Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T21:18:13.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform asymptotic solutions for potential flow about a slender body of revolution

Published online by Cambridge University Press:  29 March 2006

James Geer
James Geer
Affiliation:
School of Advanced Technology, State University of New York, Binghamton, New York 13901
Get access Rights & Permissions [Opens in a new window]

Abstract

The general problem of potential flow past a slender body of revolution is considered. The flow incident on the body is described by an arbitrary potential function and hence the results presented here extend those obtained by Handels-man & Keller (1967 α). The part of the potential due to the presence of the body is represented as a superposition of potentials due to point singularities (sources, dipoles and higher-order singularities) distributed along a segment of the axis of the body inside the body. The boundary condition on the body leads to a linear integral equation for the density of the singularities. The complete uniform asymptotic expansion of the solution of this equation, as well as the extent of the distribution, is obtained using the method of Handelsman & Keller. The special case of transverse incident flow is considered in detail. Complete expansions for the dipole moment of the distribution and the virtual mass of the body are obtained. Some general comments on the method of Handelsman & Keller are given, and may be useful to others wishing to use their method.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 4 , 25 February 1975 , pp. 817 - 827
Copyright
© 1975 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

Fraenkel, L. E. 1969 Proc. Camb. Phil. Soc. 65, 209, 233.
Geer, J. F. 1974 S.I.A.M. J. Appl. Math. 26 (to appear).
Geer, J. F. & Keller, J. B. 1968 S.I.A.M. J. Appl. Math. 16, 75.
Handelsman, R. A. & Keller, J. B. 1967a J. Fluid Mech. 28, 131.
Handelsman, R. A. & Keller, J. B. 1967b S.I.A.M. J. Appl. Math. 15, 824.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Schiffer, M. & Szeco, G. 1949 Trans. Am. Math. Soc. 67, 130.
Tillett, J. P. K. 1970 J. Fluid Mech. 44, 401.