Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-04T05:02:06.576Z Has data issue: false hasContentIssue false
  • English
  • Français

The focusing of weak shock waves at an axisymmetric arête

Published online by Cambridge University Press:  20 April 2006

M. S. Cramer
M. S. Cramer
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
Get access Rights & Permissions [Opens in a new window]

Abstract

The focusing of a weak and nearly plane shock wave at an axisymmetric arête is examined. The initial-value problem governing the flow in the focal region is derived. A similitude is introduced which shows that the details of the flow depend on the initial shape and strength of the shock only through a simple rescaling of the variables. The dependence of the pressure coefficient on the physical parameters is given. It is seen that the maximum pressure coefficient is proportional to a parameter measuring the rate of focusing of the shock and to the square root of a parameter measuring the initial strength of the shock.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981 , pp. 249 - 253
Copyright
© 1981 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

Cramer, M. S. 1980 On the focusing of a weak three-dimensional shock wave. A.I.A.A.J. (to appear).Google Scholar
Cramer, M. S. & Seebass, A. R. 1978 Focusing of weak shock waves at an arête. J. Fluid Mech. 88, 209–222.Google Scholar
Friedlander, F. G. 1958 Sound Pulses. Cambridge University Press.
Guiraud, J. P. 1965 Acoustique géometrique, bruit ballistique des avions supersoniques et focalisation. J. Méc. 4, 215–267.Google Scholar
Hayes, W. D. 1968 Similarity rules for nonlinear acoustic propagation through a caustic. 2nd Conf. Sonic Boom Res. (ed. I. R. Schwartz), N.A.S.A. Special Publ. no. 180, pp. 165–171.
Pechuzal, G. & Kevorkian, J. 1977 Supersonic — transonic flow generated by a thin airfoil in a stratified atmosphere. SIAM J. Appl. Math. 33, 8–33.Google Scholar
Sturtevant, B. & Kulkarny, V. A. 1976 The focusing of weak shock waves. J. Fluid Mech. 73, 651–671.Google Scholar
Whitham, G. B. 1957 A new approach to the problems of shock dynamics. Part 1. Twodimensional problems. J. Fluid Mech. 2, 146–171.Google Scholar
Whitham, G. B. 1959 A new approach to the problems of shock dynamics. Part 2. Threedimensional problems. J. Fluid Mech. 5, 369–386.Google Scholar