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A parametric study of self-similar blast waves

Published online by Cambridge University Press:  29 March 2006

A. K. Oppenheim ,
A. L. Kuhl ,
E. A. Lundstrom  and
M. M. Kamel
A. K. Oppenheim
Affiliation:
University of California, Berkeley
A. L. Kuhl
Affiliation:
University of California, Berkeley
E. A. Lundstrom
Affiliation:
University of California, Berkeley
M. M. Kamel
Affiliation:
University of California, Berkeley
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Abstract

The paper presents a comprehensive examination of self-similar blast waves with respect to two parameters, one describing the front velocity and the other the variation of the ambient density immediately ahead of the front. All possible front trajectories are taken into account, including limiting cases of the exponential and logarithmic form. The structure of the waves is analysed by means of a phase plane defined in terms of two reduced co-ordinates F ≡ (t/rμ) u and Z ≡ [(t/rμ)a]2, where t and r are the independent (time and space) variables, μ ≡ d ln rn/d Intn the subscript n denoting the co-ordinates of the front, and u and a are, respectively, the particle velocity and the speed of sound. Loci of extrema of the integral curves in the phase plane are traced and loci of singularities are determined on the basis of their intersections. Boundary conditions are introduced for the case when the medium into which the waves propagate is at rest. Representative solutions, pertaining to all the possible cases of blast waves bounded by shock fronts propagating into an atmosphere of uniform density, are obtained by evaluating the integral curves and determining the corresponding profiles of the gasdynamic parameters. Particular examples of integral curves for waves bounded by detonations are given and all the degenerate solutions, corresponding to cases where the integral curve is reduced to a point, are delineated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 4 , 25 April 1972 , pp. 657 - 682
Copyright
© 1972 Cambridge University Press

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