Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T23:47:57.360Z Has data issue: false hasContentIssue false
  • English
  • Français

Solutions for supersonic rotational flow around a corner using a new co-ordinate system

Published online by Cambridge University Press:  28 March 2006

T. C. Adamson
T. C. Adamson
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

A co-ordinate system consisting of the left-running characteristics (α = const.) and the streamlines (ϕ = const.) is used. The governing equations are derived in terms of α and ϕ for a two-dimensional steady supersonic rotational inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel supersonic rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic (case 1) or sonic (case 2). For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner, are found for the Mach angle and flow deflexion angle in terms of their values on the leading characteristic and at the corner. In case 2, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 4 , 23 December 1968 , pp. 735 - 758
Copyright
© 1968 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

Adamson, T. C. 1968 Univ. Michigan Inst. Sci. Tech. Rep. BAMIRAC, 8430-1-T.
Cole, J. D. 1965 RAND Corp. Rep. P-3207.
Ferri, A. 1954 General Theory of High-Speed Aerodynamics. W. R. Sears. Sec. G (vol. VI, High Speed Aerodynamics and Jet Propulsion). Princeton University Press.
Hayes, W. D. & Probstein, R. F. 1966 Hypersonic Flow Theory, 2nd ed. New York: Academic Press.
Johannesen, N. H. & Meyer, R. E. 1950 Aeronaut. Quart. 2, 127–42.
Olsson, G. R. & Messiter, A. F. 1968 A.I.A.A. 6th Aerospace Sciences Meeting, New York, 22–24 Jan., paper 68–67.
Pai, S. I. 1954 A.S.M.E. Proc. Sec. U.S. Natn. Congress Appl. Mech. 637–42.
VAGLIO-LAURIN, B. 1960 J. Fluid Mech. 9, 81–103.
VAN DYKE, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.
Weinbaum, S. 1965 Avco-Everett Res. Lab. Res. Rep. no. 204.
Weinbaum, S. 1966 A.I.A.A. J. 4, 217–26.
Weiss, R. F. 1967 A.I.A.A. J. 5, 2142–9.
Weiss, R. F. & Nelson, W. 1968 A.I.A.A. J. 6, 466–71.
Weiss, R. F. & Weinbaum, S. 1966 A.I.A.A. J. 4, 1321–30.
Whitham, G. B. 1952 Commun. Pure Appl. Math. 5, 301–48.