Velocity distribution on thin bodies of revolution at zero incidence in incompressible flow

Abstract

A new method of determining velocity distribution on slender bodies of revolution in axial flow is expounded, analogous to the linear perturbation method widely used for slender symmetrical profiles in two dimensions. The proposed method leads to simple approximate formulae for velocity distribution on a body, once the equation of the meridian line is given, either in the form of a polynomial, or a square root of one. The new method avoids many inconveniences of the older procedures, and is much more rapid. Although theoretically applicable to bodies of small thickness only, it works with satisfactory accuracy up to quite considerable thickness ratios. It has been further improved by taking into account not only axial but also radial velocity components, following a suggestion of Lighthill's supersonic theory. It may be easily applied to compressible subsonic flow. The method has been used for computing velocity distributions on twelve different bodies, of seven different thickness ratios (0.04-0.28) each, so as to exhibit the most characteristic features in typical cases, and especially to show some unexpected effects of thickness changes. Several practical conclusions have been derived from the examination and comparison of these results. The method may find useful applications in the design of fuselages, nacelles and wing junctions, and especially in determining critical Mach numbers for such bodies.