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The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves

Published online by Cambridge University Press:  28 March 2006

R. F. Chisnell
R. F. Chisnell
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

A first-order relationship between changes in area and shock strength is derived for the case of a shock moving through a small area change in a channel. By integration of this relationship the area of the channel is obtained as a function of the shock strength in closed form. This result is interpreted as giving the average strength of a shock at a given time as it moves along a channel of arbitrary shape.

By suitable choices of the shape of the channel, descriptions of converging cylindrical and spherical shocks are obtained. These descriptions are found to be in close agreement with the similarity solutions valid near the points of collapse of the shocks. The reason for such good agreement is examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 2 , Issue 3 , May 1957 , pp. 286 - 298
Copyright
© 1957 Cambridge University Press

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References

Guderley, G. 1942 Luftfahrtforsch. 19, 302.
Butler, D. 1954 Armament Research Establishment, Report no. 54/54.
Chiester, W. 1953 Quart. J. Mech. Appl. Math. 6, 440.
Chester, W. 1954 Phil. Mag. (7) 45, 1293.
Chisnell, R. F. 1955 Proc. Roy. Soc. A, 232, 350.
Laporte, O. 1954 Los Alamos Scientific Laboratory, Report L.A. 1740.
Lax, P. D. 1954 Comm. Pure Appl. Math. 7, 159.
Payne, R. B. 1957 J. Fluid Mech. 2, 185.