Laminar boundary layers on slender bodies of revolution in axial flow

Abstract

An exact similar solution of the modified boundary layer equations has been obtained for the axial incompressible flow past paraboloids of revolution. It has been shown that the usual boundary layer assumptions are justified and that the local skin friction increases as the boundary layer thickness becomes large compared with the body radius. An approximate method for obtaining the local skin friction on arbitrary slender bodies of revolution in axial incompressible flow has been developed. A comparison of the approximate results with the exact solutions for paraboloids of revolution and circular cylinders shows good agreement. The existence of energy integrals of the modified compressible boundary layer equations is established. Similarity of the governing equations for the axial compressible flow past paraboloids of revolution has been shown; for the same bodies, a hypersonic similarity law is deduced. An approximate method for obtaining the local skin friction on arbitrary slender insulated bodies of revolution in axial compressible flow has been developed. The results show that compressibility counterbalances the rise in local skin friction due to curvature at high Reynolds numbers (based on a characteristic length of the body) and increases the local skin friction at sufficiently low Reynolds numbers. Velocity profiles on a slender ogive-cylinder have been obtained experimentally at a Mach number of 5.8 and at different Reynolds numbers. The results indicate a curvature effect when compared with flat plate results.