<DOC>
<DOCNO>
131
</DOCNO>
<TITLE>
two-dimensional jet mixing of a compressible fluid .
</TITLE>
<AUTHOR>
pai,s.i.
</AUTHOR>
<BIBLIO>
j.aero.scs. 16, 1949, 463.
</BIBLIO>
<TEXT>
  the mixing and divergence of a supersonic jet exhausting into
a supersonic stream are investigated theoretically .
  in the first part of this paper, the flow is assumed to be laminar .
when the velocity and temperature in the jet are different
slightly from those of the surrounding stream, by the method of
small perturbations and under ordinary boundary layer assumptions,
the equation of motion of two-dimensional flow will be
reduced to a form of the well-known equation of heat conduction,
whose solution is known for any given boundary conditions .  it
has also been shown that the exact solution of the two-dimensional
jet mixing of viscous compressible fluids can be obtained
by successive approximations starting with the solution of small
perturbations .
  velocity and temperature distributions for two cases--one is
the mixing of two-uniform flows and the other is the mixing of a
jet of compressible fluid from a two-dimensional nozzle with full
expansion exhausting into a supersonic stream--have been calculated
.  the properties of the jet mixing depend mainly on the
momentum of the jet regardless of whether the change of momentum
is due to the change of velocity or the change of temperature--i.e.,
the change of density .  compressibility has a considerable
effect on the properties of the jet .
  in the second part, the cases of turbulent flow are investigated .
by means of reichardt's theory of free turbulence, the turbulent
shearing stress may be expressed as
  it has been shown in this paper that
where is a constant that can be determined experimentally .
the value of n lies between 0 and 1 .  the exact value of n depends
on the condition of mixing .
  when the expression of turbulent shearing stress given above
is used instead of the viscous stress in the equation of motion,
by suitable transformation of variables, it has been shown that
the equation of two-dimensional turbulent jet mixing is identical
to that of the laminar case .  hence, the solution of the first part
of this paper can be applied to the turbulent case, provided that
the characteristic constants and n have been properly chosen .
</TEXT>
</DOC>
