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cranfield0073
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<DOC>
<DOCNO>
73
</DOCNO>
<TITLE>
investigation of the stability of the laminar boundary
layer in a compressible fluid .
</TITLE>
<AUTHOR>
lees,l. and lin,c.c.
</AUTHOR>
<BIBLIO>
naca tn.1115, 1946.
</BIBLIO>
<TEXT>
in the present report the stability of two-dimensional laminar
flows of a gas is investigated by the method of small perturbations .
the chief emphasis is placed on the case of the laminar boundary layer .
part 1 of the present report deals with the general mathematical
theory . the general equations governing one normal mode of the small
velocity and temperature disturbances are derived and studied in great
detail . it is found that for reynolds numbers of the order of those
encountered in most aerodynamic problems, the temperature disturbances
have only a negligible effect on those particular velocity solutions
which depend primarily on the viscosity coefficient (/viscous solutions/)
. indeed, the latter are actually of the same form in the
compressible fluid as in the incompressible fluid, at least to the first
approximation . because of this fact, the mathematical analysis is
greatly simplified . the final equation determining the characteristic
values of the stability problem depends on the /inviscid solutions/ and
the function of tietjens in a manner very similar to the case of the incompressible
fluid . the second viscosity coefficient and the
coefficient of heat conductivity do not enter the problem,. only the
ordinary coefficient of viscosity near the solid surface is involved .
part 2 deals with the limiting case of infinite reynolds numbers .
the study of energy relations is very much emphasized . it is shown
that the disturbance will gain energy from the main flow if the gradient
of the product of mean density and mean vorticity near the solid surface
has a sign opposite to that near the outer edge of the boundary layer .
a general stability criterion has been obtained in terms of the
gradient of the product of density and vorticity, analogous to the
rayleigh-tollmien criterion for the case of an incompressible fluid .
if this gradient vanishes for some value of the velocity ratio of the
main flow exceeding 1-1/m (where m is the free stream mach number) .
</TEXT>
</DOC>