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Supersonic Flow Past Slender Bodies With Discontinuous Profile Slope

Published online by Cambridge University Press:  07 June 2016

L. E. Fraenkel  and
H. Portnoy
L. E. Fraenkel
Affiliation:
Imperial College
H. Portnoy
Affiliation:
Imperial College
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Summary

Ward’s slender-body theory is extended to derive first approximations to the external forces on slender bodies of general cross section with discontinuous profile slope. Two classes of body are considered: bodies whose profile (typified by the local radius) is continuous between the nose and base, and certain bodies whose profile is discontinuous, such as bodies with annular or side air intakes and wing-bodies on which the wing has an unswept leading edge. (Where air intakes are concerned, it is assumed that they are sharp-edged and that there is no “ spillage ” of the internal flow).

The following conclusions apply to the former class of bodies. The variation of drag with Mach number is found to depend only on the discontinuities in the longitudinal rate of change of the cross-sectional area, and is thus independent of cross-sectional shape. The drag itself is unchanged if the direction of the flow is reversed. The expressions for lift and moment assume the same forms as for smooth pointed bodies, the lift depending only on conditions at the base of the body.

The general theory is applied to winged bodies of revolution with an unswept wing leading edge: the results bear a marked resemblance to those obtained by Ward. The results for wings alone are seen to be applicable, with one modification, to subsonic as well as to supersonic speeds.

Type
Research Article
Information
Aeronautical Quarterly , Volume 6 , Issue 2 , May 1955 , pp. 114 - 124
Copyright
Copyright © Royal Aeronautical Society. 1955

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References

1. Ward, G. N. Supersonic Flow past Slender Pointed Bodies. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 2, No. 1, pp. 75–97, March 1949.CrossRefGoogle Scholar
2. Lighthill, M. J. Supersonic Flow past Slender Bodies of Revolution, the Slope of whose Meridian Section is Discontinuous. Quarterly Journal of Mechanics and Applied Mathe matics, Vol. 1, No. 1, pp. 90–102, March 1948.CrossRefGoogle Scholar
3. Fraenkel, L. E. Supersonic Flow past Slender Bodies of Elliptic Cross-Section. A.R.C. 15,166. (To be published in the R. &M. series). 1952.Google Scholar
4. Fraenkel, L. E. On the Unsteady Motion of a Slender Body through a Compressible Fluid. The Aeronautical Quarterly, Vol. VI, Part 1, pp. 59–80, February 1955.CrossRefGoogle Scholar
5. Ward, G. N. The Supersonic Flow past a Slender Ducted Body of Revolution with an Annular Intake. The Aeronautical Quarterly, Vol. I, Part 4, pp. 305–318, February 1950.CrossRefGoogle Scholar
6. Jones, R. T. Properties of Low-Aspect-Ratio Pointed Wings, at Speeds below and above the Speed of Sound. N.A.C.A. Report 835, 1945.Google Scholar
7. Stewartson, K. Supersonic Flow over an inclined Wing of Zero Aspect Ratio. Proc. Camb. Phil. Soc, Vol. 46, Part 2, pp. 307–315, April 1950.CrossRefGoogle Scholar