Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T05:57:25.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Compressible Subsonic Flow in Two-dimensional Channels*

Part 1: Basic Mathematical Theory†

Published online by Cambridge University Press:  07 June 2016

L. C. Woods
L. C. Woods*
Affiliation:
Department of Applied Mathematics, University of Sydney
Get access

Summary

Equations for the calculation of the subsonic flow of an inviscid fluid through given two-dimensional channels (the “ direct” problem), and for the design (the “ indirect” problem) of such channels are derived. The method is based on conformal mapping, and in the special case of channels with walls made from a number of straight sections, or with wall pressure prescribed as step-functions, yields the same results as the well-known Schwarz-Christoffel mapping theorem technique. However, it is more general than this latter method, since it is capable of dealing with curved walls or continuously varying wall pressures. The compressibility of the fluid is allowed for only approximately, the ideal gas being replaced by a Kàrmàn-Tsien tangent gas.

In Part II the theory is applied to various problems of aeronautical interest, perhaps the most important of which is to the setting of “ streamlined ” walls about a symmetrical aerofoil placed in the centre of the channel.

Information

Type
Research Article
Information
Aeronautical Quarterly , Volume 6 , Issue 3 , August 1955, pp. 205 - 220
Copyright
Copyright © Royal Aeronautical Society. 1955

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.)

Article purchase

Temporarily unavailable

Footnotes

*

The work described in this paper was done early in 1952 while the author was a member of the New Zealand Scientific Defence Corps, seconded to the Aerodynamics Division of the National Physical Laboratory, Teddington.

†

Part II will be published in November 1955

References

1. Lighthill, M. J. A New Method of Two-dimensional Aerodynamic Design. R. & M. 2112, 1945.Google Scholar
2. Milne-Thomson, L. M. Theoretical Hydrodynamics. Macmillan, 1949.Google Scholar
3. Stanitz, J. D. Design of Two-dimensional Channels with Prescribed Velocity Distributions along the Channel Walls. I—Relaxation Solutions. N.A.C.A. T.N. 2593, 1952.Google Scholar
4. Stanitz, J. D. Design of Two-dimensional Channels with Prescribed Velocity Distributions along the Channel Walls. II—Solution by Green's Function. N.A.C.A. T.N. 2595, 1952.Google Scholar
5. Woods, L. C. Compressible Subsonic Flow in Two-dimensional Channels with Mixed Boundary Conditions. Quarterly Journal of Mechanics and Applied Mathematics, Vol VII, Part 3, 1954.Google Scholar
6. Liepmann, H. W. and Puckett, A. E. Aerodynamics of a Compressible Fluid. John Wiley, 1947.Google Scholar
7. Thom, A. The Method of Influence Factors in Arithmetical Solutions of Certain Field Problems. R. & M. 2440, 1947.Google Scholar
8. Goldstein, S. and Lighthill, M. J. Two-dimensional Compressible Flow past a Solid Body in Unlimited Fluid or Symmetrically Placed in a Channel. A.R.C. 7184, 1943.Google Scholar
9. Kármán, Th. Von. Compressibility Effects in Aerodynamics. Journal of the Aeronautical Sciences, Vol. 8, p. 337, July 1941.Google Scholar