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

Lees, Lester (1946) A Discussion of the Application of the Prandtl-Glauert Method to Subsonic Compressible Flow over a Slender Body of Revolution. National Advisory Committee for Aeronautics , Washington, D. C.. http://resolver.caltech.edu/CaltechAUTHORS:LEEnacatn1127

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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.


Item Type:Report or Paper (Technical Report)
Record Number:CaltechAUTHORS:LEEnacatn1127
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LEEnacatn1127
Alternative URL:http://naca.larc.nasa.gov/reports/1946/naca-tn-1127/naca-tn-1127.pdf
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:458
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:21 Jun 2005
Last Modified:26 Dec 2012 08:40

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