Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T16:57:29.032Z Has data issue: false hasContentIssue false
  • English
  • Français

The vortical layer on an inclined cone

Published online by Cambridge University Press:  28 March 2006

Albert G. Munson
Albert G. Munson
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Palo Alto, California Now at National Engineering Science Company, Pasadena, California.
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of flow over a circular cone inclined slightly to a uniform stream is solved using the technique of matched asymptotic expansions. The outer expansion is equivalent to Stone's solution of the problem. The inner expansion, valid in a thin layer near the body, represents Ferri's vortical layer. The solution to first order in angle of attack so obtained is uniformly valid everywhere in the flow field. In the second-order expansion an additional non-uniformity appears near the leeward ray. This defect is removed by inspection. The first-order solution is in agreement with that of Cheng, Woods, Bulakh and Sapunkov. Formulas are given that may be used to render Kopal's numerical result uniformly valid to second order in angle of attack.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 4 , December 1964 , pp. 625 - 643
Copyright
© 1964 Cambridge University Press

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

Bulakh, B. M. 1962a Prek. Mat. Mek. 26, 430.
Bulakh, B. M. 1962b Prek. Mat. Mek. 26, 1473.
Cheng, H. K. 1962 J. Fluid Mech. 12, 169.
Erdélyi, A. 1961 Atti Acad. Torino, 95, 1.
Ferri, A. 1950 NACA, TN 2236.
Gonor, A. L. 1958 Izv. Akad. Nauk, OTN, no. 7.
Holt, M. 1954 Quart. J. Mech. 8, 438.
Kopal, Z. 1947a Mass. Inst. Tech. Dep. Elect. Engng Tech. Rep. 1.
Kopal, Z. 1947b Mass. Inst. Tech. Dep. Elect. Engng Tech. Rep. 3.
Kopal, Z. 1949 Mass. Inst. Tech. Dep. Elect. Engng Tech. Rep. 5.
Lagerstrom, P. A. 1957 J. Math. Mech. 6, 605.
Roberts, R. O. & Riley, J. D. 1954 J. Aero Sci. 21, 336.
Sapunkov, Ia. G. 1963a Prek. Mat. Mek. 27, 281.
Sapunkov, Ia. G. 1963b Prek. Mat. Mek. 27, 1422.
Stone, A. H. 1948 J. Math. Phys. 27, 67.
Stone, A. H. 1952 J. Math. Phys. 30, 200.
Taylor, G. I. & Maccoll, J. W. 1933 Proc. Roy. Soc. A, 139, 278.
Van Dyke, M. D. 1962 J. Fluid Mech. 14, 161.
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.
Woods, B. A. 1962 Aeronaut. Quart. 23, 115.