Self-similar explosion waves of variable energy at the front

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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.

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