Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-07-05T19:17:03.475Z Has data issue: false hasContentIssue false

Compressible flow past a contour and stationary vortices

Published online by Cambridge University Press:  21 April 2006

A. Barsony-Nagy
Affiliation:
Department of Aeronautical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
J. Er-El
Affiliation:
Department of Aeronautical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
S. Yungster
Affiliation:
Department of Aeronautical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel

Abstract

The Rayleigh-Janzen expansion method is extended to plane and steady flows which contain one or more point vortices interacting with a smooth or sharp-edged obstacle. A uniformly valid approximate solution of the compressible-flow equations is deduced by applying a perturbation method and by using matched asymptotic expansions to solve the resulting singular perturbation problem. The method yields compressibility corrections for the vortex positions and for the velocities. Results are presented for the flow past a circle and a pair of symmetric vortices (Föppl's flow). They show that the compressibility effects are substantial and are consistent with experimental data.

Type
Research Article
Copyright
© 1987 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

Abramowitz, M. & Stegun, I. A. (eds) 1965 Handbook of Mathematical Functions. Power.
Barsony-Nagy, A. 1985 Extension of Blasius force theorem to subsonic speeds. AIAA J. 23, 18111812.Google Scholar
Bryson, A. E. 1959 Symmetric vortex separation on circular cylinders and cones. Trans. ASME E: Appl. Mech. 26, 643648.Google Scholar
Fidler, J. E., Nielsen, J. N. & Schwind, R. G. 1977 Investigation of slender-body vortices. AIAA J. 15, 17361741.Google Scholar
FÖppl, L. 1913 Wirbelbewegung hinter einen Kreiszylinder, Sitzungberichte der Bayerischen Akad. Wiss., (Math-Phys.), pp. 117.
Huang, M. K. & Chow, C. Y. 1982 Trapping of a free-vortex by Joukowski airfoils. AIAA J. 20, 292298.Google Scholar
Jacob, C. 1959 Introduction Mathematique a la Mechanique des Fluides. Gauthier-Villars.
Jorgensen, L. J. 1977 Prediction of static aerodynamic characteristics for slender bodies alone and with lifting surfaces to very high angles of attack. NASA Tech. Rep. R474.Google Scholar
Lighthill, M. J. 1955 Higher approximations. In High Speed Aerodynamics and Jet Propulsion, vol. vi, sect. E, pp. 252396. Oxford University Press.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. MacMillan.
Moore, D. W. 1985 The effects of compressibility on the speed of propagation of a vortex ring. Proc. R. Soc. Lond. A 397, 8797.Google Scholar
Nielsen, J. N. 1960 Missile Aerodynamics. McGraw-Hill.
Owen, F. K. & Johnson, D. A. 1979 Wake vortex measurements of an ogive-cylinder at α = 36 degrees, J. Aircraft 16, 577583.Google Scholar
Saffman, P. G. & Sheffield, T. S. 1977 Flow over a wing with an attached free vortex. Stud. Appl. Maths 57, 107117.Google Scholar
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Dynamics. Academic.
Yungster, S. 1985 Subsonic flow past an inclined cylinder and a pair of stationary vortices. M.Sc. thesis, Technion, Israel Institute of Technology (in Hebrew).