over blunt-nosed slender bodies whose
shapes follow a power law variation .  in particular,
the body shape is given by where is the
transverse body ordinate, is the streamwise distance
from the nose, and m is a constant in the range .
both zero-order solutions
and first-order (small but nonvanishing values
of solutions are presented, where m is the
free-stream mach number and is a characteristic
body or streamline slope .  the zero-order shock shape
is similar to the body shape for these flows .  the
solutions are found within the framework of
hypersonic-slender-body theory .
  the limiting case m=1 corresponds to a wedge
or cone flow .  the limiting case
corresponds to a constant-energy flow .
the latter cases are included
so that the present study may be applied to all flows
wherein the zero-order shock shape is given by
with m in the range .  flow
fields associated with shock shapes having values of m
outside this range are also discussed .  for all values
of, except m=1, certain portions of the flow field
riolate the hypersonic-slender-body approximations,
while other portions are consistent with these approximations
.  for m=1, all portions of the flow field
are consistent with the approximations .
  the approximate solutions are found as follows .
the asymptotic form of the flow in the vicinity of the
body surface is used as a guide to write approximate
expressions for the dependent variables .  these
expressions exactly satisfy the continuity and
energy equations and contain arbitrary constants
which are evaluated so as to satisfy boundary conditions
at the shock .  the approximate solutions do
not satisfy the lateral momentum equation except at
the shock and (for the first-order problem) at the body
surface .
  the results of the approximate solutions are
compared with numerical integrations of the equations
of motion for various values of m and (ratio
of specific heats) .  good agreement is noted, particularly
when m and are both near one .  the
shock is relatively close to the body for the latter
cases .  sufficient results are presented to evaluate
the accuracy of the approximate method for various
values of m and .
</TEXT>
</DOC>
