A parametric study of self-similar blast waves

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-ordinatesF≡ (t/rμ)uandZ≡ [(t/rμ)a]2, wheretandrare the independent (time and space) variables, μ ≡dlnrn/dIntnthe subscriptndenoting the co-ordinates of the front, anduandaare, 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.