<DOC>
<DOCNO>
903
</DOCNO>
<TITLE>
two dimensional transonic unsteady flow with shock
waves .
</TITLE>
<AUTHOR>
eckhaus,w.
</AUTHOR>
<BIBLIO>
m.i.t. fluid dynamics res. group r.59-3, 1959.
</BIBLIO>
<TEXT>
  a study is made of the unsteady flow around an
airfoil at transonic mach numbers, the situation being
such that local supersonic regions terminated by shockwaves
are present in the vicinity of the airfoil .  for
the unsteady part of the flow, small perturbations
technique is employed and the interaction with the shock
wave is taken into account .  the case of an oscillating
aileron is considered first, and a solution is derived
for the pressure distribution on the aileron .  it is
found that the solution has a simple form when the
shock-wave is well ahead of the hinge axis of the
aileron .  as the shock approaches the hinge-axis a
correction must be added to the solution .  an interpretation
of these results is given .  the results are
compared with results of a theory which neglects the
presence of the shock and it is found that both agree
for m = 1 .  for m   1, however, neglecting the presence
of the shock waves introduces errors of the order of
magnitude (1 - m), where m is the local mach number
behind the shock .
  the theory is finally extended to include the case
in which the whole airfoil oscillates, but only the
solution for the subsonic region behind the shock is
treated .  the role of the unsteady shock-boundary layer
interaction is discussed and it is shown that this
mechanism can be included in the results of the present
theory .
</TEXT>
</DOC>
