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Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution

Published online by Cambridge University Press:  29 March 2006

P. L. Sachdev
P. L. Sachdev
Affiliation:
Department of Physics, University of Toronto
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Abstract

The shock propagation theory of Brinkley & Kirkwood (1947) is extended to provide a uniformly valid analytic solution of point-explosion problems both when the undisturbed medium is uniform and when it is stratified. This is achieved mainly by selecting the parameter expressing a similarity restraint in this theory such that initially it gives precisely the Taylor–Sedov solution, while asymptotically, in the weak regime, still retaining the well-known Landau–Whitham–Sedov form of the solution for shock overpressure. The shock overpressure, as calculated by the present method for spherical and cylindrical blast waves in the entire regime from the point of explosion to where they have become very weak, shows excellent agreement with that from the exact numerical solutions of Lutzky & Lehto (1968) and Plooster (1970). The solution for a spherical shock propagating in an exponential atmosphere stratified by a constant acceleration due to gravity also shows a good agreement with the exact numerical solution of Lutzky & Lehto.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 2 , 28 March 1972 , pp. 369 - 378
Copyright
© 1972 Cambridge University Press

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