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National Advisory Committee for Aeronautics, Report - Laminar Boundary Layer on Cone in Supersonic Flow at Large Angle of Attack

The laminar boundary-layer flow about a circular cone at
large angles of attack to a supersonic stream has been analyzed
in the plane of symmetry by a method applicable in general to
the flow about conical bodies.

At the bottom of the cone, velocity profiles were obtained show-
ing the expected tendency of the boundary layer to become thinner
on the under side of the cone as the angle of attack is increased.

At the top of the cone, the analysisfailed to yield ionic-ac
solutions, except for small angles of attack. Beyond a certain
critical angle of attack, boundary-layer flow does not exist in
the plane of symmetry, thus indicating separation. This
critical angle is presented as a function of Mach number and
cone vertex angle.

The supersonic aerodynamics of pointed bodies has con-
siderable current interest in connection with the design of
aircraft and missile fuselages. An important feature of the
flow about such bodies is the behavior of the boundary layer
and, in particular, the flow separation which may occur along
the low—pressure side of the body due to angle of attack.
The present report will consider the development of the lami—
nar boundary layer on the surface of a right circular cone at
an angle of attack to a supersonic stream (see fig. 1). The
conical configuration may be considered an idealization of‘
the nose portion of a supersonic aircraft fuselage.

In figure 2 is shown qualitatively the circumferential
pressure distribution on the cone surface predicted for var-
ious angles of attack (see ref. 4). These pressure distribu-
tions depend only on the character of the nonviscous flow
beyond the boundary layer, on the assumption that the
boundary layer is extremely thin. When the angle of attack
is very small, the pressure decreases monotonically from
the bottom of the cone around to the top. For larger
angles of attack there appears a region near the top of the
cone wherein the pressure gradient reverses and the pressure
increases toward the top.“ As the angle of attack is further
increased, this region becomes greater in extent.