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National Advisory Committee for Aeronautics, Technical Notes - Use of the Kernel Function in a Three-Dimensional Flutter Analysis with Application to a Flutter-Tested Delta-Wing ModelApproximate Method for Calculation of Laminar Boundary Layer with Heat Transfer on a Cone at Large Angle of Attack in Supersonic Flow

By the use of an integral technique, the laminar boundaryslayer
equations are reduced on the windward generator of the plane of symmetry
to a set of simultaneous algebraic equations. The Chapman-Rubesin
temperature-viscosity relation and a Prandtl number of l are assumed.

The method enables the skin friction coefficients and Stanton number to
be calculated in a much shorter time than was needed to obtain exact
numerical solutions from the boundaryhlayer equations. The solutions ob-
tained by this method are, for the most part, within 5 percentage points
of the exact solutions.

Some designs for supersonic aircraft and missiles indicate the use of
a conical nose or forebody. For design purposes it is necessary to know
the skin friction and heat transfer on the conical surface for all pos—
sible flight conditions. One important condition is flight at angle of
attack, since the boundary—layer flow is complicated.by the addition of a
crossflow, which increases with increasing angle of attack.

Several analytical papers have been published dealing with the effect
of angle of attack on the boundary layer of a cone. Laminar flow over
cones at small angle of attack has been studied (ref. 1) by using a line
earization of the nonlinear boundary— -layer equations for a cone as derived
in reference 2. In references 5 and 4, the results of reference 1 have
been extended to cover the combined effect of spin and small angle of
attack. In reference 5, the boundary-layer equations for large angles of
attack were solved by'a numerical method but the solutions were limited
to the plane of symmetry. The preceding solutions were limited to the
insulated case with a Prandtl number equal to l.

Additional numerical solutions were computed in reference 6 for the
equations for large angle of attack in the plane of symmetry. Heat-
transfer solutions were also obtained in reference 6 by noting that for
a Prandtl number of l the energy equation in the plane of symmetry could
be written in the same form as the momentum equation along the generator
and, therefore, the enthalpy profile is identical to the velocity
profile.in this direction. An approximate porrection factor for heat
transfer is given in reference 6 for the case of a Prandtl number not "
equal to l.