Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-11T22:26:10.256Z Has data issue: false hasContentIssue false
  • English
  • Français

The diffraction of a rarefaction wave by a corner

Published online by Cambridge University Press:  28 March 2006

J. B. L. Powell
J. B. L. Powell
Affiliation:
Department of Mathematics, University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

An investigation is made of the effect of a small disturbance on the flow in a complete rarefaction wave, for example, the flow produced by the rupture of a membrane originally separating a compressible gas from a vacuum. The perturbation arises from a rigid boundary slightly inclined to the direction of flow. The growth of the perturbed region is studied and the pressure field is calculated for diatomic gases.

The nature of the expanding boundary of the perturbed region is investigated. Arguments are put forward which suggest that this boundary can be a weak shock in certain circumstances. A second shock may also appear in some cases, following the first and of greater strength.

In an appendix the solutions are extended to monatomic gases and to fluids with an adiabatic index of 2. The latter results are suitable for a comparison with hydraulic experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 3 , December 1957 , pp. 243 - 254
Copyright
© 1957 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

Black, J. & Mediratta, O. P. 1951 Aeronaut. Quart. 2, 227.
Bocher, M. 1914 An Introduction to the Study of Integral Equations, 2nd Ed. Cambridge University Press.
Chester, W. 1954 Quart. J. Mech. Appl. Math. 7, 247.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New york: Interscience.
Holder, D. W. 1953 A note on shock tubes, Aero. Res. Counc., Lond., Rep. no. 14,879.Google Scholar
Lighthill, M. J. 1949a Proc. Roy. Soc.A, 198, 454.
Lighthill, M. J. 1949b Phil. Mag. (7) 40, 1202.
Powell, J. B. L. 1956 Ph.D. Thesis, Bristol University.
Tan, H. S. 1951 J. Aero. Sci. 18, 768.