Calculations of the pressure distributions and boundary-layer development on a body of revolution with various parabolic afterbodies at supersonic speeds

Abstract

Detailed calculations are made of the flow over a series of bodies at Mach numbers of 1.2, 1.4 and 1.6 and Reynolds numbers of 48 to 72 millions. The bodies consist of a basic forebody and parallel portion to which are added truncated parabolic afterbodies of three different thickness ratios. The calculations are in three main parts : (i) Calculation of the inviscid flow over the bodies, mainly by the method of characteristics. (ii) Calculation of the boundary-layer properties by what is essentially an extension to compressible flows of the method of Squire and Young. (iii) Calculation of the pressure distribution on the 'modified' afterbodies which result from adding the displacement thicknesses to the original profiles, by Ferri's method of linearized characteristics. The results indicate that the slender body' and quasi-cylinder theories predict the flow over afterbodies with only very limited accuracy for the thickness ratios and Mach numbers occurring in practice, but that the linearized similarity law remains a useful means of generalizing the particular results of exact inviscid-flow calculations. The boundary layers are seen to thicken very rapidly towards the rear of the afterbodies and this causes pressure changes of as much as 12 percent of the peaksuction. The skin-friction results agree extremely well with those for the equivalent flat plate.