Small amplitude gasdynamic disturbances in an exploding atmosphere

Abstract

The propagation of disturbances through an atmosphere that is, in its undisturbed condition, undergoing a spatially uniform chemical explosion is analysed on the assumption that the disturbances are of small amplitude. When the latter are arbitrarily small, and therefore classifiable as acoustic, the progress of the ambient explosion is undisturbed to first order and a rather complete history of the acoustic waves (including weak shock waves) can be constructed. The generally amplifying effect of the explosion on the disturbances, which has previously been identified at wave heads, is found to occur throughout the disturbed domains. When the disturbance amplitude becomes comparable to the ratio of the thermal energy of the gas to the combustion-reaction activation energy, the ambient explosion becomes involved in the disturbance to first order. For large activation energies a small disturbance theory can be constructed to account for the disturbance behaviour; at present it is limited to time intervals from initiation that are shorter than the ‘no-depletion’ homogeneous ignition time.