TRANSITION TO DETONATION IN A MODEL PROBLEM.

It is shown, within the context of a model problem, how an initial low Mach number combustion wave developes into a detonation when subjected to an externally applied gasdynamic disturbance. Explicit criteria that the external disturbance must satisfy in order for transition to be achieved are given. The governing equations are the unsteady equations for an ideal reacting gas. The reaction is assumed to be fuel going into product plus heat. The reaction terms that appear in the energy and species equation are modeled, using an ignition-temperature, flame-sheet model derived from Arrhenius kinetics in the limit of large activation energy. A small-amplitude theory is then used to take advantage of the standard techniques of linear and nonlinear acoustics by assuming that the heat released during combustion is small.