Subsonic Compressible Flow Past Bluff Bodies

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Abstract
Summary: In this paper the Janzen-Rayleigh method is used to calculate the velocity potential for the steady subsonic flow of a compressible, inviscid fluid past a prolate spheroid. The fluid velocity at a point on the body is calculated. The analytic form obtained for this velocity differs, from that giving the velocity which an incompressible fluid would possess at the same point on the body, by a correction factor. The factor is an infinite series of first derivatives of Legendre functions of the first kind and odd order. The first three coefficients in this series are computed for bodies of certain axis ratios, and graphs of the values of these coefficients against axis ratio are plotted. The behaviour of the nth coefficient for large values of n is given. Results for slender ellipsoids, considering these as a limiting case of the family of ellipsoids just referred to, are obtained and are found to agree with the usual slender-body theory. Using these an attempt is made to continue the graphs of the first three coefficients in the correction factor series for the whole range of axis ratios of the ellipsoids in the system, namely zero to unity. The results obtained for the bluff-nosed ellipsoids may be used to estimate the effects of compressibility on the pressure distribution over the front of a general bluff-nosed body in steady flow.