A Discussion of the Application of the Prandtl-Glauert Method to Subsonic Compressible Flow over a Slender Body of Revolution

Abstract

The Prandtl-Glauert method for subsonic potential flow of a compressible fluid has generally been believed to lead to an increase in the pressures over a slender body of revolution by a factor 1/([sqrt](1-M[sub]1^2)) (where M[sub]1 is Mach number in undisturbed flow) as compared with the pressures in incompressible flow. Recent German work on this problem has indicated, however, that the factor 1/([sqrt](1-M[sub]1^2)) is not applicable in this case. In the present discussion a more careful application of the Prandtl-Glauert method to three-dimensional flow gives the following results: The Prandtl-Glauert method does not lead to a universal velocity or pressure correction formula that is independent of the shape of the body. The factor 1/([sqrt](1-M[sub]1^2)) is applicable only to the case of two-dimensional flow. The increase with Mach number of the pressures over a slender body of revolution is much less rapid than for a two-dimensional airfoil. An approximate formula from which the increase can be estimated is derived theoretically. The increase with Mach number of the maximum axial interference velocity on a slender body of revolution in a closed wind tunnel is given approximately by the factor 1/((1-M[sub]1^2)^-3/2), rather than by the factor 1/([sqrt](1-M[sub]1^2)) previously obtained by Goldstein and Young and by Tsien and Lees.