On nose separation

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Abstract
When solving for three-dimensional laminar and turbulent boundary layers on smooth bodies of revolution at incidence, one has to contend with a difficulty near the nose where the usual formulations of the governing equations are singular. A transformation of the co-ordinate system is described which removes this singularity and enables the solution to be carried smoothly around the nose. A further difficulty arises if the body is slender and it is also shown how this may be overcome. As part of our continuing studies of this problem for both laminar and turbulent flows, we compute the laminar boundary layers on the line of symmetry for thin bodies taking the prolate spheroid as a paradigm. We show that if the angle of incidence α is less than 41°, separation never occurs at the nose no matter how thin the body. In contrast, the value of α which provokes separation at the leading edge of a two-dimensional airfoil tends to zero with the thickness ratio of the airfoil.

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