<DOC>
<DOCNO>
452
</DOCNO>
<TITLE>
symmetric joukowsky airfoils in shear flow .
</TITLE>
<AUTHOR>
tsien,h.s.
</AUTHOR>
<BIBLIO>
q. app. math. 1, 1943, 130.
</BIBLIO>
<TEXT>
  the velocity components of the fluid far from the airfoil
are given by where c is the chord of
the airfoil, and k are constants, u and v are velocity
components in the directions of the coordinates x and y .
the solution is sought in the form of the stream function
and satisfies laplace's equation .  a general expression for
for vanishing disturbance velocities at points far from
the origin is written, and the flows due to a source, a vortex
and a solid circular cylinder in shear flow are considered
as examples .  typical streamline patterns are shown for
these cases .  from the eulerian equations of motion the
author obtains the expression for in terms of the
parameter and derivatives of .  the general form
of is introduced and the appropriate solution for the
pressure p is obtained .  by integration around a contour
enclosing the body, expressions are obtained, analogous to
the blasius formulae, for the force and couple on any
cylinder in this type of flow .  these formulae are applied to
the case of a symmetrical joukowsky airfoil .  the method of
conformal transformation is employed in the determination
of .  the boundary condition of tangential flow at the
airfoil surface must be satisfied by the total flow in the airfoil
plane, but this condition leads to a boundary condition for
in the transformed plane .  the kutta-joukowsky condition
of finite velocity at the trailing edge also leads to a
condition on in this plane .  from these conditions and the
general expression for the circulation and the strengths
of the doublets and quadruplets required for the force and
moment are determined .  hence, the formulae for lift and
moment coefficient are obtained .  these involve, in addition
to the usual (potential-flow) terms, terms proportional to .
  the ten functions that appear in the expressions for the
lift and moment coefficients are tabulated for values of the
thickness ratio between 0 and 1 .  the aerodynamic-center
position and the coefficient of the moment about the aerodynamic
center are also calculated and are presented
graphically as functions of .
</TEXT>
</DOC>
