Effects of internal heat transfer on the structure of self-similar blast waves

Abstract

Profiles of gasdynamic parameters in self-similar blast waves, taking into account the influence of conduction and radiation fluxes due to high temperatures attained at the centre, are determined. In the blast-wave equations these fluxes are expressed in terms of the Fourier law for heat conduction and a differential expression for radiative transport in a semi-grey gas model. Various boundary conditions are considered in order to account for different ways in which blast waves are initiated and driven. Similarity requirements are implemented in the solution by compatible functional forms of gas conductivity and absorptivity, as well as the opacity of the shock front. This formulation yields a two-point boundary-value problem, which is then transformed into an initial-value problem in order to facilitate the integration. As a particular example, a detailed solution for the constant-energy case is obtained, covering the whole range of relative heat-transfer effects expressed in terms of radiative to gasdynamic energy fluxes, from the adiabatic flow field, on one extreme, to the isothermal, on the other.