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Self-similar explosion waves of variable energy at the front

Published online by Cambridge University Press:  19 April 2006

G. I. Barenblatt ,
R. H. Guirguis ,
M. M. Kamel ,
A. L. Kuhl ,
A. K. Oppenheim  and
Ya. B. Zel'Dovich
G. I. Barenblatt
Affiliation:
Moscow Physico-Technical Institute and Institute of Oceanology, U.S.S.R. Academy of Sciences, Moscow
R. H. Guirguis
Affiliation:
University of California, Berkeley, U.S.A.
M. M. Kamel
Affiliation:
Cairo University, Egypt
A. L. Kuhl
Affiliation:
R & D Associates, Marina del Rey, California, U.S.A.
A. K. Oppenheim
Affiliation:
University of California, Berkeley, U.S.A.
Ya. B. Zel'Dovich
Affiliation:
Institute of Applied Mathematics, U.S.S.R. Academy of Sciences, Moscow
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Abstract

A set of self-similar solutions for blast waves associated with the deposition of variable energy at the front is presented. As a consequence of self-similarity, the results are applicable when the ambient atmosphere into which the wave front propagates is at a negligibly low pressure and temperature. Besides the class of (1) blast waves associated with energy gain that covers a regime bounded on one side by the well-known solution for adiabatic strong explosion waves (ASE) and, on the other side, by the solution for waves having the Chapman–Jouguet condition established immediately behind the front, included within the scope of our analysis are two others: (2) blast waves associated with energy loss that occupy a regime between the ASE solution and the case of infinite density ratio across the front, and (3) a non-unique class of solutions for blast waves associated with energy deposition that may have either locally sonic or supersonic flow immediately behind the front, extending over the regime between the waves headed by the Chapman-Jouguet detonation and the case of infinite rate of energy deposition. Specific results for a number of representative cases are expressed in terms of integral curves on the phase plane of reduced blast wave co-ordinates, as well as in the form of particle velocity, temperature, density, and pressure profiles across the flow field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 4 , 29 August 1980 , pp. 841 - 858
Copyright
© 1980 Cambridge University Press

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