<DOC>
<DOCNO>
329
</DOCNO>
<TITLE>
various aerodynamic characteristics in hypersonic rarefied
gas flow .
</TITLE>
<AUTHOR>
probstein,r.f. and kemp,n.h.
</AUTHOR>
<BIBLIO>
j. ae. scs. 27, 1960.
</BIBLIO>
<TEXT>
  this paper considers the problem of calculating viscous aerodynamic
characteristics of blunt bodies at hypersonic speeds and
at sufficiently high altitudes where the appropriate mean free
path becomes too large for the use of familiar boundary-layer
theory but not so large that free molecule concepts apply .
  results of an order-of-magnitude analysis are presented to
define the regimes of rarefied gas flow and the limits of continuum
theory .  based on theoretical and experimental evidence,
the complete navier-stokes equations are used as a
model, except /very close/ to the free molecule condition .  this
model may not necessarily give the shock wave structure in
detail but satisfies overall conservation laws and should give a
reasonably accurate picture of all mean aerodynamic quantities .
  in this /intermediate/ regime there are two fundamental classes
of problems ..  a /viscous layer/ class and a /merged layer/
class, the latter corresponding to a larger degree of rarefaction .
for the viscous layer class there is a thin shock wave, but the
shock layer region between the shock and the body is fully viscous,
although the viscous stresses and conductive heat transfer
are small at the shock wave boundary .  here, the use of the
navier-stokes equations with outer boundary conditions given
by the hugoniot relations is justified .  for the merged layer
class, the shock wave is no longer thin, and the navier-stokes
equations can be used to give a solution which includes the shock
structure and has free-stream conditions as outer boundary conditions
.  a simpler procedure is presented for /incipient merged/
conditions where the shock may no longer be considered an infinitesimally
thin discontinuity but where it has not thickened
sufficiently to entail the /fully merged layer/ analysis .  in this
case we approximate the shock by a discontinuity obeying conservation
laws which include curvature effects, viscous stresses,
and heat conduction .
  for a sphere and cylinder it is shown that the navier-stokes
equations can be reduced to ordinary differential equations for
both the viscous and merged layer class of problems .  solutions
of these equations, when used in connection with hypersonic flow
problems, are in general only valid in the stagnation region .  to
illustrate the viscous layer solutions, numerical calculations
have been performed for a sphere and cylinder with the assumption
of constant density in the shock layer, which is a useful
approximation at hypersonic speeds .  to illustrate the merged
layer solution, calculations have been carried out for a sphere
using the incipient merged layer approximation .
  results are presented for detachment distance, surface shear,
and heat-transfer rate in the stagnation region of a highly cooled
sphere flying at hypersonic speed .  with decreasing reynolds
number, the shear and heat transfer are shown to increase above
the extrapolated boundary-layer values in the viscous layer
regime and then to begin falling in the incipient merged regime .
as the reynolds number decreases in the incipient merged
regime, the density in the shock layer increases, and the static
and stagnation enthalpy behind the shock decrease .
  calculations performed for an insulated sphere show that, with
decreasing reynolds number in the incipient merged regime,
the density in the shock layer decreases,. the total enthalpy behind
the shock and at the stagnation point increase so that they
are higher than the free-stream total enthalpy,. and the stagnation-point
pressure behaves like the total enthalpy .
  for the highly cooled cylinder in the viscous layer regime, the
same quantities are presented as for the sphere .  the increase
found in shear and heat transfer above extrapolated boundarylayer
theory is small, in agreement with vorticity interaction
theory .
  a discussion is given of the behavior of available experimental
data for viscous flow quantities in the intermediate regime and
the behavior predicted by the results of the present calculations .
qualitative agreement is indicated .
</TEXT>
</DOC>
