The Acceleration of Fast Deflagration Waves

In an earlier paper Stewart and Ludford gave a theory of steady deflagration waves based on an ignition‐temperature model obtained from Arrhenius kinetics. They were able to describe analytically the structure of deflagration waves for the entire range of wave speeds between zero and the maximum (Chapman‐Jouget) value. In this paper we construct a quasisteady theory of flame acceleration based on that work, which can predict the acceleration response of a preexisting flame to quite arbitrary hydrodynamic disturbances in the limit of small heat release during the combustion. Explicit formulas and criteria are developed. In particular, we find that an unsteady deflagration wave can travel at speeds in excess of the Chapman‐Jouget value, and even at arbitrarily large supersonic values.