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National Advisory Committee for Aeronautics, Technical Notes - Laminar Boundary Layer on a Circular Cone in Supersonic Flow at a Small Angle of Attack

The laminar boundary layer on a circular cone at angle of attack
to a supersonic stream is analyzed. A solution for the outer nonviscous
flow, as obtained by a method of perturbation in angle of attack, is
available and is presumed to govern the development ofcthe boundary
layer, subject to certain restrictions and corrections:

In the limit of vanishing cone angle, the boundary-layer equations
reduce to those for the flow about a yawed infinite cylinder in come
pressible flow, but may not be solved in the simple manner appropriate
to incompressible flow.

For small angle of attack, the boundary-layer quantities are con—
sidered to differ only slightly from the corresponding quantities in
the known flow at zero angle of attack.~ The system.of equations result-
ing from this assumption are solved to yield the effect of small angle
of attack on the velocity profiles, skin.friction, boundary—layer thick—
ness, and the forces and moment on the cone, or, more precisely, the
rates of change of these quantities with angle of attack, evaluated at
zero angle of attack.

All boundary-layer quantities show parabolic similarity in merid-
ional planes. Circumferentially, the boundary—layer thickness associated
with the profile of the circumferential velocity component is constant,
and the profile itself exhibits no tendency to separate; whereas the
profile of the meridional component undergoes changes caused by angle
of attack which show the expected effects of secondary flow in the
boundary layer.

The flow around bodies of revolution at positive angles of attack
is characterized by a draining of the boundary layer from.the underside
to the top, causing the formation of "lobes“ of loweenergy air near the
top of the body. For sufficiently large angles of attack, separation of
the cross.flow'may result in a transversely shed.Karman vortex street.
Under these circumstances, large viscous contributions to lift, drag,
and pitching moment on the body may be expected. Of course, viscous
lift, drag, and moment are expected at any angle of attack, whether or
not cross-flow separation occurs.