Asymptotic boundary-layer over a slender body of revolution in axial compressible flow

Abstract

The singular perturbation method developed by S. Kaplun is used to solve the thick, compressible laminar boundary layer over a slender body of revolution. The transverse curvature effect is included and is found to be characterized by a dimensionless parameter, which is essentially a function of the ratio of the thickness of the boundary layer to the radius of the body of revolution. An asymptotic series solution is developed for the region where the thickness of the boundary layer is large compared with the radius of the slender body. The nondimensional skin-friction parameter \(2ir rGTw)/(cosa. Ueve)} is calculated as a function of the thickness parameter. Interpolations are then made with another known series solution, developed by Probstein and Elliott, which is valid where the boundary layer is thin compared with the radius of the slender body. Thus, interpolation is made to cover the range where the thickness of boundary layer is in the same order as the body radius. From these interpolations, good agreement is obtained between both series for the cone and cylinder. The asymptotic series solution also indicates that the skin friction and heat-transfer rate increase with the Mach number and fall off very slowly in the reciprocal-logarithmic manner with the thickness parameter.