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The slender elliptic cone as a model for non-linear supersonic flow theory

Published online by Cambridge University Press:  28 March 2006

M. D. Van Dyke
M. D. Van Dyke
Affiliation:
Ames Aeronautical Laboratory, National Advisory Committee for Aeronautics, Moffett Field, California
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Abstract

The second-order slender-body solution is derived for an unyawed elliptic cone in supersonic flow. The result is used as the basis for a critique of various approximations in compressible flow theory: slender-body, linearized, first- and second-order thin-wing theories; edge corrections; and the method of linearized characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 1 , May 1956 , pp. 1 - 15
Copyright
© 1956 Cambridge University Press

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References

Adams, M. C. & Sears, W. R. 1953 Slender-body theory-review and extension, J. Aero. Sci. 20, 85.
Broderick, J. B. 1949 Supersonic flow round pointed bodies of revolution, Quart. J. Mech. Appl. Math., 2, 98.
Fenain, M. & Germain, P. 1955 résolution de l’équation régissant, en seconde approximation, les écoulements d'un fluide autour d'obstacles tridimensionnels, C. R. Acad. Sci., Paris, 241, 276.
Ferri, A. 1951 The linearized characteristics method and its application to practical nonlinear supersonic problems, Nat. Adv. Comm. Aero., Wash., Rep. no. 1102.
Ferri, A., Ness, N. & Kaplita, T. 1953 Supersonic flow over conical bodies without axial symmetry, J. Aero. Sci., 20, 563.
Fraenkel, L. E. 1952 Supersonic flow past slender bodies of elliptic cross-section, Aero. Res. Coun:, Lond., Rep. & Mem. no. 2954.
Imai, I. 1952 Application of the M2-expansion method to the subsonic flow of a compressible fluid past a parabolic cylinder, Proc. 1st Japan Nat. Cong. Appl. Mech. 349.
Jones, R. T. 1946 Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound, Nat. Adv. Comm. Aero., Wash., Rep. no. 835.
Jones, R. T. 1950 Leading-edge singularities in thin-airfoil theory, J. Aero. Sci., 17, 307.
Kahane, A. & Solarski, A. 1953 Supersonic flow about slender bodies of elliptic cross-section, J. Aero. Sci., 20, 513.
Kaplan, C. 1942 On the use of residue theory for treating the subsonic flow of a compressible fluid, Nat. Adv. Comm. Aero., Wash., Rep. no. 728.
Lighthill, M. J. 1954 Higher approximations, section E of General theory of high-speed aerodynamics, Princeton University Press.
Moore, F. K. 1950 Second approximation to supersonic conical flow, J. Aero. Sci., 17, 328.
Rogers, E. W. E. & Berry, C. J. 1956 Experiments at M = 1.41 on elliptic cones with subsonic leading edges (to be published as a Rep. & Mem., Aero. Res. Counc., Lond.).
Squire, H. B. 1947 An example in wing theory at supersonic speed, Aero. Res. Counc., Lond., Rep. & Mem. no. 2549.
Van Dyke, M. D. 1952 A study of second-order supersonic flow theory, Nat. Adv. Comm. Aero., Wash., Rep. no. 1081.
Van Dyke, M. D. 1954 Subsonic edges in thin-wing and slender-body theory, Nat. Adv. Comm. Aero., Wash., Tech. Note no. 3343.
Van Dyke, M. D. 1956 Second-order slender-body theory (to be published).
Ward, G. N. 1949 Supersonic flow past slender pointed bodies, Quart. J. Mech. Appl. Math., 2, 75.