Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T20:58:55.886Z Has data issue: false hasContentIssue false
  • English
  • Français

The Supersonic Flow Past an Elliptic Cone

Published online by Cambridge University Press:  07 June 2016

B. A. Woods
B. A. Woods*
Affiliation:
Department of Mathematics, University of Leeds*
Get access

Summary

The supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 4 , November 1969 , pp. 382 - 404
Copyright
Copyright © Royal Aeronautical Society. 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Stone, A. H. On supersonic flow past a slightly yawing cone. Journal of Mathematical Physics, Vol. 27, pp 67–81, 1948.CrossRefGoogle Scholar
2. Stone, A. H. On supersonic flow past a slightly yawing cone, II. Journal of Mathematical Physics, Vol. 30, pp 200–213, 1951.Google Scholar
3. Ferri, A., Ness, N. and Kaplita, T. Supersonic flow over conical bodies without axial symmetry. Journal of the Aeronautical Sciences, Vol. 20, pp 563–571, 1953.CrossRefGoogle Scholar
4. Ness, N. and Kaplita, T. Tabulated values of linearized conical flow solutions for solution of supersonic conical flows without axial symmetry. Polytechnic Institute of Brooklyn, PIBAL Report 220, 1954.Google Scholar
5. Martelluci, A. An extension of the linearized characteristics method for calculating the supersonic flow around elliptic cones. Journal of the Aeronautical Sciences, Vol. 27, pp 667–674, 1960.Google Scholar
6. Van Dyke, M. D. Perturbation methods in fluid mechanics. Academic Press, New York, 1964.Google Scholar
7. Woods, B. A. The supersonic flow past a circular cone at incidence. ARC R & M 3413, 1965.Google Scholar
8. Munson, A. G. The vortical layer on an inclined cone. Journal of Fluid Mechanics, Vol. 20, pp 625–643, 1964.Google Scholar
9. Sims, J. L. Tables of supersonic flow around right circular cones at small angles of attack. NASA Sp 3007, 1964.Google Scholar
10. Briggs, B. R. Calculation of supersonic flow past bodies supporting shock waves shaped like elliptic cones. NASA TN D-24, 1959.Google Scholar
11. Taylor, G. I. and Maccoll, J. W. The air pressure on a cone moving at high speed. Proc. Roy. Soc, A, Vol. 139, pp 278–311, 1933.Google Scholar